Quantum speed limit for arbitrary initial states

PubMed Central

Zhang, Ying-Jie; Han, Wei; Xia, Yun-Jie; Cao, Jun-Peng; Fan, Heng

2014-01-01

The minimal time a system needs to evolve from an initial state to its one orthogonal state is defined as the quantum speed limit time, which can be used to characterize the maximal speed of evolution of a quantum system. This is a fundamental question of quantum physics. We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, when the system starts from the excited state, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed. PMID:24809395

Lower bound on the time complexity of local adiabatic evolution

NASA Astrophysics Data System (ADS)

Chen, Zhenghao; Koh, Pang Wei; Zhao, Yan

2006-11-01

The adiabatic theorem of quantum physics has been, in recent times, utilized in the design of local search quantum algorithms, and has been proven to be equivalent to standard quantum computation, that is, the use of unitary operators [D. Aharonov in Proceedings of the 45th Annual Symposium on the Foundations of Computer Science, 2004, Rome, Italy (IEEE Computer Society Press, New York, 2004), pp. 42-51]. Hence, the study of the time complexity of adiabatic evolution algorithms gives insight into the computational power of quantum algorithms. In this paper, we present two different approaches of evaluating the time complexity for local adiabatic evolution using time-independent parameters, thus providing effective tests (not requiring the evaluation of the entire time-dependent gap function) for the time complexity of newly developed algorithms. We further illustrate our tests by displaying results from the numerical simulation of some problems, viz. specially modified instances of the Hamming weight problem.

Quantum versus classical hyperfine-induced dynamics in a quantum dota)

NASA Astrophysics Data System (ADS)

Coish, W. A.; Loss, Daniel; Yuzbashyan, E. A.; Altshuler, B. L.

2007-04-01

In this article we analyze spin dynamics for electrons confined to semiconductor quantum dots due to the contact hyperfine interaction. We compare mean-field (classical) evolution of an electron spin in the presence of a nuclear field with the exact quantum evolution for the special case of uniform hyperfine coupling constants. We find that (in this special case) the zero-magnetic-field dynamics due to the mean-field approximation and quantum evolution are similar. However, in a finite magnetic field, the quantum and classical solutions agree only up to a certain time scale t <τc, after which they differ markedly.

Understanding squeezing of quantum states with the Wigner function

NASA Technical Reports Server (NTRS)

Royer, Antoine

1994-01-01

The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

Spatial evolution of quantum mechanical states

NASA Astrophysics Data System (ADS)

Christensen, N. D.; Unger, J. E.; Pinto, S.; Su, Q.; Grobe, R.

2018-02-01

The time-dependent Schrödinger equation is solved traditionally as an initial-time value problem, where its solution is obtained by the action of the unitary time-evolution propagator on the quantum state that is known at all spatial locations but only at t = 0. We generalize this approach by examining the spatial evolution from a state that is, by contrast, known at all times t, but only at one specific location. The corresponding spatial-evolution propagator turns out to be pseudo-unitary. In contrast to the real energies that govern the usual (unitary) time evolution, the spatial evolution can therefore require complex phases associated with dynamically relevant solutions that grow exponentially. By introducing a generalized scalar product, for which the spatial generator is Hermitian, one can show that the temporal integral over the probability current density is spatially conserved, in full analogy to the usual norm of the state, which is temporally conserved. As an application of the spatial propagation formalism, we introduce a spatial backtracking technique that permits us to reconstruct any quantum information about an atom from the ionization data measured at a detector outside the interaction region.

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Real time visualization of quantum walk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyazaki, Akihide; Hamada, Shinji; Sekino, Hideo

2014-02-20

Time evolution of quantum particles like electrons is described by time-dependent Schrödinger equation (TDSE). The TDSE is regarded as the diffusion equation of electrons with imaginary diffusion coefficients. And the TDSE is solved by quantum walk (QW) which is regarded as a quantum version of a classical random walk. The diffusion equation is solved in discretized space/time as in the case of classical random walk with additional unitary transformation of internal degree of freedom typical for quantum particles. We call the QW for solution of the TDSE a Schrödinger walk (SW). For observation of one quantum particle evolution under amore » given potential in atto-second scale, we attempt a successive computation and visualization of the SW. Using Pure Data programming, we observe the correct behavior of a probability distribution under the given potential in real time for observers of atto-second scale.« less

Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.

PubMed

Heyl, Markus; Vojta, Matthias

2014-10-31

One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in cases where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium, one particular symmetry-broken state is chosen as a result of an infinitesimal symmetry-breaking perturbation. From a dynamical point of view the question is: Can such an infinitesimal perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

On the physical realizability of quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno; Govia, Luke; Schuhmacher, Peter; Wilhelm, Frank

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks.

Student Understanding of Time Dependence in Quantum Mechanics

ERIC Educational Resources Information Center

Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

2015-01-01

The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

Investigations of quantum pendulum dynamics in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We investigate the quantum spin dynamics of a spin-1 BEC initialized to an unstable critical point of the dynamical phase space. The subsequent evolution of the collective states of the system is analogous to an inverted simple pendulum in the quantum limit and yields non-classical states with quantum correlations. For short evolution times in the low depletion limit, we observe squeezed states and for longer times beyond the low depletion limit we observe highly non-Gaussian distributions. C.D. Hamley, C.S. Gerving, T.M. Hoang, E.M. Bookjans, and M.S. Chapman, ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Physical realizability of continuous-time quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno G.; Govia, Luke C. G.; Wilhelm, Frank K.

2018-05-01

Quantum walks are a promising methodology that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with that of a classical random walk, through open system evolution of a quantum system. Quantum stochastic walks have been shown to have applications in as far reaching fields as artificial intelligence. However, there are significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution and the physical assumptions underpinning them. We show that general direct implementations would require the complete solution of the underlying unitary dynamics and sophisticated reservoir engineering, thus weakening the benefits of experimental implementation.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

On the geometrization of quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tavernelli, Ivano, E-mail: ita@zurich.ibm.com

Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is inducedmore » by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.« less

Evolution of entanglement between distinguishable light states.

PubMed

Stevenson, R Mark; Hudson, Andrew J; Bennett, Anthony J; Young, Robert J; Nicoll, Christine A; Ritchie, David A; Shields, Andrew J

2008-10-24

We investigate the evolution of quantum correlations over the lifetime of a multiphoton state. Measurements reveal time-dependent oscillations of the entanglement fidelity for photon pairs created by a single semiconductor quantum dot. The oscillations are attributed to the phase acquired in the intermediate, nondegenerate, exciton-photon state and are consistent with simulations. We conclude that emission of photon pairs by a typical quantum dot with finite polarization splitting is in fact entangled in a time-evolving state, and not classically correlated as previously regarded.

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oberreuter, Johannes M., E-mail: johannes.oberreuter@theorie.physik.uni-goettingen.de; Homrighausen, Ingo; Kehrein, Stefan

We study the time evolution of entanglement in a new quantum version of the Kac ring, where two spin chains become dynamically entangled by quantum gates, which are used instead of the classical markers. The features of the entanglement evolution are best understood by using knowledge about the behavior of an ensemble of classical Kac rings. For instance, the recurrence time of the quantum many-body system is twice the length of the chain and “thermalization” only occurs on time scales much smaller than the dimension of the Hilbert space. The model thus elucidates the relation between the results of measurementsmore » in quantum and classical systems: While in classical systems repeated measurements are performed over an ensemble of systems, the corresponding result is obtained by measuring the same quantum system prepared in an appropriate superposition repeatedly.« less

Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion

NASA Astrophysics Data System (ADS)

Krumm, F.; Vogel, W.

2018-04-01

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.

Decoherence in quantum systems in a static gravitational field

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Loran, Farhang

2016-09-01

A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.

Unitary evolution of the quantum Universe with a Brown-Kuchař dust

NASA Astrophysics Data System (ADS)

Maeda, Hideki

2015-12-01

We study the time evolution of a wave function for the spatially flat Friedmann-Lemaître-Robertson-Walker Universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchař dust as a matter field in order to introduce a ‘clock’ in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the Universe obeys the classical-time evolution in the late time but its variance diverges.

Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench.

PubMed

Banerjee, D; Dalmonte, M; Müller, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P

2012-10-26

Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.

Effect of local minima on adiabatic quantum optimization.

PubMed

Amin, M H S

2008-04-04

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.

Brachistochrone of entanglement for spin chains

NASA Astrophysics Data System (ADS)

Carlini, Alberto; Koike, Tatsuhiko

2017-03-01

We analytically investigate the role of entanglement in time-optimal state evolution as an application of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly coupled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entanglement plays a role for W and Greenberger-Horne-Zeilinger (GHz) initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.

Quantum information, oscillations and the psyche

NASA Astrophysics Data System (ADS)

Martin, F.; Carminati, F.; Galli Carminati, G.

2010-05-01

In this paper, taking the theory of quantum information as a model, we consider the human unconscious, pre-consciousness and consciousness as sets of quantum bits (qubits). We view how there can be communication between these various qubit sets. In doing this we are inspired by the theory of nuclear magnetic resonance. In this way we build a model of handling a mental qubit with the help of pulses of a mental field. Starting with an elementary interaction between two qubits we build two-qubit quantum logic gates that allow information to be transferred from one qubit to the other. In this manner we build a quantum process that permits consciousness to "read" the unconscious and vice versa. The elementary interaction, e.g. between a pre-consciousness qubit and a consciousness one, allows us to predict the time evolution of the pre-consciousness + consciousness system in which pre-consciousness and consciousness are quantum entangled. This time evolution exhibits Rabi oscillations that we name mental Rabi oscillations. This time evolution shows how for example the unconscious can influence consciousness. In a process like mourning the influence of the unconscious on consciousness, as the influence of consciousness on the unconscious, are in agreement with what is observed in psychiatry.

Coherent spin-exchange via a quantum mediator.

PubMed

Baart, Timothy Alexander; Fujita, Takafumi; Reichl, Christian; Wegscheider, Werner; Vandersypen, Lieven Mark Koenraad

2017-01-01

Coherent interactions at a distance provide a powerful tool for quantum simulation and computation. The most common approach to realize an effective long-distance coupling 'on-chip' is to use a quantum mediator, as has been demonstrated for superconducting qubits and trapped ions. For quantum dot arrays, which combine a high degree of tunability with extremely long coherence times, the experimental demonstration of the time evolution of coherent spin-spin coupling via an intermediary system remains an important outstanding goal. Here, we use a linear triple-quantum-dot array to demonstrate a coherent time evolution of two interacting distant spins via a quantum mediator. The two outer dots are occupied with a single electron spin each, and the spins experience a superexchange interaction through the empty middle dot, which acts as mediator. Using single-shot spin readout, we measure the coherent time evolution of the spin states on the outer dots and observe a characteristic dependence of the exchange frequency as a function of the detuning between the middle and outer dots. This approach may provide a new route for scaling up spin qubit circuits using quantum dots, and aid in the simulation of materials and molecules with non-nearest-neighbour couplings such as MnO (ref. 27), high-temperature superconductors and DNA. The same superexchange concept can also be applied in cold atom experiments.

Generalized Geometric Quantum Speed Limits

NASA Astrophysics Data System (ADS)

Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.

2016-04-01

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

Manifestations of classical physics in the quantum evolution of correlated spin states in pulsed NMR experiments.

PubMed

Ligare, Martin

2016-05-01

Multiple-pulse NMR experiments are a powerful tool for the investigation of molecules with coupled nuclear spins. The product operator formalism provides a way to understand the quantum evolution of an ensemble of weakly coupled spins in such experiments using some of the more intuitive concepts of classical physics and semi-classical vector representations. In this paper I present a new way in which to interpret the quantum evolution of an ensemble of spins. I recast the quantum problem in terms of mixtures of pure states of two spins whose expectation values evolve identically to those of classical moments. Pictorial representations of these classically evolving states provide a way to calculate the time evolution of ensembles of weakly coupled spins without the full machinery of quantum mechanics, offering insight to anyone who understands precession of magnetic moments in magnetic fields.

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

Time reversal and charge conjugation in an embedding quantum simulator.

PubMed

Zhang, Xiang; Shen, Yangchao; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jing-Ning; Kim, Kihwan

2015-08-04

A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a (171)Yb(+) ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones.

Time reversal and charge conjugation in an embedding quantum simulator

PubMed Central

Zhang, Xiang; Shen, Yangchao; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jing-Ning; Kim, Kihwan

2015-01-01

A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a 171Yb+ ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones. PMID:26239028

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence.

PubMed

Rossi, Luca; Torsello, Andrea; Hancock, Edwin R

2015-02-01

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

Long-time efficacy of the surface code in the presence of a super-Ohmic environment

NASA Astrophysics Data System (ADS)

López-Delgado, D. A.; Novais, E.; Mucciolo, E. R.; Caldeira, A. O.

2017-06-01

We study the long-time evolution of a quantum memory coupled to a bosonic environment on which quantum error correction (QEC) is performed using the surface code. The memory's evolution encompasses N QEC cycles, each of them yielding a nonerror syndrome. This assumption makes our analysis independent of the recovery process. We map the expression for the time evolution of the memory onto the partition function of an equivalent statistical-mechanical spin system. In the super-Ohmic dissipation case the long-time evolution of the memory has the same behavior as the time evolution for just one QEC cycle. For this case we find analytical expressions for the critical parameters of the order-disorder phase transition of an equivalent spin system. These critical parameters determine the threshold value for the system-environment coupling below which it is possible to preserve the memory's state.

Signatures of a Nonthermal Metastable State in Copropagating Quantum Hall Edge Channels

NASA Astrophysics Data System (ADS)

Itoh, Kosuke; Nakazawa, Ryo; Ota, Tomoaki; Hashisaka, Masayuki; Muraki, Koji; Fujisawa, Toshimasa

2018-05-01

A Tomonaga-Luttinger (TL) liquid is known as an integrable system, in which a nonequilibrium many-body state survives without relaxing to a thermalized state. This intriguing characteristic is tested experimentally in copropagating quantum Hall edge channels at bulk filling factor ν =2 . The unidirectional transport allows us to investigate the time evolution by measuring the spatial evolution of the electronic states. The initial state is prepared with a biased quantum point contact, and its spatial evolution is measured with a quantum-dot energy spectrometer. We find strong evidence for a nonthermal metastable state in agreement with the TL theory before the system relaxes to thermal equilibrium with coupling to the environment.

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

Efficient Online Optimized Quantum Control for Adiabatic Quantum Computation

NASA Astrophysics Data System (ADS)

Quiroz, Gregory

Adiabatic quantum computation (AQC) relies on controlled adiabatic evolution to implement a quantum algorithm. While control evolution can take many forms, properly designed time-optimal control has been shown to be particularly advantageous for AQC. Grover's search algorithm is one such example where analytically-derived time-optimal control leads to improved scaling of the minimum energy gap between the ground state and first excited state and thus, the well-known quadratic quantum speedup. Analytical extensions beyond Grover's search algorithm present a daunting task that requires potentially intractable calculations of energy gaps and a significant degree of model certainty. Here, an in situ quantum control protocol is developed for AQC. The approach is shown to yield controls that approach the analytically-derived time-optimal controls for Grover's search algorithm. In addition, the protocol's convergence rate as a function of iteration number is shown to be essentially independent of system size. Thus, the approach is potentially scalable to many-qubit systems.

Noise-resilient quantum evolution steered by dynamical decoupling

PubMed Central

Liu, Gang-Qin; Po, Hoi Chun; Du, Jiangfeng; Liu, Ren-Bao; Pan, Xin-Yu

2013-01-01

Realistic quantum computing is subject to noise. Therefore, an important frontier in quantum computing is to implement noise-resilient quantum control over qubits. At the same time, dynamical decoupling can protect the coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects. We design and implement a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling control on the electron spin. Final state fidelity of 0.91(1) is observed in preparation of a Bell state using the gate. At the same time, the qubit coherence time is elongated at least 30 fold. The design scheme does not require the dynamical decoupling control to commute with the qubit interaction and therefore works for general qubit systems. This work marks a step towards implementing realistic quantum computing systems. PMID:23912335

Noise-resilient quantum evolution steered by dynamical decoupling.

PubMed

Liu, Gang-Qin; Po, Hoi Chun; Du, Jiangfeng; Liu, Ren-Bao; Pan, Xin-Yu

2013-01-01

Realistic quantum computing is subject to noise. Therefore, an important frontier in quantum computing is to implement noise-resilient quantum control over qubits. At the same time, dynamical decoupling can protect the coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects. We design and implement a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling control on the electron spin. Final state fidelity of 0.91(1) is observed in preparation of a Bell state using the gate. At the same time, the qubit coherence time is elongated at least 30 fold. The design scheme does not require the dynamical decoupling control to commute with the qubit interaction and therefore works for general qubit systems. This work marks a step towards implementing realistic quantum computing systems.

Wavepacket revivals in monolayer and bilayer graphene rings.

PubMed

García, Trinidad; Rodríguez-Bolívar, Salvador; Cordero, Nicolás A; Romera, Elvira

2013-06-12

We have studied the existence of quantum revivals in graphene quantum rings within a simplified model. The time evolution of a Gaussian-populated wavepacket shows revivals in monolayer and bilayer graphene rings. We have also studied this behavior for quantum rings in a perpendicular magnetic field. We have found that revival time is an observable that shows different values for monolayer and bilayer graphene quantum rings. In addition, the revival time shows valley degeneracy breaking.

Quantum ratchet effect in a time non-uniform double-kicked model

NASA Astrophysics Data System (ADS)

Chen, Lei; Wang, Zhen-Yu; Hui, Wu; Chu, Cheng-Yu; Chai, Ji-Min; Xiao, Jin; Zhao, Yu; Ma, Jin-Xiang

2017-07-01

The quantum ratchet effect means that the directed transport emerges in a quantum system without a net force. The delta-kicked model is a quantum Hamiltonian model for the quantum ratchet effect. This paper investigates the quantum ratchet effect based on a time non-uniform double-kicked model, in which two flashing potentials alternately act on a particle with a homogeneous initial state of zero momentum, while the intervals between adjacent actions are not equal. The evolution equation of the state of the particle is derived from its Schrödinger equation, and the numerical method to solve the evolution equation is pointed out. The results show that quantum resonances can induce the ratchet effect in this time non-uniform double-kicked model under certain conditions; some quantum resonances, which cannot induce the ratchet effect in previous models, can induce the ratchet effect in this model, and the strengths of the ratchet effect in this model are stronger than those in previous models under certain conditions. These results enrich people’s understanding of the delta-kicked model, and provides a new optional scheme to control the quantum transport of cold atoms in experiment.

General Relativity without paradigm of space-time covariance, and resolution of the problem of time

NASA Astrophysics Data System (ADS)

Soo, Chopin; Yu, Hoi-Lai

2014-01-01

The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full space-time covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical structure, yield transparent physical dynamics and a resolution of the problem of time. The deep divide between quantum mechanics and conventional canonical formulations of quantum gravity is overcome with a Schrödinger equation for quantum geometrodynamics that describes evolution in intrinsic time. Unitary time development with gauge-invariant temporal ordering is also viable. All Kuchar observables become physical; and classical space-time, with direct correlation between its proper times and intrinsic time intervals, emerges from constructive interference. The framework not only yields a physical Hamiltonian for Einstein's theory, but also prompts natural extensions and improvements towards a well behaved quantum theory of gravity. It is a consistent canonical scheme to discuss Horava-Lifshitz theories with intrinsic time evolution, and of the many possible alternatives that respect 3-covariance (rather than the more restrictive 4-covariance of Einstein's theory), Horava's "detailed balance" form of the Hamiltonian constraint is essentially pinned down by this framework. Issues in quantum gravity that depend on radiative corrections and the rigorous definition and regularization of the Hamiltonian operator are not addressed in this work.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution.

PubMed

Djordjevic, Ivan B

2015-08-24

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

PubMed Central

Djordjevic, Ivan B.

2015-01-01

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled. PMID:26305258

Continuous Time in Consistent Histories

NASA Astrophysics Data System (ADS)

Savvidou, Konstantina

1999-12-01

We discuss the case of histories labelled by a continuous time parameter in the History Projection Operator consistent-histories quantum theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about time averages of the energy. We define the action operator for the consistent histories formalism, as the quantum analogue of the classical action functional, for the simple harmonic oscillator case. We show that the action operator is the generator of two types of time transformations that may be related to the two laws of time-evolution of the standard quantum theory: the `state-vector reduction' and the unitary time-evolution. We construct the corresponding classical histories and demonstrate the relevance with the quantum histories; we demonstrate how the requirement of the temporal logic structure of the theory is sufficient for the definition of classical histories. Furthermore, we show the relation of the action operator to the decoherence functional which describes the dynamics of the system. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.

Uncertainty relation for non-Hamiltonian quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E.

2013-01-15

General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.

Dynamical pairwise entanglement and two-point correlations in the three-ligand spin-star structure

NASA Astrophysics Data System (ADS)

Motamedifar, M.

2017-10-01

We consider the three-ligand spin-star structure through homogeneous Heisenberg interactions (XXX-3LSSS) in the framework of dynamical pairwise entanglement. It is shown that the time evolution of the central qubit ;one-particle; state (COPS) brings about the generation of quantum W states at periodical time instants. On the contrary, W states cannot be generated from the time evolution of a ligand ;one-particle; state (LOPS). We also investigate the dynamical behavior of two-point quantum correlations as well as the expectation values of the different spin-components for each element in the XXX-3LSSS. It is found that when a W state is generated, the same value of the concurrence between any two arbitrary qubits arises from the xx and yy two-point quantum correlations. On the opposite, zz quantum correlation between any two qubits vanishes at these time instants.

Entanglement and thermodynamics after a quantum quench in integrable systems.

PubMed

Alba, Vincenzo; Calabrese, Pasquale

2017-07-25

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. Recently, the study of quantum quenches revealed that these concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure state maintains the system at zero entropy, local properties at long times are captured by a statistical ensemble with nonzero thermodynamic entropy, which is the entanglement accumulated during the dynamics. Therefore, understanding the entanglement evolution unveils how thermodynamics emerges in isolated systems. Alas, an exact computation of the entanglement dynamics was available so far only for noninteracting systems, whereas it was deemed unfeasible for interacting ones. Here, we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of the entanglement dynamics in the space-time scaling limit. We thoroughly check our result for the paradigmatic Heisenberg chain.

Entanglement and thermodynamics after a quantum quench in integrable systems

NASA Astrophysics Data System (ADS)

Alba, Vincenzo; Calabrese, Pasquale

2017-07-01

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. Recently, the study of quantum quenches revealed that these concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure state maintains the system at zero entropy, local properties at long times are captured by a statistical ensemble with nonzero thermodynamic entropy, which is the entanglement accumulated during the dynamics. Therefore, understanding the entanglement evolution unveils how thermodynamics emerges in isolated systems. Alas, an exact computation of the entanglement dynamics was available so far only for noninteracting systems, whereas it was deemed unfeasible for interacting ones. Here, we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of the entanglement dynamics in the space-time scaling limit. We thoroughly check our result for the paradigmatic Heisenberg chain.

Entanglement and thermodynamics after a quantum quench in integrable systems

PubMed Central

Alba, Vincenzo; Calabrese, Pasquale

2017-01-01

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. Recently, the study of quantum quenches revealed that these concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure state maintains the system at zero entropy, local properties at long times are captured by a statistical ensemble with nonzero thermodynamic entropy, which is the entanglement accumulated during the dynamics. Therefore, understanding the entanglement evolution unveils how thermodynamics emerges in isolated systems. Alas, an exact computation of the entanglement dynamics was available so far only for noninteracting systems, whereas it was deemed unfeasible for interacting ones. Here, we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of the entanglement dynamics in the space–time scaling limit. We thoroughly check our result for the paradigmatic Heisenberg chain. PMID:28698379

Observing single quantum trajectories of a superconducting quantum bit

NASA Astrophysics Data System (ADS)

Murch, K. W.; Weber, S. J.; Macklin, C.; Siddiqi, I.

2013-10-01

The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture--a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a `quantum trajectory' determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or the amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring, and validate the foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing `quantum steering'--the harnessing of action at a distance to manipulate quantum states through measurement.

Observing single quantum trajectories of a superconducting quantum bit.

PubMed

Murch, K W; Weber, S J; Macklin, C; Siddiqi, I

2013-10-10

The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum state with the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture--a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a 'quantum trajectory' determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or the amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring, and validate the foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing 'quantum steering'--the harnessing of action at a distance to manipulate quantum states through measurement.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Quantum break-time of de Sitter

NASA Astrophysics Data System (ADS)

Dvali, Gia; Gómez, César; Zell, Sebastian

2017-06-01

The quantum break-time of a system is the time-scale after which its true quantum evolution departs from the classical mean field evolution. For capturing it, a quantum resolution of the classical background—e.g., in terms of a coherent state—is required. In this paper, we first consider a simple scalar model with anharmonic oscillations and derive its quantum break-time. Next, following [1], we apply these ideas to de Sitter space. We formulate a simple model of a spin-2 field, which for some time reproduces the de Sitter metric and simultaneously allows for its well-defined representation as quantum coherent state of gravitons. The mean occupation number N of background gravitons turns out to be equal to the de Sitter horizon area in Planck units, while their frequency is given by the de Sitter Hubble parameter. In the semi-classical limit, we show that the model reproduces all the known properties of de Sitter, such as the redshift of probe particles and thermal Gibbons-Hawking radiation, all in the language of quantum S-matrix scatterings and decays of coherent state gravitons. Most importantly, this framework allows to capture the 1/N-effects to which the usual semi-classical treatment is blind. They violate the de Sitter symmetry and lead to a finite quantum break-time of the de Sitter state equal to the de Sitter radius times N. We also point out that the quantum-break time is inversely proportional to the number of particle species in the theory. Thus, the quantum break-time imposes the following consistency condition: older and species-richer universes must have smaller cosmological constants. For the maximal, phenomenologically acceptable number of species, the observed cosmological constant would saturate this bound if our Universe were 10100 years old in its entire classical history.

Proceedings of the Quantum Computation for Physical Modeling Workshop 2004. Held in North Falmouth, MA on 12-15 September 2004

DTIC Science & Technology

2005-10-01

late the difficulty of some basic 1-bit and n-bit quantum and classical operations in an simple unconstrained scenario. KEY WORDS: Time evolution... quantum circuit and design are presented for an optimized entangling probe attacking the BB84 Protocol of quantum key distribution (QKD) and yielding...unambiguous, at least some of the time. It follows that the BB84 (Bennett-Brassard 1984) proto- col of quantum key distribution has a vulnerability similar to

Superadiabatic Controlled Evolutions and Universal Quantum Computation.

PubMed

Santos, Alan C; Sarandy, Marcelo S

2015-10-29

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts.

Superadiabatic Controlled Evolutions and Universal Quantum Computation

PubMed Central

Santos, Alan C.; Sarandy, Marcelo S.

2015-01-01

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts. PMID:26511064

Thermalization and its mechanism for generic quantum isolated systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim; Dunjko, Vanja; Rigol, Marcos

2008-05-01

Time dynamics of isolated many-body quantum systems has long been an elusive subject, perhaps most urgently needed in the foundations of quantum statistical mechanics. In generic systems, one expects the nonequilibrium dynamics to lead to thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. The relaxation mechanism is not obvious, however; dynamical chaos cannot play the key role as it does in classical systems since quantum evolution is linear. Here we demonstrateootnotetextM. Rigol, V. Dunjko, and M. Olshanii, to appear in Nature (2008), using the results of an ab initio numerical experiment with 5 hard-core bosons moving in a 5x5 lattice, that in quantum systems thermalization happens not in course of time evolution but instead at the level of individual eigenstates, as first proposed by DeutschootnotetextJ. M. Deutsch, Phys.Rev. A 43, 2046 (1991) and SrednickiootnotetextM. Srednicki, Phys. Rev. E 50, 888 (1994).

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

DOE PAGES

Yang, Zhi -Cheng; Rahmani, Armin; Shabani, Alireza; ...

2017-05-18

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale ofmore » the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Moreover, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.« less

Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Zhi -Cheng; Rahmani, Armin; Shabani, Alireza

We use Pontryagin’s minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence. Our findings support the choice of evolution ansatz in the recently proposed quantum approximate optimization algorithm. Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian. The optimality of the bang-bang protocols and the characteristic time scale ofmore » the pulses provide an efficient parametrization of the protocol and inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems. Moreover, we find that the success rates of our optimal bang-bang protocols remain high even in the presence of weak external noise and coupling to a thermal bath.« less

Quantum trajectories for time-dependent adiabatic master equations

NASA Astrophysics Data System (ADS)

Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.

2018-02-01

We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension N instead of a complex density matrix of dimension N2, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor N advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor N2 is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for 8-qubit quantum annealing examples. We also apply the quantum trajectories method to a 16-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.

Geometric diffusion of quantum trajectories

PubMed Central

Yang, Fan; Liu, Ren-Bao

2015-01-01

A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bisio, Alessandro; D’Ariano, Giacomo Mauro; Tosini, Alessandro, E-mail: alessandro.tosini@unipv.it

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound withmore » experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of a hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics. - Highlights: • The free Dirac field in one space dimension as a quantum cellular automaton. • Large scale limit of the automaton and the emergence of the Dirac equation. • Dispersive differential equation for the evolution of smooth states on the automaton. • Optimal discrimination between the automaton evolution and the Dirac equation.« less

Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

NASA Astrophysics Data System (ADS)

Lendi, K.

A few particular marked properties of quantum dynamical equations accounting for general relaxation and dissipation are selected and summarized in brief. Most results derive from the universal concept of complete positivity. The considerations mainly regard genuinely irreversible processes as characterized by a unique asymptotically stationary final state for arbitrary initial conditions. From ordinary Markovian master equations and associated quantum dynamical semigroup time-evolution, derivations of higher order Onsager coefficients and related entropy production are discussed. For general processes including non-faithful states a regularized version of quantum relative entropy is introduced. Further considerations extend to time-dependent infinitesimal generators of time-evolution and to a possible description of propagation of initial states entangled between open system and environment. In the coherence-vector representation of the full non-Markovian equations including entangled initial states, first results are outlined towards identifying mathematical properties of a restricted class of trial integral-kernel functions suited to phenomenological applications.

Spectrum, symmetries, and dynamics of Heisenberg spin-1/2 chains

NASA Astrophysics Data System (ADS)

Joel, Kira; Kollmar, Davida; Santos, Lea

2013-03-01

Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. Here we provide an introduction to the subject by focusing on the time evolution of Heisenberg spin-1/2 chains with couplings between nearest-neighbor sites only. We study how the anisotropy parameter and the symmetries of the model affect its time evolution. Our predictions are based on the analysis of the eigenvalues and eigenstates of the system and then confirmed with actual numerical results.

Effective time-independent analysis for quantum kicked systems.

PubMed

Bandyopadhyay, Jayendra N; Guha Sarkar, Tapomoy

2015-03-01

We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.

Effective time-independent analysis for quantum kicked systems

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Jayendra N.; Guha Sarkar, Tapomoy

2015-03-01

We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.

Resonance and decay phenomena lead to quantum mechanical time asymmetry

NASA Astrophysics Data System (ADS)

Bohm, A.; Bui, H. V.

2013-04-01

The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over -∞ < t < +∞. This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t0 <= t < +∞, which predicts a finite "beginning of time" t0, where t0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ = hslash/Γ.

Comparisons of different witnesses of non-Markovianity

NASA Astrophysics Data System (ADS)

Zuo, Wei; Qian, Xiao-Qing; Liang, Xian-Ting

2017-01-01

In this paper, the evolutions of two kinds of witnesses of the non-Markovianity and their rates of changes with time are investigated and compared. Four definitions, the trace distance, fidelity, quantum relative entropy, and quantum Fisher information are used for the first kind of witnesses which are based on the completely positive maps (CPM). Three definitions, the quantum entanglement, quantum mutual information, and quantum discord are used for the second kind of witnesses, and they are based on the local completely positive maps (LCPM). An open two-level quantum system model and a numerically quantum dissipative dynamics method, hierarchy equation of motion (HEM) are used in the investigations. It is shown that the evolutions of the witnesses and their rates of the changes calculated with different definitions clearly show the characteristics of the non-Markovianity and they are in agreement with each other.

Quantum Speed Limits across the Quantum-to-Classical Transition

NASA Astrophysics Data System (ADS)

Shanahan, B.; Chenu, A.; Margolus, N.; del Campo, A.

2018-02-01

Quantum speed limits set an upper bound to the rate at which a quantum system can evolve. Adopting a phase-space approach, we explore quantum speed limits across the quantum-to-classical transition and identify equivalent bounds in the classical world. As a result, and contrary to common belief, we show that speed limits exist for both quantum and classical systems. As in the quantum domain, classical speed limits are set by a given norm of the generator of time evolution.

Quantum Markov Semigroups with Unbounded Generator and Time Evolution of the Support Projection of a State

NASA Astrophysics Data System (ADS)

Gliouez, Souhir; Hachicha, Skander; Nasroui, Ikbel

We characterize the support projection of a state evolving under the action of a quantum Markov semigroup with unbounded generator represented in the generalized GKSL form and a quantum version of the classical Lévy-Austin-Ornstein theorem.

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

Continuous measurement of an atomic current

NASA Astrophysics Data System (ADS)

Laflamme, C.; Yang, D.; Zoller, P.

2017-04-01

We are interested in dynamics of quantum many-body systems under continuous observation, and its physical realizations involving cold atoms in lattices. In the present work we focus on continuous measurement of atomic currents in lattice models, including the Hubbard model. We describe a Cavity QED setup, where measurement of a homodyne current provides a faithful representation of the atomic current as a function of time. We employ the quantum optical description in terms of a diffusive stochastic Schrödinger equation to follow the time evolution of the atomic system conditional to observing a given homodyne current trajectory, thus accounting for the competition between the Hamiltonian evolution and measurement back action. As an illustration, we discuss minimal models of atomic dynamics and continuous current measurement on rings with synthetic gauge fields, involving both real space and synthetic dimension lattices (represented by internal atomic states). Finally, by "not reading" the current measurements the time evolution of the atomic system is governed by a master equation, where—depending on the microscopic details of our CQED setups—we effectively engineer a current coupling of our system to a quantum reservoir. This provides interesting scenarios of dissipative dynamics generating "dark" pure quantum many-body states.

Coherence-generating power of quantum dephasing processes

NASA Astrophysics Data System (ADS)

Styliaris, Georgios; Campos Venuti, Lorenzo; Zanardi, Paolo

2018-03-01

We provide a quantification of the capability of various quantum dephasing processes to generate coherence out of incoherent states. The measures defined, admitting computable expressions for any finite Hilbert-space dimension, are based on probabilistic averages and arise naturally from the viewpoint of coherence as a resource. We investigate how the capability of a dephasing process (e.g., a nonselective orthogonal measurement) to generate coherence depends on the relevant bases of the Hilbert space over which coherence is quantified and the dephasing process occurs, respectively. We extend our analysis to include those Lindblad time evolutions which, in the infinite-time limit, dephase the system under consideration and calculate their coherence-generating power as a function of time. We further identify specific families of such time evolutions that, although dephasing, have optimal (over all quantum processes) coherence-generating power for some intermediate time. Finally, we investigate the coherence-generating capability of random dephasing channels.

Efficient Quantum Pseudorandomness.

PubMed

Brandão, Fernando G S L; Harrow, Aram W; Horodecki, Michał

2016-04-29

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum systems, but in many cases pseudorandom operations can emulate certain properties of truly random ones. Indeed, in the classical realm there is by now a well-developed theory regarding such pseudorandom operations. However, the construction of such objects turns out to be much harder in the quantum case. Here, we show that random quantum unitary time evolutions ("circuits") are a powerful source of quantum pseudorandomness. This gives for the first time a polynomial-time construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography, and understanding the self-equilibration of closed quantum dynamics.

Coherent quantum dynamics of a superconducting flux qubit.

PubMed

Chiorescu, I; Nakamura, Y; Harmans, C J P M; Mooij, J E

2003-03-21

We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving, it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.

Observing Quantum State Diffusion by Heterodyne Detection of Fluorescence

NASA Astrophysics Data System (ADS)

Campagne-Ibarcq, P.; Six, P.; Bretheau, L.; Sarlette, A.; Mirrahimi, M.; Rouchon, P.; Huard, B.

2016-01-01

A qubit can relax by fluorescence, which prompts the release of a photon into its electromagnetic environment. By counting the emitted photons, discrete quantum jumps of the qubit state can be observed. The succession of states occupied by the qubit in a single experiment, its quantum trajectory, depends in fact on the kind of detector. How are the quantum trajectories modified if one measures continuously the amplitude of the fluorescence field instead? Using a superconducting parametric amplifier, we perform heterodyne detection of the fluorescence of a superconducting qubit. For each realization of the measurement record, we can reconstruct a different quantum trajectory for the qubit. The observed evolution obeys quantum state diffusion, which is characteristic of quantum measurements subject to zero-point fluctuations. Independent projective measurements of the qubit at various times provide a quantitative verification of the reconstructed trajectories. By exploring the statistics of quantum trajectories, we demonstrate that the qubit states span a deterministic surface in the Bloch sphere at each time in the evolution. Additionally, we show that when monitoring fluorescence field quadratures, coherent superpositions are generated during the decay from excited to ground state. Counterintuitively, measuring light emitted during relaxation can give rise to trajectories with increased excitation probability.

Quantum break-time of de Sitter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dvali, Gia; Gómez, César; Zell, Sebastian, E-mail: georgi.dvali@physik.uni-muenchen.de, E-mail: cesar.gomez@uam.es, E-mail: sebastian.zell@campus.lmu.de

The quantum break-time of a system is the time-scale after which its true quantum evolution departs from the classical mean field evolution. For capturing it, a quantum resolution of the classical background—e.g., in terms of a coherent state—is required. In this paper, we first consider a simple scalar model with anharmonic oscillations and derive its quantum break-time. Next, following [1], we apply these ideas to de Sitter space. We formulate a simple model of a spin-2 field, which for some time reproduces the de Sitter metric and simultaneously allows for its well-defined representation as quantum coherent state of gravitons. Themore » mean occupation number N of background gravitons turns out to be equal to the de Sitter horizon area in Planck units, while their frequency is given by the de Sitter Hubble parameter. In the semi-classical limit, we show that the model reproduces all the known properties of de Sitter, such as the redshift of probe particles and thermal Gibbons-Hawking radiation, all in the language of quantum S -matrix scatterings and decays of coherent state gravitons. Most importantly, this framework allows to capture the 1/ N -effects to which the usual semi-classical treatment is blind. They violate the de Sitter symmetry and lead to a finite quantum break-time of the de Sitter state equal to the de Sitter radius times N . We also point out that the quantum-break time is inversely proportional to the number of particle species in the theory. Thus, the quantum break-time imposes the following consistency condition: older and species-richer universes must have smaller cosmological constants. For the maximal, phenomenologically acceptable number of species, the observed cosmological constant would saturate this bound if our Universe were 10{sup 100} years old in its entire classical history.« less

Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems

NASA Astrophysics Data System (ADS)

Meyer, Gregory; Machado, Francisco; Yao, Norman

2017-04-01

Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.

A variational eigenvalue solver on a photonic quantum processor

PubMed Central

Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter; Yung, Man-Hong; Zhou, Xiao-Qi; Love, Peter J.; Aspuru-Guzik, Alán; O’Brien, Jeremy L.

2014-01-01

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry—calculating the ground-state molecular energy for He–H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future. PMID:25055053

Estimating the time evolution of NMR systems via a quantum-speed-limit-like expression

NASA Astrophysics Data System (ADS)

Villamizar, D. V.; Duzzioni, E. I.; Leal, A. C. S.; Auccaise, R.

2018-05-01

Finding the solutions of the equations that describe the dynamics of a given physical system is crucial in order to obtain important information about its evolution. However, by using estimation theory, it is possible to obtain, under certain limitations, some information on its dynamics. The quantum-speed-limit (QSL) theory was originally used to estimate the shortest time in which a Hamiltonian drives an initial state to a final one for a given fidelity. Using the QSL theory in a slightly different way, we are able to estimate the running time of a given quantum process. For that purpose, we impose the saturation of the Anandan-Aharonov bound in a rotating frame of reference where the state of the system travels slower than in the original frame (laboratory frame). Through this procedure it is possible to estimate the actual evolution time in the laboratory frame of reference with good accuracy when compared to previous methods. Our method is tested successfully to predict the time spent in the evolution of nuclear spins 1/2 and 3/2 in NMR systems. We find that the estimated time according to our method is better than previous approaches by up to four orders of magnitude. One disadvantage of our method is that we need to solve a number of transcendental equations, which increases with the system dimension and parameter discretization used to solve such equations numerically.

Time-ordered exponential on the complex plane and Gell-Mann—Low formula as a mathematical theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Futakuchi, Shinichiro; Usui, Kouta

2016-04-15

The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann—Low formula under certain abstract conditions, in mathematically rigorous manner. We apply the abstract results to quantum electrodynamics with cutoffs.

Manipulation of quantum evolution

NASA Technical Reports Server (NTRS)

Cabera, David Jose Fernandez; Mielnik, Bogdan

1994-01-01

The free evolution of a non-relativistic charged particle is manipulated using time-dependent magnetic fields. It is shown that the application of a programmed sequence of magnetic pulses can invert the free evolution process, forcing an arbitrary wave packet to 'go back in time' to recover its past shape. The possibility of more general operations upon the Schrodinger wave packet is discussed.

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

NASA Astrophysics Data System (ADS)

Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer

2016-06-01

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.

Protecting quantum Fisher information in curved space-time

NASA Astrophysics Data System (ADS)

Huang, Zhiming

2018-03-01

In this work, we investigate the quantum Fisher information (QFI) dynamics of a two-level atom interacting with quantized conformally coupled massless scalar fields in de Sitter-invariant vacuum. We first derive the master equation that governs its evolution. It is found that the QFI decays with evolution time. Furthermore, we propose two schemes to protect QFI by employing prior weak measurement (WM) and post measurement reversal (MR). We find that the first scheme can not always protect QFI and the second scheme has prominent advantage over the first scheme.

Feynman’s clock, a new variational principle, and parallel-in-time quantum dynamics

PubMed Central

McClean, Jarrod R.; Parkhill, John A.; Aspuru-Guzik, Alán

2013-01-01

We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics. PMID:24062428

Evolution of complexity following a quantum quench in free field theory

NASA Astrophysics Data System (ADS)

Alves, Daniel W. F.; Camilo, Giancarlo

2018-06-01

Using a recent proposal of circuit complexity in quantum field theories introduced by Jefferson and Myers, we compute the time evolution of the complexity following a smooth mass quench characterized by a time scale δ t in a free scalar field theory. We show that the dynamics has two distinct phases, namely an early regime of approximately linear evolution followed by a saturation phase characterized by oscillations around a mean value. The behavior is similar to previous conjectures for the complexity growth in chaotic and holographic systems, although here we have found that the complexity may grow or decrease depending on whether the quench increases or decreases the mass, and also that the time scale for saturation of the complexity is of order δ t (not parametrically larger).

Solvable Hydrodynamics of Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2017-12-01

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

On the substructure of the cosmological constant

NASA Astrophysics Data System (ADS)

Dvali, G.; Gomez, C.; Zell, S.

We summarize the findings of our paper arXiv:1701.08776 [hep-th]. We start by defining the quantum break-time. Once one understands a classical solution as expectation value of an underlying quantum state, it emerges as time-scale after which the true quantum evolution departs from the classical mean field evolution. We apply this idea to de Sitter space. Following earlier work, we construct a simple model of a spin-2 field, which for some time reproduces the de Sitter metric and simultaneously allows for its well-defined representation as coherent quantum state of gravitons. The mean occupation number N of background gravitons turns out to be equal to the de Sitter horizon area in Planck units, while their frequency is given by the de Sitter Hubble parameter. In the semi-classical limit, we show that the model reproduces all semi-classical calculations in de Sitter, such as thermal Gibbons-Hawking radiation, all in the language of quantum S-matrix scatterings and decays of coherent state gravitons. Most importantly, this framework allows to capture the (1/N)-effects of back reaction to which the usual semi-classical treatment is blind. They violate the de Sitter symmetry and lead to a finite quantum break-time of the de Sitter state equal to the de Sitter radius times N. We also point out that the quantum-break time is inversely proportional to the number of particle species in the theory. Thus, the quantum break-time imposes the following consistency condition: Older and species-richer universes must have smaller cosmological constants. For the maximal, phenomenologically acceptable number of species, the observed cosmological constant would saturate this bound if our Universe were 10100 years old in its entire classical history.

Entanglement dynamics in short- and long-range harmonic oscillators

NASA Astrophysics Data System (ADS)

Nezhadhaghighi, M. Ghasemi; Rajabpour, M. A.

2014-11-01

We study the time evolution of the entanglement entropy in the short- and long-range-coupled harmonic oscillators that have well-defined continuum limit field theories. We first introduce a method to calculate the entanglement evolution in generic coupled harmonic oscillators after quantum quench. Then we study the entanglement evolution after quantum quench in harmonic systems in which the couplings decay effectively as 1 /rd +α with the distance r . After quenching the mass from a nonzero value to zero we calculate numerically the time evolution of von Neumann and Rényi entropies. We show that for 1 <α <2 we have a linear growth of entanglement and then saturation independent of the initial state. For 0 <α <1 depending on the initial state we can have logarithmic growth or just fluctuation of entanglement. We also calculate the mutual information dynamics of two separated individual harmonic oscillators. Our findings suggest that in our system there is no particular connection between having a linear growth of entanglement after quantum quench and having a maximum group velocity or generalized Lieb-Robinson bound.

Evolution and Survival of Quantum Entanglement

DTIC Science & Technology

2009-11-21

for quantum information as well as the central feature in the Einstein-Podolsky-Rosen so-called paradox and in discussions of the fate of Schrödinger’s...has been the focus of foundational discussions of quantum mechanics since the time of Schrödinger (who gave it its name) and the famous EPR paper of

Time evolution of Rényi entropy under the Lindblad equation.

PubMed

Abe, Sumiyoshi

2016-08-01

In recent years, the Rényi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Rényi entropy is studied. A compact general formula is presented for the lower bound on the entropy rate.

Relativistic kicked rotor.

PubMed

Matrasulov, D U; Milibaeva, G M; Salomov, U R; Sundaram, Bala

2005-07-01

Transport properties in the relativistic analog of the periodically kicked rotor are contrasted under classically and quantum mechanical dynamics. The quantum rotor is treated by solving the Dirac equation in the presence of the time-periodic delta-function potential resulting in a relativistic quantum mapping describing the evolution of the wave function. The transition from the quantum suppression behavior seen in the nonrelativistic limit to agreement between quantum and classical analyses in the relativistic regime is discussed. The absence of quantum resonances in the relativistic case is also addressed.

Adiabatic evolution of decoherence-free subspaces and its shortcuts

NASA Astrophysics Data System (ADS)

Wu, S. L.; Huang, X. L.; Li, H.; Yi, X. X.

2017-10-01

The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.

Quantum dynamics of a plane pendulum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leibscher, Monika; Schmidt, Burkhard

A semianalytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schroedinger equation is solved for pendular analogs of coherent and squeezed states of a harmonic oscillator, induced by instantaneous changes of the periodic potential energy function. Coherent pendular states are discussed between the harmonic limit for small displacements and the inverted pendulum limit, while squeezed pendular states are shown to interpolate between vibrational and free rotational motion. In the latter case, full and fractional revivals as well as spatiotemporal structures in the time evolution ofmore » the probability densities (quantum carpets) are quantitatively analyzed. Corresponding expressions for the mean orientation are derived in terms of Mathieu functions in time. For periodic double well potentials, different revival schemes, and different quantum carpets are found for the even and odd initial states forming the ground tunneling doublet. Time evolution of the mean alignment allows the separation of states with different parity. Implications for external (rotational) and internal (torsional) motion of molecules induced by intense laser fields are discussed.« less

Method for discovering relationships in data by dynamic quantum clustering

DOEpatents

Weinstein, Marvin; Horn, David

2017-05-09

Data clustering is provided according to a dynamical framework based on quantum mechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent Hamiltonian formalism by a truncated calculation within a set of Gaussian wave-functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition and/or feature filtering.

Method for discovering relationships in data by dynamic quantum clustering

DOEpatents

Weinstein, Marvin; Horn, David

2014-10-28

Data clustering is provided according to a dynamical framework based on quantum mechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent Hamiltonian formalism by a truncated calculation within a set of Gaussian wave-functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition and/or feature filtering.

Parrondo's game using a discrete-time quantum walk

NASA Astrophysics Data System (ADS)

Chandrashekar, C. M.; Banerjee, Subhashish

2011-04-01

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A ( B) to have a winning probability more than player B ( A). Significance of the game strategy in information theory and physical applications are also discussed.

Multitime correlation functions in nonclassical stochastic processes

NASA Astrophysics Data System (ADS)

Krumm, F.; Sperling, J.; Vogel, W.

2016-06-01

A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.

Measurement-based quantum computation on two-body interacting qubits with adiabatic evolution.

PubMed

Kyaw, Thi Ha; Li, Ying; Kwek, Leong-Chuan

2014-10-31

A cluster state cannot be a unique ground state of a two-body interacting Hamiltonian. Here, we propose the creation of a cluster state of logical qubits encoded in spin-1/2 particles by adiabatically weakening two-body interactions. The proposal is valid for any spatial dimensional cluster states. Errors induced by thermal fluctuations and adiabatic evolution within finite time can be eliminated ensuring fault-tolerant quantum computing schemes.

Quantum no-scale regimes in string theory

NASA Astrophysics Data System (ADS)

Coudarchet, Thibaut; Fleming, Claude; Partouche, Hervé

2018-05-01

We show that in generic no-scale models in string theory, the flat, expanding cosmological evolutions found at the quantum level can be attracted to a "quantum no-scale regime", where the no-scale structure is restored asymptotically. In this regime, the quantum effective potential is dominated by the classical kinetic energies of the no-scale modulus and dilaton. We find that this natural preservation of the classical no-scale structure at the quantum level occurs when the initial conditions of the evolutions sit in a subcritical region of their space. On the contrary, supercritical initial conditions yield solutions that have no analogue at the classical level. The associated intrinsically quantum universes are sentenced to collapse and their histories last finite cosmic times. Our analysis is done at 1-loop, in perturbative heterotic string compactified on tori, with spontaneous supersymmetry breaking implemented by a stringy version of the Scherk-Schwarz mechanism.

Quantum and classical behavior in interacting bosonic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hertzberg, Mark P.

It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular differencemore » in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.« less

Coherence evolution in two-qubit system going through amplitude damping channel

NASA Astrophysics Data System (ADS)

Zhao, MingJing; Ma, Teng; Ma, YuQuan

2018-02-01

In this paper, we analyze the evolution of quantum coherence in a two-qubit system going through the amplitude damping channel. After they have gone through this channel many times, we analyze the systems with respect to the coherence of their output states. When only one subsystem goes through the channel, frozen coherence occurs if and only if this subsystem is incoherent and an auxiliary condition is satisfied for the other subsystem. When two subsystems go through this quantum channel, quantum coherence can be frozen if and only if the two subsystems are both incoherent. We also investigate the evolution of coherence for maximally incoherent-coherent states and derive an equation for the output states after one or two subsystems have gone through the amplitude damping channel.

Aging dynamics of quantum spin glasses of rotors

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio; Ye, Jinwu

2001-12-01

We study the long time dynamics of quantum spin glasses of rotors using the nonequilibrium Schwinger-Keldysh formalism. These models are known to have a quantum phase transition from a paramagnetic to a spin-glass phase, which we approach by looking at the divergence of the spin-relaxation rate at the transition point. In the aging regime, we determine the dynamical equations governing the time evolution of the spin response and correlation functions, and show that all terms in the equations that arise solely from quantum effects are irrelevant at long times under time reparametrization group (RPG) transformations. At long times, quantum effects enter only through the renormalization of the parameters in the dynamical equations for the classical counterpart of the rotor model. Consequently, quantum effects only modify the out-of-equilibrium fluctuation-dissipation relation (OEFDR), i.e. the ratio X between the temperature and the effective temperature, but not the form of the classical OEFDR.

Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space

NASA Astrophysics Data System (ADS)

Volkoff, T. J.; Whaley, K. B.

2014-12-01

We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch-distinguishability measure is obtained and applied to superposition states of N quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well-known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., NOON states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra.

On quantum effects in a theory of biological evolution.

PubMed

Martin-Delgado, M A

2012-01-01

We construct a descriptive toy model that considers quantum effects on biological evolution starting from Chaitin's classical framework. There are smart evolution scenarios in which a quantum world is as favorable as classical worlds for evolution to take place. However, in more natural scenarios, the rate of evolution depends on the degree of entanglement present in quantum organisms with respect to classical organisms. If the entanglement is maximal, classical evolution turns out to be more favorable.

On Quantum Effects in a Theory of Biological Evolution

PubMed Central

Martin-Delgado, M. A.

2012-01-01

We construct a descriptive toy model that considers quantum effects on biological evolution starting from Chaitin's classical framework. There are smart evolution scenarios in which a quantum world is as favorable as classical worlds for evolution to take place. However, in more natural scenarios, the rate of evolution depends on the degree of entanglement present in quantum organisms with respect to classical organisms. If the entanglement is maximal, classical evolution turns out to be more favorable. PMID:22413059

On the definition of the time evolution operator for time-independent Hamiltonians in non-relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.

2017-09-01

The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.

Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alonso, J. L.; Instituto de Biocomputacion y Fisica de Sistemas Complejos; Unidad Asociada IQFR-BIFI, Universidad de Zaragoza, Mariano Esquillor s/n, E-50018 Zaragoza

2012-08-07

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamicsmore » makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.« less

A Blueprint for Demonstrating Quantum Supremacy with Superconducting Qubits

NASA Technical Reports Server (NTRS)

Kechedzhi, Kostyantyn

2018-01-01

Long coherence times and high fidelity control recently achieved in scalable superconducting circuits paved the way for the growing number of experimental studies of many-qubit quantum coherent phenomena in these devices. Albeit full implementation of quantum error correction and fault tolerant quantum computation remains a challenge the near term pre-error correction devices could allow new fundamental experiments despite inevitable accumulation of errors. One such open question foundational for quantum computing is achieving the so called quantum supremacy, an experimental demonstration of a computational task that takes polynomial time on the quantum computer whereas the best classical algorithm would require exponential time and/or resources. It is possible to formulate such a task for a quantum computer consisting of less than a 100 qubits. The computational task we consider is to provide approximate samples from a non-trivial quantum distribution. This is a generalization for the case of superconducting circuits of ideas behind boson sampling protocol for quantum optics introduced by Arkhipov and Aaronson. In this presentation we discuss a proof-of-principle demonstration of such a sampling task on a 9-qubit chain of superconducting gmon qubits developed by Google. We discuss theoretical analysis of the driven evolution of the device resulting in output approximating samples from a uniform distribution in the Hilbert space, a quantum chaotic state. We analyze quantum chaotic characteristics of the output of the circuit and the time required to generate a sufficiently complex quantum distribution. We demonstrate that the classical simulation of the sampling output requires exponential resources by connecting the task of calculating the output amplitudes to the sign problem of the Quantum Monte Carlo method. We also discuss the detailed theoretical modeling required to achieve high fidelity control and calibration of the multi-qubit unitary evolution in the device. We use a novel cross-entropy statistical metric as a figure of merit to verify the output and calibrate the device controls. Finally, we demonstrate the statistics of the wave function amplitudes generated on the 9-gmon chain and verify the quantum chaotic nature of the generated quantum distribution. This verifies the implementation of the quantum supremacy protocol.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Omkar, S.; Srikanth, R., E-mail: srik@poornaprajna.org; Banerjee, Subhashish

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.

Decoherence and discrete symmetries in deformed relativistic kinematics

NASA Astrophysics Data System (ADS)

Arzano, Michele

2018-01-01

Models of deformed Poincaré symmetries based on group valued momenta have long been studied as effective modifications of relativistic kinematics possibly capturing quantum gravity effects. In this contribution we show how they naturally lead to a generalized quantum time evolution of the type proposed to model fundamental decoherence for quantum systems in the presence of an evaporating black hole. The same structures which determine such generalized evolution also lead to a modification of the action of discrete symmetries and of the CPT operator. These features can in principle be used to put phenomenological constraints on models of deformed relativistic symmetries using precision measurements of neutral kaons.

Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Tamascelli, D.; Smirne, A.; Huelga, S. F.; Plenio, M. B.

2018-01-01

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments—one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.

Quantum Entanglement Growth under Random Unitary Dynamics

NASA Astrophysics Data System (ADS)

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haah, Jeongwan

2017-07-01

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time )1/3 and are spatially correlated over a distance ∝(time )2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.

Quantum entanglement in strong-field ionization

NASA Astrophysics Data System (ADS)

Majorosi, Szilárd; Benedict, Mihály G.; Czirják, Attila

2017-10-01

We investigate the time evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion core. Since the standard procedure is numerically prohibitive in this case, we propose a method to quantify the quantum correlation in such a system: we use the reduced density matrices of the directional subspaces along the polarization of the laser pulse and along the transverse directions as building blocks for an approximate entanglement entropy. We present our results, based on accurate numerical simulations, in terms of several of these entropies, for selected values of the peak electric-field strength and the carrier-envelope phase difference of the laser pulse. The time evolution of the mutual entropy of the electron and the ion-core motion along the direction of the laser polarization is similar to our earlier results based on a simple one-dimensional model. However, taking into account also the dynamics perpendicular to the laser polarization reveals a surprisingly different entanglement dynamics above the laser intensity range corresponding to pure tunneling: the quantum entanglement decreases with time in the over-the-barrier ionization regime.

Quantum quenches in two spatial dimensions using chain array matrix product states

DOE PAGES

A. J. A. James; Konik, R.

2015-10-15

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions (2D). The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular, it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum [(2+1)-dimensional] Ising model. As a result, in quenches that cross a phase boundary we find that the return probability shows nonanalyticities in time.

Driven-dissipative quantum Monte Carlo method for open quantum systems

NASA Astrophysics Data System (ADS)

Nagy, Alexandra; Savona, Vincenzo

2018-05-01

We develop a real-time full configuration-interaction quantum Monte Carlo approach to model driven-dissipative open quantum systems with Markovian system-bath coupling. The method enables stochastic sampling of the Liouville-von Neumann time evolution of the density matrix thanks to a massively parallel algorithm, thus providing estimates of observables on the nonequilibrium steady state. We present the underlying theory and introduce an initiator technique and importance sampling to reduce the statistical error. Finally, we demonstrate the efficiency of our approach by applying it to the driven-dissipative two-dimensional X Y Z spin-1/2 model on a lattice.

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

NASA Astrophysics Data System (ADS)

Abanin, Dmitry; De Roeck, Wojciech; Ho, Wen Wei; Huveneers, François

2017-09-01

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency {ν}. We prove that up to a quasi-exponential time {τ_* ˜ e^{c ν/log^3 ν}}, the system barely absorbs energy. Instead, there is an effective local Hamiltonian {\\widehat D} that governs the time evolution up to {τ_*}, and hence this effective Hamiltonian is a conserved quantity up to {τ_*}. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction U is much larger than the hopping J. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time {τ_*} that is (almost) exponential in {U/J}.

Bath-induced correlations in an infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Nizama, Marco; Cáceres, Manuel O.

2017-09-01

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

Quantum diffusion of prices and profits

NASA Astrophysics Data System (ADS)

Piotrowski, Edward W.; Sładkowski, Jan

2005-01-01

We discuss the time evolution of quotations of stocks and commodities and show that corrections to the orthodox Bachelier model inspired by quantum mechanical time evolution of particles may be important. Our analysis shows that traders tactics can interfere as waves do and trader's strategies can be reproduced from the corresponding Wigner functions. The proposed interpretation of the chaotic movement of market prices imply that the Bachelier behaviour follows from short-time interference of tactics adopted (paths followed) by the rest of the world considered as a single trader and the Ornstein-Uhlenbeck corrections to the Bachelier model should qualitatively matter only for large time scales. The famous smithonian invisible hand is interpreted as a short-time tactics of whole the market considered as a single opponent. We also propose a solution to the currency preference paradox.

Quantum Mechanics predicts evolutionary biology.

PubMed

Torday, J S

2018-07-01

Nowhere are the shortcomings of conventional descriptive biology more evident than in the literature on Quantum Biology. In the on-going effort to apply Quantum Mechanics to evolutionary biology, merging Quantum Mechanics with the fundamentals of evolution as the First Principles of Physiology-namely negentropy, chemiosmosis and homeostasis-offers an authentic opportunity to understand how and why physics constitutes the basic principles of biology. Negentropy and chemiosmosis confer determinism on the unicell, whereas homeostasis constitutes Free Will because it offers a probabilistic range of physiologic set points. Similarly, on this basis several principles of Quantum Mechanics also apply directly to biology. The Pauli Exclusion Principle is both deterministic and probabilistic, whereas non-localization and the Heisenberg Uncertainty Principle are both probabilistic, providing the long-sought after ontologic and causal continuum from physics to biology and evolution as the holistic integration recognized as consciousness for the first time. Copyright © 2018 Elsevier Ltd. All rights reserved.

Speedup for quantum optimal control from automatic differentiation based on graphics processing units

NASA Astrophysics Data System (ADS)

Leung, Nelson; Abdelhafez, Mohamed; Koch, Jens; Schuster, David

2017-04-01

We implement a quantum optimal control algorithm based on automatic differentiation and harness the acceleration afforded by graphics processing units (GPUs). Automatic differentiation allows us to specify advanced optimization criteria and incorporate them in the optimization process with ease. We show that the use of GPUs can speedup calculations by more than an order of magnitude. Our strategy facilitates efficient numerical simulations on affordable desktop computers and exploration of a host of optimization constraints and system parameters relevant to real-life experiments. We demonstrate optimization of quantum evolution based on fine-grained evaluation of performance at each intermediate time step, thus enabling more intricate control on the evolution path, suppression of departures from the truncated model subspace, as well as minimization of the physical time needed to perform high-fidelity state preparation and unitary gates.

The evolving block universe and the meshing together of times.

PubMed

Ellis, George F R

2014-10-01

It has been proposed that spacetime should be regarded as an evolving block universe, bounded to the future by the present time, which continually extends to the future. This future boundary is defined at each time by measuring proper time along Ricci eigenlines from the start of the universe. A key point, then, is that physical reality can be represented at many different scales: hence, the passage of time may be seen as different at different scales, with quantum gravity determining the evolution of spacetime itself at the Planck scale, but quantum field theory and classical physics determining the evolution of events within spacetime at larger scales. The fundamental issue then arises as to how the effective times at different scales mesh together, leading to the concepts of global and local times. © 2014 New York Academy of Sciences.

Model dynamics for quantum computing

NASA Astrophysics Data System (ADS)

Tabakin, Frank

2017-08-01

A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.

Schramm-Loewner evolution and Liouville quantum gravity.

PubMed

Duplantier, Bertrand; Sheffield, Scott

2011-09-23

We show that when two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary length-preserving way) the resulting interface is a random curve called the Schramm-Loewner evolution. We also develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under conformal welding maps related to Schramm-Loewner evolution. As an application, we construct quantum length and boundary intersection measures on the Schramm-Loewner evolution curve itself.

Speedup of quantum evolution of multiqubit entanglement states

PubMed Central

Zhang, Ying-Jie; Han, Wei; Xia, Yun-Jie; Tian, Jian-Xiang; Fan, Heng

2016-01-01

As is well known, quantum speed limit time (QSLT) can be used to characterize the maximal speed of evolution of quantum systems. We mainly investigate the QSLT of generalized N-qubit GHZ-type states and W-type states in the amplitude-damping channels. It is shown that, in the case N qubits coupled with independent noise channels, the QSLT of the entangled GHZ-type state is closely related to the number of qubits in the small-scale system. And the larger entanglement of GHZ-type states can lead to the shorter QSLT of the evolution process. However, the QSLT of the W-type states are independent of the number of qubits and the initial entanglement. Furthermore, by considering only M qubits among the N-qubit system respectively interacting with their own noise channels, QSLTs for these two types states are shorter than in the case N qubits coupled with independent noise channels. We therefore reach the interesting result that the potential speedup of quantum evolution of a given N-qubit GHZ-type state or W-type state can be realized in the case the number of the applied noise channels satisfying M < N. PMID:27283757

Quantum Hamiltonian identification from measurement time traces.

PubMed

Zhang, Jun; Sarovar, Mohan

2014-08-22

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

Time evolution as refining, coarse graining and entangling

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Steinhaus, Sebastian

2014-12-01

We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows construction of a (cylindrically) consistent continuum limit of the theory.

Dynamical quantum phase transitions: a review

NASA Astrophysics Data System (ADS)

Heyl, Markus

2018-05-01

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.

Dynamical quantum phase transitions: a review.

PubMed

Heyl, Markus

2018-05-01

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.

Decoherence and thermalization of a pure quantum state in quantum field theory.

PubMed

Giraud, Alexandre; Serreau, Julien

2010-06-11

We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.

Quantum Entanglement Growth under Random Unitary Dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement growsmore » linearly in time, while fluctuations grow like (time) 1/3 and are spatially correlated over a distance ∝(time) 2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.« less

Quantum Entanglement Growth under Random Unitary Dynamics

DOE PAGES

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; ...

2017-07-24

Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement growsmore » linearly in time, while fluctuations grow like (time) 1/3 and are spatially correlated over a distance ∝(time) 2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.« less

Holographic control of information and dynamical topology change for composite open quantum systems

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Volovich, I. V.; Inozemcev, O. V.

2017-12-01

We analyze how the compositeness of a system affects the characteristic time of equilibration. We study the dynamics of open composite quantum systems strongly coupled to the environment after a quantum perturbation accompanied by nonequilibrium heating. We use a holographic description of the evolution of entanglement entropy. The nonsmooth character of the evolution with holographic entanglement is a general feature of composite systems, which demonstrate a dynamical change of topology in the bulk space and a jumplike velocity change of entanglement entropy propagation. Moreover, the number of jumps depends on the system configuration and especially on the number of composite parts. The evolution of the mutual information of two composite systems inherits these jumps. We present a detailed study of the mutual information for two subsystems with one of them being bipartite. We find five qualitatively different types of behavior of the mutual information dynamics and indicate the corresponding regions of the system parameters.

Adiabatic gate teleportation.

PubMed

Bacon, Dave; Flammia, Steven T

2009-09-18

The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation, which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space. This construction allows for geometric robustness based upon the control of two independent qubit interactions. Further, our piecewise adiabatic evolution easily relates to the quantum circuit model, enabling the use of standard methods from fault-tolerance theory for establishing thresholds.

Tunneling in quantum cosmology and holographic SYM theory

NASA Astrophysics Data System (ADS)

Ghoroku, Kazuo; Nakano, Yoshimasa; Tachibana, Motoi; Toyoda, Fumihiko

2018-03-01

We study the time evolution of the early Universe, which is developed by a cosmological constant Λ4 and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker space-time. The renormalized vacuum expectation value of the energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as C . The evolution is controlled by this radiation C and the cosmological constant Λ4. For positive Λ4, an inflationary solution is obtained at late time. When C is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.

Extended space expectation values in quantum dynamical system evolutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demiralp, Metin

2014-10-06

The time variant power series expansion for the expectation value of a given quantum dynamical operator is well-known and well-investigated issue in quantum dynamics. However, depending on the operator and Hamiltonian singularities this expansion either may not exist or may not converge for all time instances except the beginning of the evolution. This work focuses on this issue and seeks certain cures for the negativities. We work in the extended space obtained by adding all images of the initial wave function under the system Hamiltonian’s positive integer powers. This requires the introduction of certain appropriately defined weight operators. The resultingmore » better convergence in the temporal power series urges us to call the new defined entities “extended space expectation values” even though they are constructed over certain weight operators and are somehow pseudo expectation values.« less

Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium

NASA Astrophysics Data System (ADS)

Santos, Lea F.; Torres-Herrera, E. Jonathan

2017-12-01

Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of solvable models and of full random matrices. None of the two approaches represent actual realistic systems, but they serve as references for the studies of these ones. We take the second path and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we then propose an approximate expression that matches very well numerical results for the evolution of realistic finite quantum systems that are strongly chaotic and quenched far from equilibrium. In the case of the survival probability, the expression proposed covers all different time scales, from the moment the system is taken out of equilibrium to the moment it reaches a new equilibrium. The realistic systems considered are described by one-dimensional spin-1/2 models.

Student understanding of time dependence in quantum mechanics

NASA Astrophysics Data System (ADS)

Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

2015-12-01

[This paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantum mechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.

Mixing times in quantum walks on two-dimensional grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-15

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and themore » running time of the corresponding abstract search algorithm is discussed.« less

Mixing times in quantum walks on two-dimensional grids

NASA Astrophysics Data System (ADS)

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-01

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.

Loop Quantum Cosmology.

PubMed

Bojowald, Martin

2008-01-01

Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time. Supplementary material is available for this article at 10.12942/lrr-2008-4.

Experimental two-dimensional quantum walk on a photonic chip

PubMed Central

Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin

2018-01-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon–level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems. PMID:29756040

Experimental two-dimensional quantum walk on a photonic chip.

PubMed

Tang, Hao; Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin; Jin, Xian-Min

2018-05-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.

Correlated Errors in the Surface Code

NASA Astrophysics Data System (ADS)

Lopez, Daniel; Mucciolo, E. R.; Novais, E.

2012-02-01

A milestone step into the development of quantum information technology would be the ability to design and operate a reliable quantum memory. The greatest obstacle to create such a device has been decoherence due to the unavoidable interaction between the quantum system and its environment. Quantum Error Correction is therefore an essential ingredient to any quantum computing information device. A great deal of attention has been given to surface codes, since it has very good scaling properties. In this seminar, we discuss the time evolution of a qubit encoded in the logical basis of a surface code. The system is interacting with a bosonic environment at zero temperature. Our results show how much spatial and time correlations can be detrimental to the efficiency of the code.

Ensembles of physical states and random quantum circuits on graphs

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Santra, Siddhartha; Zanardi, Paolo

2012-11-01

In this paper we continue and extend the investigations of the ensembles of random physical states introduced in Hamma [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.040502 109, 040502 (2012)]. These ensembles are constructed by finite-length random quantum circuits (RQC) acting on the (hyper)edges of an underlying (hyper)graph structure. The latter encodes for the locality structure associated with finite-time quantum evolutions generated by physical, i.e., local, Hamiltonians. Our goal is to analyze physical properties of typical states in these ensembles; in particular here we focus on proxies of quantum entanglement as purity and α-Renyi entropies. The problem is formulated in terms of matrix elements of superoperators which depend on the graph structure, choice of probability measure over the local unitaries, and circuit length. In the α=2 case these superoperators act on a restricted multiqubit space generated by permutation operators associated to the subsets of vertices of the graph. For permutationally invariant interactions the dynamics can be further restricted to an exponentially smaller subspace. We consider different families of RQCs and study their typical entanglement properties for finite time as well as their asymptotic behavior. We find that area law holds in average and that the volume law is a typical property (that is, it holds in average and the fluctuations around the average are vanishing for the large system) of physical states. The area law arises when the evolution time is O(1) with respect to the size L of the system, while the volume law arises as is typical when the evolution time scales like O(L).

Elementary derivation of the quantum propagator for the harmonic oscillator

NASA Astrophysics Data System (ADS)

Shao, Jiushu

2016-10-01

Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.

Event Horizon Telescope observations as probes for quantum structure of astrophysical black holes

NASA Astrophysics Data System (ADS)

Giddings, Steven B.; Psaltis, Dimitrios

2018-04-01

The need for a consistent quantum evolution for black holes has led to proposals that their semiclassical description is modified not just near the singularity, but at horizon or larger scales. If such modifications extend beyond the horizon, they influence regions accessible to distant observation. Natural candidates for these modifications behave like metric fluctuations, with characteristic length scales and timescales set by the horizon radius. We investigate the possibility of using the Event Horizon Telescope to observe these effects, if they have a strength sufficient to make quantum evolution consistent with unitarity, without introducing new scales. We find that such quantum fluctuations can introduce a strong time dependence for the shape and size of the shadow that a black hole casts on its surrounding emission. For the black hole in the center of the Milky Way, detecting the rapid time variability of its shadow will require nonimaging timing techniques. However, for the much larger black hole in the center of the M87 galaxy, a variable black-hole shadow, if present with these parameters, would be readily observable in the individual snapshots that will be obtained by the Event Horizon Telescope.

Dynamical manifestations of quantum chaos: correlation hole and bulge

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; Santos, Lea F.

2017-10-01

A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and to a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. By contrast, the evolution of these quantities at shorter times reflects the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Error correction in short time steps during the application of quantum gates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castro, L.A. de, E-mail: leonardo.castro@usp.br; Napolitano, R.D.J.

2016-04-15

We propose a modification of the standard quantum error-correction method to enable the correction of errors that occur due to the interaction with a noisy environment during quantum gates without modifying the codification used for memory qubits. Using a perturbation treatment of the noise that allows us to separate it from the ideal evolution of the quantum gate, we demonstrate that in certain cases it is necessary to divide the logical operation in short time steps intercalated by correction procedures. A prescription of how these gates can be constructed is provided, as well as a proof that, even for themore » cases when the division of the quantum gate in short time steps is not necessary, this method may be advantageous for reducing the total duration of the computation.« less

Efficient solution of the Wigner-Liouville equation using a spectral decomposition of the force field

NASA Astrophysics Data System (ADS)

Van de Put, Maarten L.; Sorée, Bart; Magnus, Wim

2017-12-01

The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the spectral force Wigner-Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non-locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time-evolution of a one-dimensional resonant tunneling diode driven out of equilibrium.

Shortcuts to adiabaticity using flow fields

NASA Astrophysics Data System (ADS)

Patra, Ayoti; Jarzynski, Christopher

2017-12-01

A shortcut to adiabaticity is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a counterdiabatic (CD) Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a fast-forward (FF) potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from flow fields that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both CD Hamiltonians and FF potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the FF approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.

Examination of China’s performance and thematic evolution in quantum cryptography research using quantitative and computational techniques

PubMed Central

2018-01-01

This study performed two phases of analysis to shed light on the performance and thematic evolution of China’s quantum cryptography (QC) research. First, large-scale research publication metadata derived from QC research published from 2001–2017 was used to examine the research performance of China relative to that of global peers using established quantitative and qualitative measures. Second, this study identified the thematic evolution of China’s QC research using co-word cluster network analysis, a computational science mapping technique. The results from the first phase indicate that over the past 17 years, China’s performance has evolved dramatically, placing it in a leading position. Among the most significant findings is the exponential rate at which all of China’s performance indicators (i.e., Publication Frequency, citation score, H-index) are growing. China’s H-index (a normalized indicator) has surpassed all other countries’ over the last several years. The second phase of analysis shows how China’s main research focus has shifted among several QC themes, including quantum-key-distribution, photon-optical communication, network protocols, and quantum entanglement with an emphasis on applied research. Several themes were observed across time periods (e.g., photons, quantum-key-distribution, secret-messages, quantum-optics, quantum-signatures); some themes disappeared over time (e.g., computer-networks, attack-strategies, bell-state, polarization-state), while others emerged more recently (e.g., quantum-entanglement, decoy-state, unitary-operation). Findings from the first phase of analysis provide empirical evidence that China has emerged as the global driving force in QC. Considering China is the premier driving force in global QC research, findings from the second phase of analysis provide an understanding of China’s QC research themes, which can provide clarity into how QC technologies might take shape. QC and science and technology policy researchers can also use these findings to trace previous research directions and plan future lines of research. PMID:29385151

Examination of China's performance and thematic evolution in quantum cryptography research using quantitative and computational techniques.

PubMed

Olijnyk, Nicholas V

2018-01-01

This study performed two phases of analysis to shed light on the performance and thematic evolution of China's quantum cryptography (QC) research. First, large-scale research publication metadata derived from QC research published from 2001-2017 was used to examine the research performance of China relative to that of global peers using established quantitative and qualitative measures. Second, this study identified the thematic evolution of China's QC research using co-word cluster network analysis, a computational science mapping technique. The results from the first phase indicate that over the past 17 years, China's performance has evolved dramatically, placing it in a leading position. Among the most significant findings is the exponential rate at which all of China's performance indicators (i.e., Publication Frequency, citation score, H-index) are growing. China's H-index (a normalized indicator) has surpassed all other countries' over the last several years. The second phase of analysis shows how China's main research focus has shifted among several QC themes, including quantum-key-distribution, photon-optical communication, network protocols, and quantum entanglement with an emphasis on applied research. Several themes were observed across time periods (e.g., photons, quantum-key-distribution, secret-messages, quantum-optics, quantum-signatures); some themes disappeared over time (e.g., computer-networks, attack-strategies, bell-state, polarization-state), while others emerged more recently (e.g., quantum-entanglement, decoy-state, unitary-operation). Findings from the first phase of analysis provide empirical evidence that China has emerged as the global driving force in QC. Considering China is the premier driving force in global QC research, findings from the second phase of analysis provide an understanding of China's QC research themes, which can provide clarity into how QC technologies might take shape. QC and science and technology policy researchers can also use these findings to trace previous research directions and plan future lines of research.

Cosmological evolution of the Higgs boson's vacuum expectation value

NASA Astrophysics Data System (ADS)

Calmet, Xavier

2017-11-01

We point out that the expansion of the universe leads to a cosmological time evolution of the vacuum expectation of the Higgs boson. Within the standard model of particle physics, the cosmological time evolution of the vacuum expectation of the Higgs leads to a cosmological time evolution of the masses of the fermions and of the electroweak gauge bosons, while the scale of Quantum Chromodynamics (QCD) remains constant. Precise measurements of the cosmological time evolution of μ =m_e/m_p, where m_e and m_p are, respectively, the electron and proton mass (which is essentially determined by the QCD scale), therefore provide a test of the standard models of particle physics and of cosmology. This ratio can be measured using modern atomic clocks.

Effects of Shannon entropy and electric field on polaron in RbCl triangular quantum dot

NASA Astrophysics Data System (ADS)

M, Tiotsop; A, J. Fotue; S, C. Kenfack; N, Issofa; H, Fotsin; L, C. Fai

2016-04-01

In this paper, the time evolution of the quantum mechanical state of a polaron is examined using the Pekar type variational method on the condition of the electric-LO-phonon strong-coupling and polar angle in RbCl triangular quantum dot. We obtain the eigenenergies, and the eigenfunctions of the ground state, and the first excited state respectively. This system in a quantum dot can be treated as a two-level quantum system qubit and the numerical calculations are performed. The effects of Shannon entropy and electric field on the polaron in the RbCl triangular quantum dot are also studied.

Wigner flow reveals topological order in quantum phase space dynamics.

PubMed

Steuernagel, Ole; Kakofengitis, Dimitris; Ritter, Georg

2013-01-18

The behavior of classical mechanical systems is characterized by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.

Thermodynamic output of single-atom quantum optical amplifiers and their phase-space fingerprint

NASA Astrophysics Data System (ADS)

Perl, Y.; Band, Y. B.; Boukobza, E.

2017-05-01

We analyze a resonant single-atom two-photon quantum optical amplifier both dynamically and thermodynamically. A detailed thermodynamic analysis shows that the nonlinear amplifier is thermodynamically equivalent to the linear amplifier. However, by calculating the Wigner quasiprobability distribution for various initial field states, we show that unique quantum features in optical phase space, absent in the linear amplifier, are retained for extended times, despite the fact that dissipation tends to wash out dynamical features observed at early evolution times. These features are related to the discrete nature of the two-photon matter-field interaction and fingerprint the initial field state at thermodynamic times.

Quantum Jarzynski equality of measurement-based work extraction

NASA Astrophysics Data System (ADS)

Morikuni, Yohei; Tajima, Hiroyasu; Hatano, Naomichi

2017-03-01

Many studies of quantum-size heat engines assume that the dynamics of an internal system is unitary and that the extracted work is equal to the energy loss of the internal system. Both assumptions, however, should be under scrutiny. In the present paper, we analyze quantum-scale heat engines, employing the measurement-based formulation of the work extraction recently introduced by Hayashi and Tajima [M. Hayashi and H. Tajima, arXiv:1504.06150]. We first demonstrate the inappropriateness of the unitary time evolution of the internal system (namely, the first assumption above) using a simple two-level system; we show that the variance of the energy transferred to an external system diverges when the dynamics of the internal system is approximated to a unitary time evolution. Second, we derive the quantum Jarzynski equality based on the formulation of Hayashi and Tajima as a relation for the work measured by an external macroscopic apparatus. The right-hand side of the equality reduces to unity for "natural" cyclic processes but fluctuates wildly for noncyclic ones, exceeding unity often. This fluctuation should be detectable in experiments and provide evidence for the present formulation.

Thermalization of topological entropy after a quantum quench

NASA Astrophysics Data System (ADS)

Zeng, Yu; Hamma, Alioscia; Fan, Heng

2016-09-01

Topologically ordered quantum phases are robust in the sense that perturbations in the Hamiltonian of the system will not change the topological nature of the ground-state wave function. However, in order to exploit topological order for applications such as self-correcting quantum memories and information processing, these states need to be also robust both dynamically and at finite temperature in the presence of an environment. It is well known that systems like the toric code in two spatial dimensions are fragile in temperature. In this paper, we show a completely analytic treatment of the toric code away from equilibrium, after a quantum quench of the system Hamiltonian. We show that, despite being subject to unitary evolution (and at zero temperature), the long-time behavior of the topological entropy is thermal, therefore vanishing. If the quench preserves a local gauge structure, there is a residual long-lived topological entropy. This also is the thermal behavior in presence of such gauge constraints. The result is obtained by studying the time evolution of the topological 2-Rényi entropy in a fully analytical, exact way.

Quantum Jarzynski equality of measurement-based work extraction.

PubMed

Morikuni, Yohei; Tajima, Hiroyasu; Hatano, Naomichi

2017-03-01

Many studies of quantum-size heat engines assume that the dynamics of an internal system is unitary and that the extracted work is equal to the energy loss of the internal system. Both assumptions, however, should be under scrutiny. In the present paper, we analyze quantum-scale heat engines, employing the measurement-based formulation of the work extraction recently introduced by Hayashi and Tajima [M. Hayashi and H. Tajima, arXiv:1504.06150]. We first demonstrate the inappropriateness of the unitary time evolution of the internal system (namely, the first assumption above) using a simple two-level system; we show that the variance of the energy transferred to an external system diverges when the dynamics of the internal system is approximated to a unitary time evolution. Second, we derive the quantum Jarzynski equality based on the formulation of Hayashi and Tajima as a relation for the work measured by an external macroscopic apparatus. The right-hand side of the equality reduces to unity for "natural" cyclic processes but fluctuates wildly for noncyclic ones, exceeding unity often. This fluctuation should be detectable in experiments and provide evidence for the present formulation.

Decoherence in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Albash, Tameem; Lidar, Daniel A.

2015-06-01

Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master-equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed-system setting, remain beneficial in the open-system setting. To address the high computational cost of master-equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.

Controlled ultrafast transfer and stability degree of generalized coherent states of a kicked two-level ion

NASA Astrophysics Data System (ADS)

Chen, Hao; Kong, Chao; Hai, Wenhua

2018-06-01

We investigate quantum dynamics of a two-level ion trapped in the Lamb-Dicke regime of a δ -kicked optical lattice, based on the exact generalized coherent states rotated by a π / 2 pulse of Ramsey type experiment. The spatiotemporal evolutions of the spin-motion entangled states in different parameter regions are illustrated, and the parameter regions of different degrees of quantum stability described by the quantum fidelity are found. Time evolutions of the probability for the ion being in different pseudospin states reveal that the ultrafast entanglement generation and population transfers of the system can be analytically controlled by managing the laser pulses. The probability in an initially disentangled state shows periodic collapses (entanglement) and revivals (de-entanglement). Reduction of the stability degree results in enlarging the period of de-entanglement, while the instability and potential chaos will cause the sustained entanglement. The results could be justified experimentally in the existing setups and may be useful in engineering quantum dynamics for quantum information processing.

Quantum and classical dissipation of charged particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.

2013-08-15

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle.more » •Classical and quantum dynamics of a damped electric charge.« less

Entanglement negativity after a local quantum quench in conformal field theories

NASA Astrophysics Data System (ADS)

Wen, Xueda; Chang, Po-Yao; Ryu, Shinsei

2015-08-01

We study the time evolution of the entanglement negativity after a local quantum quench in (1 + 1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their end points. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a light-cone behavior is observed in the negativity evolution; in addition, a long-range entanglement, which is independent of the distance between two intervals, can be created. Our results agree with the heuristic picture that quasiparticles, which carry entanglement, are emitted from the joining point and propagate freely through the system. Our analytical results are confirmed by numerical calculations based on a critical harmonic chain.

Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory

NASA Astrophysics Data System (ADS)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-04-01

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.

Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory.

PubMed

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-04-13

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.

Multiple exciton generation for photoelectrochemical hydrogen evolution reactions with quantum yields exceeding 100%

DOE PAGES

Yan, Yong; Crisp, Ryan W.; Gu, Jing; ...

2017-04-03

Multiple exciton generation (MEG) in quantum dots (QDs) has the potential to greatly increase the power conversion efficiency in solar cells and in solar-fuel production. During the MEG process, two electron-hole pairs (excitons) are created from the absorption of one high-energy photon, bypassing hot-carrier cooling via phonon emission. Here we demonstrate that extra carriers produced via MEG can be used to drive a chemical reaction with quantum efficiency above 100%. We developed a lead sulfide (PbS) QD photoelectrochemical cell that is able to drive hydrogen evolution from aqueous Na 2S solution with a peak external quantum efficiency exceeding 100%. QDmore » photoelectrodes that were measured all demonstrated MEG when the incident photon energy was larger than 2.7 times the bandgap energy. Finally, our results demonstrate a new direction in exploring high-efficiency approaches to solar fuels.« less

Time-dependent generalized Gibbs ensembles in open quantum systems

NASA Astrophysics Data System (ADS)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

Time dependent Schrödinger equation for black hole evaporation: No information loss

NASA Astrophysics Data System (ADS)

Corda, Christian

2015-02-01

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state".1 In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

PubMed

Gosset, David; Terhal, Barbara M; Vershynina, Anna

2015-04-10

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

NASA Astrophysics Data System (ADS)

Gosset, David; Terhal, Barbara M.; Vershynina, Anna

2015-04-01

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic X X Z chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q -deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Double-time correlation functions of two quantum operations in open systems

NASA Astrophysics Data System (ADS)

Ban, Masashi

2017-10-01

A double-time correlation function of arbitrary two quantum operations is studied for a nonstationary open quantum system which is in contact with a thermal reservoir. It includes a usual correlation function, a linear response function, and a weak value of an observable. Time evolution of the correlation function can be derived by means of the time-convolution and time-convolutionless projection operator techniques. For this purpose, a quasidensity operator accompanied by a fictitious field is introduced, which makes it possible to derive explicit formulas for calculating a double-time correlation function in the second-order approximation with respect to a system-reservoir interaction. The derived formula explicitly shows that the quantum regression theorem for calculating the double-time correlation function cannot be used if a thermal reservoir has a finite correlation time. Furthermore, the formula is applied for a pure dephasing process and a linear dissipative process. The quantum regression theorem and the the Leggett-Garg inequality are investigated for an open two-level system. The results are compared with those obtained by exact calculation to examine whether the formula is a good approximation.

Effective equations for the quantum pendulum from momentous quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120

In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

Time evolution and dynamical phase transitions at a critical time in a system of one-dimensional bosons after a quantum quench.

PubMed

Mitra, Aditi

2012-12-28

A renormalization group approach is used to show that a one-dimensional system of bosons subject to a lattice quench exhibits a finite-time dynamical phase transition where an order parameter within a light cone increases as a nonanalytic function of time after a critical time. Such a transition is also found for a simultaneous lattice and interaction quench where the effective scaling dimension of the lattice becomes time dependent, crucially affecting the time evolution of the system. Explicit results are presented for the time evolution of the boson interaction parameter and the order parameter for the dynamical transition as well as for more general quenches.

On a quantum mechanical system theory of the origin of life: from the Stapp-model to the origin of natural symbols

NASA Astrophysics Data System (ADS)

Balázs, András

2016-01-01

The Heisenberg-James-Stapp (quantum mechanical) mind model is surveyed and criticized briefly. The criticism points out that the model, while being essentially consistent concerning (human) consciousness, fundamentally lacks the evolutional point of view both onto- and phylogenetically. Ethology and other than Jamesian psychology is quoted and a quantum mechanical theoretical scheme is suggested to essentially extend Stapp's frame in an evolutionary context. It is proposed that its central supposition, spontaneous quantum measurement can be better utilized in an investigation of the origin of the "subjective" process, having come about concomitantly with the chemistry of the origin of life. We dwell on its applicability at this latter process, at its heart standing, it is supposed, the endophysical nonlinear "self-measurement" of (quantum mechanically describable) matter, and so our investigation is extended to this primeval phenomenon. It is suggested that the life phenomenon is an indirect C* → (W*) → C* quantum algebraic process transition, where the (W*) system would represent the living state. Summarized also are our previous results on an internalized, "reversed", time process, introduced originally by Gunji, which is subordinated to the external "forwards" time evolution, driving towards symmetry by gradual space-mappings, where the original splitting-up must have come about in a spontaneous symmetry breaking nonlinear "self-measurement" of matter in an endophysical World.

Overcoming Misconceptions in Quantum Mechanics with the Time Evolution Operator

ERIC Educational Resources Information Center

Quijas, P. C. Garcia; Aguilar, L. M. Arevalo

2007-01-01

Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary…

Quantum corrections of the truncated Wigner approximation applied to an exciton transport model.

PubMed

Ivanov, Anton; Breuer, Heinz-Peter

2017-04-01

We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time evolution of the system observables is obtained by calculating the average of a stochastic difference equation which is weighted with a product of pseudoprobability density functions. From the exact equation of motion one can clearly identify the terms that are also present if we apply the truncated Wigner approximation. This description of the problem is used as a basis for the derivation of a new approximation, whose validity goes beyond the truncated Wigner approximation. To demonstrate this we apply the formalism to a donor-acceptor transport model.

Disentanglement versus decoherence of two qubits in thermal noise.

PubMed

Zampetaki, A V; Diakonos, F K

2012-08-31

We show that the influence of thermal noise, simulated by a 2D ferromagnetic Ising spin lattice on a pair of noninteracting, initially entangled qubits, represented by quantum spins, leads to unexpected evolution of quantum correlations. The high temperature noise leads to ultraslow decay of the quantum correlations. Decreasing the noise temperature we observe a decrease of the characteristic decay time scale. When the noise originates from a critical state, a revival of the quantum correlations is observed. This revival becomes oscillatory with a slowly decaying amplitude when the temperature is decreased below the critical region, leading to persistence of the quantum correlations.

Direct detection of time-resolved Rabi oscillations in a single quantum dot via resonance fluorescence

NASA Astrophysics Data System (ADS)

Schaibley, J. R.; Burgers, A. P.; McCracken, G. A.; Steel, D. G.; Bracker, A. S.; Gammon, D.; Sham, L. J.

2013-03-01

Optical Rabi oscillations are coherent population oscillations of a two-level system coupled by an electric dipole transition when driven by a strong nearly resonant optical field. In quantum dot structures, these measurements have typically been performed as a function of the total pulse area ∫Ω0(t)dt where the pulse area varies as a function of Rabi frequency. Here, we report direct detection of the time-resolved coherent transient response of the resonance fluorescence to measure the time evolution of the optical Rabi oscillations in a single charged InAs quantum dot. We extract a decoherence rate consistent with the limit from the excited state lifetime.

H-theorem and Maxwell demon in quantum physics

NASA Astrophysics Data System (ADS)

Kirsanov, N. S.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.; Blatter, G.; Lesovik, G. B.

2018-02-01

The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.

Investigations of the Quantum Correlation in Two-Qubit Heisenberg XYZ Model with Decoherence

NASA Astrophysics Data System (ADS)

Guo-Hui, Yang

2017-03-01

Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated with the use of concurrence C and quantum discord (QD). With the Werner state as the initial state, we discuss the influence of mixture degree r on the dynamics. There are some difference between the time evolution behaviors of these two correlation measures with different value of r. For 0 ≤ r ≤ 1/3, there exists quantum discord but no entanglement; For 1/3< r<1, there is a "entanglement sudden death and birth" phenomenon in the concurrence but not in the QD; For r=1, there is one interesting thing that the concurrence decays from 1 to a minimum value close to 0 but the QD vanish. In addition, we have investigated the influence of different parameters on the two correlation measures. It has been found that, the concurrence and QD both exhibit osillatory behaviors with the time evolution, which is independent on the magnetic field B and the coupling coefficient J z . However, the Dzyaloshinskii-Moriya interaction (D) and coupling coefficient J have strong influence on concurrence and QD. With the increasing of the D or J, the frequency of the oscillation getting larger. When time is fixed, with the increasing of D or J, the concurrence and QD change periodically.

Topology of quantum discord

NASA Astrophysics Data System (ADS)

Nguyen, Nga T. T.; Joynt, Robert

2017-04-01

Quantum discord is an important measure of quantum correlations that can serve as a resource for certain types of quantum information processing. Like entanglement, discord is subject to destruction by external noise. The routes by which this destruction can take place depends on the shape of the hypersurface of zero discord C in the space of generalized Bloch vectors. For 2 qubits, we show that with a few points subtracted, this hypersurface is a simply-connected 9-dimensional manifold embedded in a 15-dimensional background space. We do this by constructing an explicit homeomorphism from a known manifold to the subtracted version of C . We also construct a coordinate map on C that can be used for integration or other purposes. This topological characterization of C has important implications for the classification of the possible time evolutions of discord in physical models. The classification for discord contrasts sharply with the possible evolutions of entanglement. We classify the possible joint evolutions of entanglement and discord. There are 9 allowed categories: 6 categories for a Markovian process and 3 categories for a non-Markovian process, respectively. We illustrate these conclusions with an anisotropic XY spin model. All 9 categories can be obtained by adjusting parameters in this model.

Self-Organized Critical Behavior:. the Evolution of Frozen Spin Networks Model in Quantum Gravity

NASA Astrophysics Data System (ADS)

Chen, Jian-Zhen; Zhu, Jian-Yang

In quantum gravity, we study the evolution of a two-dimensional planar open frozen spin network, in which the color (i.e. the twice spin of an edge) labeling edge changes but the underlying graph remains fixed. The mainly considered evolution rule, the random edge model, is depending on choosing an edge randomly and changing the color of it by an even integer. Since the change of color generally violate the gauge invariance conditions imposed on the system, detailed propagation rule is needed and it can be defined in many ways. Here, we provided one new propagation rule, in which the involved even integer is not a constant one as in previous works, but changeable with certain probability. In random edge model, we do find the evolution of the system under the propagation rule exhibits power-law behavior, which is suggestive of the self-organized criticality (SOC), and it is the first time to verify the SOC behavior in such evolution model for the frozen spin network. Furthermore, the increase of the average color of the spin network in time can show the nature of inflation for the universe.

Quantum Darwinism for mixed-state environment

NASA Astrophysics Data System (ADS)

Quan, Haitao; Zwolak, Michael; Zurek, Wojciech

2009-03-01

We exam quantum darwinism when a system is in the presence of a mixed environment, and we find a general relation between the mutual information for the mixed-state environment and the change of the entropy of the fraction of the environment. We then look at a particular solvable model, and we numerically exam the time evolution of the ``mutual information" for large environment. Finally we discuss about the exact expressions for all entropies and the mutual information at special time.

Classical and quantum dynamics of a kicked relativistic particle in a box

NASA Astrophysics Data System (ADS)

Yusupov, J. R.; Otajanov, D. M.; Eshniyazov, V. E.; Matrasulov, D. U.

2018-03-01

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

Quantum interference of position and momentum: A particle propagation paradox

NASA Astrophysics Data System (ADS)

Hofmann, Holger F.

2017-08-01

Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time t . Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantum mechanics changes the laws of motion at a fundamental level, providing a different perspective on causality relations and time evolution in quantum mechanics.

Integrating machine learning to achieve an automatic parameter prediction for practical continuous-variable quantum key distribution

NASA Astrophysics Data System (ADS)

Liu, Weiqi; Huang, Peng; Peng, Jinye; Fan, Jianping; Zeng, Guihua

2018-02-01

For supporting practical quantum key distribution (QKD), it is critical to stabilize the physical parameters of signals, e.g., the intensity, phase, and polarization of the laser signals, so that such QKD systems can achieve better performance and practical security. In this paper, an approach is developed by integrating a support vector regression (SVR) model to optimize the performance and practical security of the QKD system. First, a SVR model is learned to precisely predict the time-along evolutions of the physical parameters of signals. Second, such predicted time-along evolutions are employed as feedback to control the QKD system for achieving the optimal performance and practical security. Finally, our proposed approach is exemplified by using the intensity evolution of laser light and a local oscillator pulse in the Gaussian modulated coherent state QKD system. Our experimental results have demonstrated three significant benefits of our SVR-based approach: (1) it can allow the QKD system to achieve optimal performance and practical security, (2) it does not require any additional resources and any real-time monitoring module to support automatic prediction of the time-along evolutions of the physical parameters of signals, and (3) it is applicable to any measurable physical parameter of signals in the practical QKD system.

Quantum power functional theory for many-body dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt, Matthias, E-mail: Matthias.Schmidt@uni-bayreuth.de

2015-11-07

We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems.

Secret loss of unitarity due to the classical background

NASA Astrophysics Data System (ADS)

Yang, I.-Sheng

2017-07-01

We show that a quantum subsystem can become significantly entangled with a classical background through a process with few or no semiclassical backreactions. We study two quantum harmonic oscillators coupled to each other in a time-independent Hamiltonian. We compare it to its semiclassical approximation in which one of the oscillators is treated as the classical background. In this approximation, the remaining quantum oscillator has an effective Hamiltonian which is time-dependent, and its evolution appears to be unitary. However, in the fully quantum model, the two oscillators can entangle each other. Thus, the unitarity of either individual oscillator is never guaranteed. We derive the critical time scale after which the unitarity of either individual oscillator is irrevocably lost. In particular, we give an example that in the adiabatic limit, unitarity is lost before other relevant questions can be addressed.

Geometry of Quantum Computation with Qudits

PubMed Central

Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-01-01

The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710

Dirac Cellular Automaton from Split-step Quantum Walk

PubMed Central

Mallick, Arindam; Chandrashekar, C. M.

2016-01-01

Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory. PMID:27184159

Continuous time quantum random walks in free space

NASA Astrophysics Data System (ADS)

Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander

2014-05-01

We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.

Weak Measurement and Quantum Smoothing of a Superconducting Qubit

NASA Astrophysics Data System (ADS)

Tan, Dian

In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix rho(t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix rho(t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [rho(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix rho(t) with only diagonal elements in a given basis |n〉 may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal rho(t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.

No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox

NASA Astrophysics Data System (ADS)

Perez, Alejandro

2015-04-01

In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation can be described by a unitary evolution without the problems encountered by the standard remnant scenario or the schemes where information is assumed to come out with the radiation during evaporation (firewalls and complementarity). The final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler), which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.

Experimental investigation of measurement-induced disturbance and time symmetry in quantum physics

NASA Astrophysics Data System (ADS)

Curic, D.; Richardson, M. C.; Thekkadath, G. S.; Flórez, J.; Giner, L.; Lundeen, J. S.

2018-04-01

Unlike regular time evolution governed by the Schrödinger equation, standard quantum measurement appears to violate time-reversal symmetry. Measurement creates random disturbances (e.g., collapse) that prevent back-tracing the quantum state of the system. The effect of these disturbances is explicit in the results of subsequent measurements. In this way, the joint result of sequences of measurements depends on the order in time in which those measurements are performed. One might expect that if the disturbance could be eliminated this time-ordering dependence would vanish. Following a recent theoretical proposal [Bednorz, Franke, and Belzig, New J. Phys. 15, 023043 (2013), 10.1088/1367-2630/15/2/023043], we experimentally investigate this dependence for a kind of measurement that creates an arbitrarily small disturbance: weak measurement. We perform various sequences of a set of polarization weak measurements on photons. We experimentally demonstrate that, although the weak measurements are minimally disturbing, their time ordering affects the outcome of the measurement sequence for quantum systems.

Quantum Tic-Tac-Toe as Metaphor for Quantum Physics

NASA Astrophysics Data System (ADS)

Goff, Allan; Lehmann, Dale; Siegel, Joel

2004-02-01

Quantum Tic-Tac-Toe is presented as an abstract quantum system derived from the rules of Classical Tic-Tac-Toe. Abstract quantum systems can be constructed from classical systems by the addition of three types of rules; rules of Superposition, rules of Entanglement, and rules of Collapse. This is formally done for Quantum Tic-Tac-Toe. As a part of this construction it is shown that abstract quantum systems can be viewed as an ensemble of classical systems. That is, the state of a quantum game implies a set of simultaneous classical games. The number and evolution of the ensemble of classical games is driven by the superposition, entanglement, and collapse rules. Various aspects and play situations provide excellent metaphors for standard features of quantum mechanics. Several of the more significant metaphors are discussed, including a measurement mechanism, the correspondence principle, Everett's Many Worlds Hypothesis, an ascertainity principle, and spooky action at a distance. Abstract quantum systems also show the consistency of backwards-in-time causality, and the influence on the present of both pasts and futures that never happened. The strongest logical argument against faster-than-light (FTL) phenomena is that since FTL implies backwards-in-time causality, temporal paradox is an unavoidable consequence of FTL; hence FTL is impossible. Since abstract quantum systems support backwards-in-time causality but avoid temporal paradox through pruning of the classical ensemble, it may be that quantum based FTL schemes are possible allowing backwards-in-time causality, but prohibiting temporal paradox.

Path-sum solution of the Weyl quantum walk in 3 + 1 dimensions

NASA Astrophysics Data System (ADS)

D'Ariano, G. M.; Mosco, N.; Perinotti, P.; Tosini, A.

2017-10-01

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group , which in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i.e. transition amplitude from a node of the graph to another node in a finite number of steps. The quantum nature of the walk manifests itself in the interference of the paths on the graph joining the given nodes. The solution is based on the binary encoding of the admissible paths on the graph and on the semigroup structure of the walk transition matrices. This article is part of the themed issue `Second quantum revolution: foundational questions'.

A scalable quantum computer with ions in an array of microtraps

PubMed

Cirac; Zoller

2000-04-06

Quantum computers require the storage of quantum information in a set of two-level systems (called qubits), the processing of this information using quantum gates and a means of final readout. So far, only a few systems have been identified as potentially viable quantum computer models--accurate quantum control of the coherent evolution is required in order to realize gate operations, while at the same time decoherence must be avoided. Examples include quantum optical systems (such as those utilizing trapped ions or neutral atoms, cavity quantum electrodynamics and nuclear magnetic resonance) and solid state systems (using nuclear spins, quantum dots and Josephson junctions). The most advanced candidates are the quantum optical and nuclear magnetic resonance systems, and we expect that they will allow quantum computing with about ten qubits within the next few years. This is still far from the numbers required for useful applications: for example, the factorization of a 200-digit number requires about 3,500 qubits, rising to 100,000 if error correction is implemented. Scalability of proposed quantum computer architectures to many qubits is thus of central importance. Here we propose a model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times).

On the Origin of Quantum Diffusion Coefficient and Quantum Potential

NASA Astrophysics Data System (ADS)

Gupta, Aseem

2016-03-01

Synchronizability of space and time experiences between different inhabitants of a spacetime is abstracted as a fundamental premise of Classical physics. Absence thereof i.e. desynchronization between space and time experiences of a system under study and the observer is then studied for a single dimension single particle system. Desynchronization fundamentally makes probability concepts enter physics ab-initio and not as secondary tools to deal with situations wherein incomplete information in situation following perfectly deterministic dynamics demands its introduction. Desynchronization model based on Poisson distribution of events vis-à-vis an observer, leads to expectation of particle's motion as a Brownian motion deriving Nelson's quantum diffusion coefficient naturally, without needing to postulate it. This model also incorporates physical effects akin to those of Bohm's Quantum Potential, again without needing any sub-quantum medium. Schrodinger's equation is shown to be derivable incorporating desynchronization only of space while Quantum Field Theory is shown to model desynchronization of time as well. Fundamental suggestion of the study is that it is desynchronization that is at the root of quantum phenomena rather than sub-micro scales of spacetime. Absence of possibility of synchronization between system's space and time and those of observer is studied. Mathematical modeling of desynchronized evolution explains some intriguing aspects of Quantum Mechanical theory.

Experimental investigation of different regimes of mode-locking in a high repetition rate passively mode-locked semiconductor quantum-dot laser.

PubMed

Kéfélian, Fabien; O'Donoghue, Shane; Todaro, Maria Teresa; McInerney, John; Huyet, Guillaume

2009-04-13

We report experimental investigations on a two-section 16-GHz repetition rate InAs/GaAs quantum dot passively mode-locked laser. Near the threshold current, pseudo-periodic Q-switching with complex dynamics is exhibited. Mode-locking operation regimes characterized by different repetition rates and timing jitter levels are encountered up to twice the threshold current. Evolution of the RF spectrum and optical spectrum with current is compared. The different mode-locked regimes are shown to be associated with different spectral and temporal shapes, ranging from 1.3 to 6 ps. This point is discussed by introducing the existence of two different supermodes. Repetition rate evolution and timing jitter increase is attributed to the coupling between the dominant and the secondary supermodes.

Feynman propagator for spin foam quantum gravity.

PubMed

Oriti, Daniele

2005-03-25

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".

Josephson junction in the quantum mesoscopic electric circuits with charge discreteness

NASA Astrophysics Data System (ADS)

Pahlavani, H.

2018-04-01

A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.

Quantum Simulation of Tunneling in Small Systems

PubMed Central

Sornborger, Andrew T.

2012-01-01

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures. PMID:22916333

Heat-machine control by quantum-state preparation: from quantum engines to refrigerators.

PubMed

Gelbwaser-Klimovsky, D; Kurizki, G

2014-08-01

We explore the dependence of the performance bounds of heat engines and refrigerators on the initial quantum state and the subsequent evolution of their piston, modeled by a quantized harmonic oscillator. Our goal is to provide a fully quantized treatment of self-contained (autonomous) heat machines, as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath and parametrically driven by a classical time-dependent piston or field. Here, by contrast, there is no external time-dependent driving. Instead, the evolution is caused by the stationary simultaneous interaction of two heat baths (having distinct spectra and temperatures) with a single two-level system that is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum-optical amplifier and dissipation theory, particularly, by the analysis of amplified or dissipated phase-plane quasiprobability distributions. Our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle, or control, on the efficiency of the heat machine. In particular, a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the Carnot bound in the linear amplification regime. In the refrigeration regime, the coefficient of performance can transgress the Carnot bound if the piston is initialized in a Fock state. The piston may be realized by a vibrational mode, as in nanomechanical setups, or an electromagnetic field mode, as in cavity-based scenarios.

Heat-machine control by quantum-state preparation: From quantum engines to refrigerators

NASA Astrophysics Data System (ADS)

Gelbwaser-Klimovsky, D.; Kurizki, G.

2014-08-01

We explore the dependence of the performance bounds of heat engines and refrigerators on the initial quantum state and the subsequent evolution of their piston, modeled by a quantized harmonic oscillator. Our goal is to provide a fully quantized treatment of self-contained (autonomous) heat machines, as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath and parametrically driven by a classical time-dependent piston or field. Here, by contrast, there is no external time-dependent driving. Instead, the evolution is caused by the stationary simultaneous interaction of two heat baths (having distinct spectra and temperatures) with a single two-level system that is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum-optical amplifier and dissipation theory, particularly, by the analysis of amplified or dissipated phase-plane quasiprobability distributions. Our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle, or control, on the efficiency of the heat machine. In particular, a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the Carnot bound in the linear amplification regime. In the refrigeration regime, the coefficient of performance can transgress the Carnot bound if the piston is initialized in a Fock state. The piston may be realized by a vibrational mode, as in nanomechanical setups, or an electromagnetic field mode, as in cavity-based scenarios.

A NEW QUANTUM MECHANICAL THEORY OF EVOLUTION OF UNIVERSE AND LIFE

PubMed Central

Nigam, M C

1990-01-01

Based upon the principles of ancient science of Life, which admits both consciousness and matter, a new Quantum Mechanical theory of evolution of universe and life is propounded. The theory advocates: Right from the time, the evolution of universe takes place, life also starts evolving energies and ethereal – consciousness (subtler and real) in anti-electrons, as the complimentary partners. The material body acquires electrons for cordoning of atomic nuclei and displaying its manifestation, in the three spatial dimensions in scale of time. The ethereal consciousness acquires anti electrons for gaining necessary energy for superimposing itself over any of the manifested bodies of equivalent electronic energy and deriving the bliss of materialization. The theory is based upon the solid foundation of the ancient science (ethereal consciousness) laid down by the ancient seekers of knowledge like Kapila and Caraka who interpret many of the riddles of modern science on the frontiers of various disciplines of knowledge. PMID:22556513

Landau-Zener-Stückelberg-Majorana interference in a 3D transmon driven by a chirped microwave

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gong, Ming; Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045; Zhou, Yu

2016-03-14

By driving a 3D transmon with microwave fields, we generate an effective avoided energy-level crossing. Then we chirp microwave frequency, which is equivalent to driving the system through the avoided energy-level crossing by sweeping the avoided crossing. A double-passage chirp produces Landau-Zener-Stückelberg-Majorana (LZSM) interference that agree well with the numerical results, especially with the initial state being an eigen-energy state in the center of an avoided level crossing. A time-resolved state tomography measurement is performed in the evolution of LZSM interference, showing an experimental evidence for the dynamical evolution of quantum state. Our method is fully applicable to other quantummore » systems that contain no intrinsic avoided level crossing, providing an alternative approach for quantum control and quantum simulation.« less

Quantum reversibility is relative, or does a quantum measurement reset initial conditions?

PubMed

Zurek, Wojciech H

2018-07-13

I compare the role of the information in classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer's retention of the information about the measurement outcome. By contrast-even though quantum dynamics is unitary, hence, reversible-reversing quantum evolution that led to a measurement becomes, in principle, impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss-rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer's (branch of) the Universe. Nevertheless, I also show that the observer's friend-an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result-can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Partition-based discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Konno, Norio; Portugal, Renato; Sato, Iwao; Segawa, Etsuo

2018-04-01

We introduce a family of discrete-time quantum walks, called two-partition model, based on two equivalence-class partitions of the computational basis, which establish the notion of local dynamics. This family encompasses most versions of unitary discrete-time quantum walks driven by two local operators studied in literature, such as the coined model, Szegedy's model, and the 2-tessellable staggered model. We also analyze the connection of those models with the two-step coined model, which is driven by the square of the evolution operator of the standard discrete-time coined walk. We prove formally that the two-step coined model, an extension of Szegedy model for multigraphs, and the two-tessellable staggered model are unitarily equivalent. Then, selecting one specific model among those families is a matter of taste not generality.

1−1=Counterfactual: on the potency and significance of quantum non-events

PubMed Central

Cohen, E.

2016-01-01

We study the unique role played in quantum mechanics by non-events or ‘counterfactuals’. Our earlier analysis of ‘quantum oblivion’ has revealed some subtle stages in the measurement process, which may end up in self-cancellation. To these findings, we now add two insights derived by two time-symmetric interpretations of quantum mechanics. (i) Like all quantum interactions, the non-event is formed by the conjunction of forward-plus-backward-evolving wave functions. (ii) Then, it is another feature of such dual evolutions, namely the involvement of negative masses and energies, that enables Nature to make some events ‘unhappen’ while leaving causal traces. PMID:27091159

1-1=Counterfactual: on the potency and significance of quantum non-events.

PubMed

Elitzur, A C; Cohen, E

2016-05-28

We study the unique role played in quantum mechanics by non-events or 'counterfactuals'. Our earlier analysis of 'quantum oblivion' has revealed some subtle stages in the measurement process, which may end up in self-cancellation. To these findings, we now add two insights derived by two time-symmetric interpretations of quantum mechanics. (i) Like all quantum interactions, the non-event is formed by the conjunction of forward-plus-backward-evolving wave functions. (ii) Then, it is another feature of such dual evolutions, namely the involvement of negative masses and energies, that enables Nature to make some events 'unhappen' while leaving causal traces. © 2016 The Author(s).

Hybrid Semiclassical Theory of Quantum Quenches in One-Dimensional Systems

NASA Astrophysics Data System (ADS)

Moca, Cǎtǎlin Paşcu; Kormos, Márton; Zaránd, Gergely

2017-09-01

We develop a hybrid semiclassical method to study the time evolution of one-dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time-evolving block decimation method while treating orbital quasiparticle motion classically. We can follow dynamics up to time scales well beyond the reach of standard numerical methods to observe the crossover between preequilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel-coupled one-dimensional Bose condensates. We demonstrate the emergence of soliton-collision-induced phase propagation, soliton-entropy production, and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.

Vibrational Schroedinger Cats

NASA Technical Reports Server (NTRS)

Kis, Z.; Janszky, J.; Vinogradov, An. V.; Kobayashi, T.

1996-01-01

The optical Schroedinger cat states are simple realizations of quantum states having nonclassical features. It is shown that vibrational analogues of such states can be realized in an experiment of double pulse excitation of vibrionic transitions. To track the evolution of the vibrational wave packet we derive a non-unitary time evolution operator so that calculations are made in a quasi Heisenberg picture.

Entropy for quantum pure states and quantum H theorem

NASA Astrophysics Data System (ADS)

Han, Xizhi; Wu, Biao

2015-06-01

We construct a complete set of Wannier functions that are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long-time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the quantum H theorem proved by von Neumann [Zeitschrift für Physik 57, 30 (1929), 10.1007/BF01339852]. Our entropy is different from the standard von Neumann entropy, which is always zero for quantum pure states. According to our definition, a system always has bigger entropy than its subsystem even when the system is described by a pure state. As the construction of the Wannier basis can be implemented numerically, the dynamical evolution of our entropy is illustrated with an example.

Accuracy of the adiabatic-impulse approximation for closed and open quantum systems

NASA Astrophysics Data System (ADS)

Tomka, Michael; Campos Venuti, Lorenzo; Zanardi, Paolo

2018-03-01

We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states when driven through a region of small gap. Such small-gap regions are a common situation in adiabatic quantum computing and having reliable approximations is important in this context. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead, here we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times or fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times or slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counterintuitive modification consists in crossing the region of small gap twice. Our findings are illustrated by several examples of driven closed and open quantum systems.

Ekpyrosis and inflationary dynamics in heavy ion collisions: the role of quantum fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dusling, K.; Venugopalan, R.; Gelis, F.

We summarize recent significant progress in the development of a first-principles formalism to describe the formation and evolution of matter in very high energy heavy ion collisions. The key role of quantum fluctuations both before and after a collision is emphasized. Systematic computations are now feasible to address early time isotropization, flow, parton energy loss and the Chiral Magnetic Effect.

Covariance and Quantum Cosmology: A Comparison of Two Matter Clocks

NASA Astrophysics Data System (ADS)

Halnon, Theodore; Bojowald, Martin

2017-01-01

In relativity, time is relative between reference frames. However, quantum mechanics requires a specific time coordinate in order to write an evolution equation for wave functions. This difference between the two theories leads to the problem of time in quantum gravity. One method to study quantum relativity is to interpret the dynamics of a matter field as a clock. In order to test the relationship between different reference frames, an isotropic cosmological model with two matter ingredients is introduced. One is given by a scalar field and one by vacuum energy or a cosmological constant. There are two matter fields, and thus two different Hamiltonians are derived from the respective clock rates. Semi-classical solutions are found for these equations and a comparison is made of the physical predictions that they imply. Partial funding from the Ronald E. McNair Postbaccalaureate Achievement Program.

Coherent dynamics of a telecom-wavelength entangled photon source.

PubMed

Ward, M B; Dean, M C; Stevenson, R M; Bennett, A J; Ellis, D J P; Cooper, K; Farrer, I; Nicoll, C A; Ritchie, D A; Shields, A J

2014-01-01

Quantum networks can interconnect remote quantum information processors, allowing interaction between different architectures and increasing net computational power. Fibre-optic telecommunications technology offers a practical platform for routing weakly interacting photonic qubits, allowing quantum correlations and entanglement to be established between distant nodes. Although entangled photons have been produced at telecommunications wavelengths using spontaneous parametric downconversion in nonlinear media, as system complexity increases their inherent excess photon generation will become limiting. Here we demonstrate entangled photon pair generation from a semiconductor quantum dot at a telecommunications wavelength. Emitted photons are intrinsically anti-bunched and violate Bell's inequality by 17 standard deviations High-visibility oscillations of the biphoton polarization reveal the time evolution of the emitted state with exceptional clarity, exposing long coherence times. Furthermore, we introduce a method to evaluate the fidelity to a time-evolving Bell state, revealing entanglement between photons emitted up to 5 ns apart, exceeding the exciton lifetime.

Steady state quantum discord for circularly accelerated atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Jiawei, E-mail: hujiawei@nbu.edu.cn; Yu, Hongwei, E-mail: hwyu@hunnu.edu.cn; Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081

2015-12-15

We study, in the framework of open quantum systems, the dynamics of quantum entanglement and quantum discord of two mutually independent circularly accelerated two-level atoms in interaction with a bath of fluctuating massless scalar fields in the Minkowski vacuum. We assume that the two atoms rotate synchronically with their separation perpendicular to the rotating plane. The time evolution of the quantum entanglement and quantum discord of the two-atom system is investigated. For a maximally entangled initial state, the entanglement measured by concurrence diminishes to zero within a finite time, while the quantum discord can either decrease monotonically to an asymptoticmore » value or diminish to zero at first and then followed by a revival depending on whether the initial state is antisymmetric or symmetric. When both of the two atoms are initially excited, the generation of quantum entanglement shows a delayed feature, while quantum discord is created immediately. Remarkably, the quantum discord for such a circularly accelerated two-atom system takes a nonvanishing value in the steady state, and this is distinct from what happens in both the linear acceleration case and the case of static atoms immersed in a thermal bath.« less

Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor.

PubMed

Mitra, Avik; Ghosh, Arindam; Das, Ranabir; Patel, Apoorva; Kumar, Anil

2005-12-01

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.

Artificial Life in Quantum Technologies

NASA Astrophysics Data System (ADS)

Alvarez-Rodriguez, Unai; Sanz, Mikel; Lamata, Lucas; Solano, Enrique

2016-02-01

We develop a quantum information protocol that models the biological behaviours of individuals living in a natural selection scenario. The artificially engineered evolution of the quantum living units shows the fundamental features of life in a common environment, such as self-replication, mutation, interaction of individuals, and death. We propose how to mimic these bio-inspired features in a quantum-mechanical formalism, which allows for an experimental implementation achievable with current quantum platforms. This study paves the way for the realization of artificial life and embodied evolution with quantum technologies.

Nongeometric conditional phase shift via adiabatic evolution of dark eigenstates: a new approach to quantum computation.

PubMed

Zheng, Shi-Biao

2005-08-19

We propose a new approach to quantum phase gates via the adiabatic evolution. The conditional phase shift is neither of dynamical nor geometric origin. It arises from the adiabatic evolution of the dark state itself. Taking advantage of the adiabatic passage, this kind of quantum logic gates is robust against moderate fluctuations of experimental parameters. In comparison with the geometric phase gates, it is unnecessary to drive the system to undergo a desired cyclic evolution to obtain a desired solid angle. Thus, the procedure is simplified, and the fidelity may be further improved since the errors in obtaining the required solid angle are avoided. We illustrate such a kind of quantum logic gates in the ion trap system. The idea can also be realized in other systems, opening a new perspective for quantum information processing.

Generalized Bell states map physical systems’ quantum evolution into a grammar for quantum information processing

NASA Astrophysics Data System (ADS)

Delgado, Francisco

2017-12-01

Quantum information processing should be generated through control of quantum evolution for physical systems being used as resources, such as superconducting circuits, spinspin couplings in ions and artificial anyons in electronic gases. They have a quantum dynamics which should be translated into more natural languages for quantum information processing. On this terrain, this language should let to establish manipulation operations on the associated quantum information states as classical information processing does. This work shows how a kind of processing operations can be settled and implemented for quantum states design and quantum processing for systems fulfilling a SU(2) reduction in their dynamics.

Optimum quantum receiver for detecting weak signals in PAM communication systems

NASA Astrophysics Data System (ADS)

Sharma, Navneet; Rawat, Tarun Kumar; Parthasarathy, Harish; Gautam, Kumar

2017-09-01

This paper deals with the modeling of an optimum quantum receiver for pulse amplitude modulator (PAM) communication systems. The information bearing sequence {I_k}_{k=0}^{N-1} is estimated using the maximum likelihood (ML) method. The ML method is based on quantum mechanical measurements of an observable X in the Hilbert space of the quantum system at discrete times, when the Hamiltonian of the system is perturbed by an operator obtained by modulating a potential V with a PAM signal derived from the information bearing sequence {I_k}_{k=0}^{N-1}. The measurement process at each time instant causes collapse of the system state to an observable eigenstate. All probabilities of getting different outcomes from an observable are calculated using the perturbed evolution operator combined with the collapse postulate. For given probability densities, calculation of the mean square error evaluates the performance of the receiver. Finally, we present an example involving estimating an information bearing sequence that modulates a quantum electromagnetic field incident on a quantum harmonic oscillator.

Nonlinear Riccati equations as a unifying link between linear quantum mechanics and other fields of physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-04-01

Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.

Quantum tomography of a molecular bond in ice.

PubMed

Goldschleger, I U; Golschleger, I U; van Staveren, M N; Apkarian, V Ara

2013-07-21

We present the moving picture of a molecular bond, in phase-space, in real-time, at resolution limited by quantum uncertainty. The images are tomographically reconstructed Wigner distribution functions (WDF) obtained from four-wave mixing measurements on Br2-doped ice. The WDF completely characterizes the dissipative quantum evolution of the system, which despite coupling to the environment retains quantum coherence, as evidenced by its persistent negative Wigner hole. The spectral decomposition of the WDF allows a direct visualization of wavefunctions and spatiotemporal coherences of the system and the system-bath interaction. The measurements vividly illustrate nonclassical wave mechanics in a many-body system, in ordinary condensed matter.

Lieb-Robinson bound and locality for general markovian quantum dynamics.

PubMed

Poulin, David

2010-05-14

The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a powerful tool in theoretical condensed matter physics and quantum information science. Here, we extend the scope of this seminal result by considering general markovian quantum evolution, where we prove that an equivalent bound holds. In addition, we use the generalized bound to demonstrate that correlations in the stationary state of a Markov process decay on a length scale set by the Lieb-Robinson velocity and the system's relaxation time.

Surface-hopping dynamics and decoherence with quantum equilibrium structure.

PubMed

Grunwald, Robbie; Kim, Hyojoon; Kapral, Raymond

2008-04-28

In open quantum systems, decoherence occurs through interaction of a quantum subsystem with its environment. The computation of expectation values requires a knowledge of the quantum dynamics of operators and sampling from initial states of the density matrix describing the subsystem and bath. We consider situations where the quantum evolution can be approximated by quantum-classical Liouville dynamics and examine the circumstances under which the evolution can be reduced to surface-hopping dynamics, where the evolution consists of trajectory segments exclusively evolving on single adiabatic surfaces, with probabilistic hops between these surfaces. The justification for the reduction depends on the validity of a Markovian approximation on a bath averaged memory kernel that accounts for quantum coherence in the system. We show that such a reduction is often possible when initial sampling is from either the quantum or classical bath initial distributions. If the average is taken only over the quantum dispersion that broadens the classical distribution, then such a reduction is not always possible.

Phase diagram and quench dynamics of the cluster-XY spin chain

NASA Astrophysics Data System (ADS)

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Entanglement renormalization, quantum error correction, and bulk causality

NASA Astrophysics Data System (ADS)

Kim, Isaac H.; Kastoryano, Michael J.

2017-04-01

Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progres-sively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

Phase diagram and quench dynamics of the cluster-XY spin chain.

PubMed

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

New insights on emergence from the perspective of weak values and dynamical non-locality

NASA Astrophysics Data System (ADS)

Tollaksen, Jeff

2014-04-01

In this article, we will examine new fundamental aspects of "emergence" and "information" using novel approaches to quantum mechanics which originated from the group around Aharonov. The two-state vector formalism provides a complete description of pre- and post-selected quantum systems and has uncovered a host of new quantum phenomena which were previously hidden. The most important feature is that any weak coupling to a pre- and post-selected system is effectively a coupling to a "weak value" which is given by a simple expression depending on the two-state vector. In particular, weak values, are the outcomes of so called "weak measurements" which have recently become a very powerful tool for ultra-sensitive measurements. Using weak values, we will show how to separate a particle from its properties, not unlike the Cheshire cat story: "Well! I've often seen a cat without a grin," thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life!" Next, we address the question whether the physics on different scales "emerges" from quantum mechanics or whether the laws of physics at those scales are fundamental. We show that the classical limit of quantum mechanics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects. Next we show that novel experimental aspects of contextuality can be demonstrated with weak measurements and these suggest new restrictions on hidden variable approaches. Next we emphasize that the most important implication of the Aharonov-Bohm effect is the existence of non-local interactions which do not violate causality. Finally, we review some generalizations of quantum mechanics and their implications for "emergence" and "information." First, we review an alternative approach to quantum evolution in which each moment of time is viewed as a new "universe" and time evolution is given by correlations between different moments. Next, we present a new solution to the measurement problem involving future boundary conditions placed on the universe as a whole. Finally, we introduce another fundamental approach to quantum evolution which allows for tremendous richness in the types of allowable Hamiltonians.

Quantum quenches and work distributions in ultralow-density systems.

PubMed

Shchadilova, Yulia E; Ribeiro, Pedro; Haque, Masudul

2014-02-21

We present results on quantum quenches in lattice systems with a fixed number of particles in a much larger number of sites. Both local and global quenches in this limit generically have power-law work distributions ("edge singularities"). We show that this regime allows for large edge singularity exponents beyond that allowed by the constraints of the usual thermodynamic limit. This large-exponent singularity has observable consequences in the time evolution, leading to a distinct intermediate power-law regime in time. We demonstrate these results first using local quantum quenches in a low-density Kondo-like system, and additionally through global and local quenches in Bose-Hubbard, Aubry-Andre, and hard-core boson systems at low densities.

Thermal Casimir-Polder forces on a V-type three-level atom

NASA Astrophysics Data System (ADS)

Xu, Chen-Ran; Xu, Jing-Ping; Al-amri, M.; Zhu, Cheng-Jie; Xie, Shuang-Yuan; Yang, Ya-Ping

2017-09-01

We study the thermal Casimir-Polder (CP) forces on a V-type three-level atom. The competition between the thermal effect and the quantum interference of the two transition dipoles on the force is investigated. To shed light onto the role of the quantum interference, we analyze two kinds of initial states of the atom, i.e., the superradiant state and the subradiant state. Considering the atom being in the thermal reservoir, the resonant CP force arising from the real photon emission dominates in the evolution of the CP force. Under the zero-temperature condition, the quantum interference can effectively modify the amplitude and the evolution of the force, leading to a long-time force or even the cancellation of the force. Our results reveal that in the finite-temperature case, the thermal photons can enhance the amplitude of all force elements, but have no influence on the net resonant CP force in the steady state, which means that the second law of thermodynamics still works. For the ideal degenerate V-type atom with parallel dipoles under the initial subradiant state, the robust destructive quantum interference overrides the thermal fluctuations, leading to the trapping of the atom in the subradiant state and the disappearance of the CP force. However, in terms of a realistic Zeeman atom, the thermal photons play a significant role during the evolution of the CP force. The thermal fluctuations can enhance the amplitude of the initial CP force by increasing the temperature, and weaken the influence of the quantum interference on the evolution of the CP force from the initial superradiant (subradiant) state to the steady state.

Generalized shortcuts to adiabaticity and enhanced robustness against decoherence

NASA Astrophysics Data System (ADS)

Santos, Alan C.; Sarandy, Marcelo S.

2018-01-01

Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the counter-diabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.

Ultrafast adiabatic quantum algorithm for the NP-complete exact cover problem

PubMed Central

Wang, Hefeng; Wu, Lian-Ao

2016-01-01

An adiabatic quantum algorithm may lose quantumness such as quantum coherence entirely in its long runtime, and consequently the expected quantum speedup of the algorithm does not show up. Here we present a general ultrafast adiabatic quantum algorithm. We show that by applying a sequence of fast random or regular signals during evolution, the runtime can be reduced substantially, whereas advantages of the adiabatic algorithm remain intact. We also propose a randomized Trotter formula and show that the driving Hamiltonian and the proposed sequence of fast signals can be implemented simultaneously. We illustrate the algorithm by solving the NP-complete 3-bit exact cover problem (EC3), where NP stands for nondeterministic polynomial time, and put forward an approach to implementing the problem with trapped ions. PMID:26923834

Quantum snake walk on graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosmanis, Ansis

2011-02-15

I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, whichmore » asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.« less

Higher-order spin and charge dynamics in a quantum dot-lead hybrid system.

PubMed

Otsuka, Tomohiro; Nakajima, Takashi; Delbecq, Matthieu R; Amaha, Shinichi; Yoneda, Jun; Takeda, Kenta; Allison, Giles; Stano, Peter; Noiri, Akito; Ito, Takumi; Loss, Daniel; Ludwig, Arne; Wieck, Andreas D; Tarucha, Seigo

2017-09-22

Understanding the dynamics of open quantum systems is important and challenging in basic physics and applications for quantum devices and quantum computing. Semiconductor quantum dots offer a good platform to explore the physics of open quantum systems because we can tune parameters including the coupling to the environment or leads. Here, we apply the fast single-shot measurement techniques from spin qubit experiments to explore the spin and charge dynamics due to tunnel coupling to a lead in a quantum dot-lead hybrid system. We experimentally observe both spin and charge time evolution via first- and second-order tunneling processes, and reveal the dynamics of the spin-flip through the intermediate state. These results enable and stimulate the exploration of spin dynamics in dot-lead hybrid systems, and may offer useful resources for spin manipulation and simulation of open quantum systems.

Characterizing quantum channels with non-separable states of classical light

NASA Astrophysics Data System (ADS)

Ndagano, Bienvenu; Perez-Garcia, Benjamin; Roux, Filippus S.; McLaren, Melanie; Rosales-Guzman, Carmelo; Zhang, Yingwen; Mouane, Othmane; Hernandez-Aranda, Raul I.; Konrad, Thomas; Forbes, Andrew

2017-04-01

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links that cannot be repaired without performing quantum tomography on the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterize quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled photons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories, and thus enables precise quantum error correction in short- and long-haul optical communication, in both free space and fibre.

Time dependent Schrödinger equation for black hole evaporation: No information loss

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corda, Christian, E-mail: cordac.galilei@gmail.com

2015-02-15

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. This was the starting point of the popular “black hole (BH) information paradox”. In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model,more » a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect ’t Hooft’s assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.« less

Experimental investigation of the no-signalling principle in parity-time symmetric theory using an open quantum system

NASA Astrophysics Data System (ADS)

Tang, Jian-Shun; Wang, Yi-Tao; Yu, Shang; He, De-Yong; Xu, Jin-Shi; Liu, Bi-Heng; Chen, Geng; Sun, Yong-Nan; Sun, Kai; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can

2016-10-01

The experimental progress achieved in parity-time () symmetry in classical optics is the most important accomplishment in the past decade and stimulates many new applications, such as unidirectional light transport and single-mode lasers. However, in the quantum regime, some controversial effects are proposed for -symmetric theory, for example, the potential violation of the no-signalling principle. It is therefore important to understand whether -symmetric theory is consistent with well-established principles. Here, we experimentally study this no-signalling problem related to the -symmetric theory using two space-like separated entangled photons, with one of them passing through a post-selected quantum gate, which effectively simulates a -symmetric evolution. Our results suggest that the superluminal information transmission can be simulated when the successfully -symmetrically evolved subspace is solely considered. However, considering this subspace is only a part of the full Hermitian system, additional information regarding whether the -symmetric evolution is successful is necessary, which transmits to the receiver at maximally light speed, maintaining the no-signalling principle.

Experimental investigation of the no-signalling principle in parity-time symmetric theory using an open quantum system

NASA Astrophysics Data System (ADS)

Tang, Jian-Shun; Wang, Yi-Tao; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can

The experimental progress achieved in parity-time (PT) symmetry in classical optics is the most important accomplishment in the past decade and stimulates many new applications, such as unidirectional light transport and single-mode lasers. However, in the quantum regime, some controversial effects are proposed for PT-symmetric theory, for example, the potential violation of the no-signalling principle. It is therefore important to understand whether PT-symmetric theory is consistent with well-established principles. Here, we experimentally study this no-signalling problem related to the PT-symmetric theory using two space-like separated entangled photons, with one of them passing through a post-selected quantum gate, which effectively simulates a PT-symmetric evolution. Our results suggest that the superluminal information transmission can be simulated when the successfully PT-symmetrically evolved subspace is solely considered. However, considering this subspace is only a part of the full Hermitian system, additional information regarding whether the PT-symmetric evolution is successful is necessary, which transmits to the receiver at maximally light speed, maintaining the no-signalling principle.

Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

NASA Astrophysics Data System (ADS)

Cook, Robert L.; Riofrío, Carlos A.; Deutsch, Ivan H.

2014-09-01

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a non-negligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem: state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal generalized measurement. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

PubMed

Garashchuk, Sophya; Rassolov, Vitaly A

2008-07-14

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

FAST TRACK COMMUNICATION: Semiclassical Klein Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

NASA Astrophysics Data System (ADS)

Coffey, W. T.; Kalmykov, Yu P.; Titov, S. V.; Mulligan, B. P.

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(planck4) and in the classical limit, planck → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived.

Waking and scrambling in holographic heating up

NASA Astrophysics Data System (ADS)

Ageev, D. S.; Aref'eva, I. Ya.

2017-10-01

Using holographic methods, we study the heating up process in quantum field theory. As a holographic dual of this process, we use absorption of a thin shell on a black brane. We find the explicit form of the time evolution of the quantum mutual information during heating up from the temperature Ti to the temperature T f in a system of two intervals in two-dimensional space-time. We determine the geometric characteristics of the system under which the time dependence of the mutual information has a bell shape: it is equal to zero at the initial instant, becomes positive at some subsequent instant, further attains its maximum, and again decreases to zero. Such a behavior of the mutual information occurs in the process of photosynthesis. We show that if the distance x between the intervals is less than log 2/2π T i, then the evolution of the holographic mutual information has a bell shape only for intervals whose lengths are bounded from above and below. For sufficiently large x, i.e., for x < log 2/2π T i, the bell-like shape of the time dependence of the quantum mutual information is present only for sufficiently large intervals. Moreover, the zone narrows as T i increases and widens as T f increases.

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jang, Seogjoo, E-mail: sjang@qc.cuny.edu

2016-06-07

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functionalmore » but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.« less

Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition

NASA Astrophysics Data System (ADS)

Jang, Seogjoo

2016-06-01

This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.

Diffeomorphism groups and nonlinear quantum mechanics

NASA Astrophysics Data System (ADS)

Goldin, Gerald A.

2012-02-01

This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.

A modified Lax-Phillips scattering theory for quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strauss, Y., E-mail: ystrauss@cs.bgu.ac.il

The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for themore » quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.« less

Nonlinear dynamics and quantum entanglement in optomechanical systems.

PubMed

Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2014-03-21

To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

Quantum correlation of high dimensional system in a dephasing environment

NASA Astrophysics Data System (ADS)

Ji, Yinghua; Ke, Qiang; Hu, Juju

2018-05-01

For a high dimensional spin-S system embedded in a dephasing environment, we theoretically analyze the time evolutions of quantum correlation and entanglement via Frobenius norm and negativity. The quantum correlation dynamics can be considered as a function of the decoherence parameters, including the ratio between the system oscillator frequency ω0 and the reservoir cutoff frequency ωc , and the different environment temperature. It is shown that the quantum correlation can not only measure nonclassical correlation of the considered system, but also perform a better robustness against the dissipation. In addition, the decoherence presents the non-Markovian features and the quantum correlation freeze phenomenon. The former is much weaker than that in the sub-Ohmic or Ohmic thermal reservoir environment.

Quantum transfer energy in the framework of time-dependent dipole-dipole interaction

NASA Astrophysics Data System (ADS)

El-Shishtawy, Reda M.; Haddon, Robert C.; Al-Heniti, Saleh H.; Raffah, Bahaaudin M.; Berrada, K.; Abdel-Khalek, S.; Al-Hadeethi, Yas F.

2018-03-01

In this work, we examine the process of the quantum transfer of energy considering time-dependent dipole-dipole interaction in a dimer system characterized by two-level atom systems. By taking into account the effect of the acceleration and speed of the atoms in the dimer coupling, we demonstrate that the improvement of the probability for a single-excitation transfer energy extremely benefits from the incorporation of atomic motion effectiveness and the energy detuning. We explore the relevance between the population and entanglement during the time-evolution and show that this kind of nonlocal correlation may be generated during the process of the transfer of energy. Our work may provide optimal conditions to implement realistic experimental scenario in the transfer of the quantum energy.

Artificial Life in Quantum Technologies

PubMed Central

Alvarez-Rodriguez, Unai; Sanz, Mikel; Lamata, Lucas; Solano, Enrique

2016-01-01

We develop a quantum information protocol that models the biological behaviours of individuals living in a natural selection scenario. The artificially engineered evolution of the quantum living units shows the fundamental features of life in a common environment, such as self-replication, mutation, interaction of individuals, and death. We propose how to mimic these bio-inspired features in a quantum-mechanical formalism, which allows for an experimental implementation achievable with current quantum platforms. This study paves the way for the realization of artificial life and embodied evolution with quantum technologies. PMID:26853918

Numerical simulations of loop quantum Bianchi-I spacetimes

NASA Astrophysics Data System (ADS)

Diener, Peter; Joe, Anton; Megevand, Miguel; Singh, Parampreet

2017-05-01

Due to the numerical complexities of studying evolution in an anisotropic quantum spacetime, in comparison to the isotropic models, the physics of loop quantized anisotropic models has remained largely unexplored. In particular, robustness of bounce and the validity of effective dynamics have so far not been established. Our analysis fills these gaps for the case of vacuum Bianchi-I spacetime. To efficiently solve the quantum Hamiltonian constraint we perform an implementation of the Cactus framework which is conventionally used for applications in numerical relativity. Using high performance computing, numerical simulations for a large number of initial states with a wide variety of fluctuations are performed. Big bang singularity is found to be replaced by anisotropic bounces for all the cases. We find that for initial states which are sharply peaked at the late times in the classical regime and bounce at a mean volume much greater than the Planck volume, effective dynamics is an excellent approximation to the underlying quantum dynamics. Departures of the effective dynamics from the quantum evolution appear for the states probing deep Planck volumes. A detailed analysis of the behavior of this departure reveals a non-monotonic and subtle dependence on fluctuations of the initial states. We find that effective dynamics in almost all of the cases underestimates the volume and hence overestimates the curvature at the bounce, a result in synergy with earlier findings in the isotropic case. The expansion and shear scalars are found to be bounded throughout the evolution.

Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haro, Jaume de, E-mail: jaime.haro@upc.edu

It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent waymore » to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.« less

Emergence of entanglement with temperature and time in factorization-surface states

NASA Astrophysics Data System (ADS)

Chanda, Titas; Das, Tamoghna; Sadhukhan, Debasis; Pal, Amit Kumar; SenDe, Aditi; Sen, Ujjwal

2018-01-01

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting with the system through that spin-pair via a repetitive quantum interaction.

Probability distributions of continuous measurement results for conditioned quantum evolution

NASA Astrophysics Data System (ADS)

Franquet, A.; Nazarov, Yuli V.

2017-02-01

We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the latter is achieved by the postselection in the end of the evolution. The statistics may drastically differ from the nonconditioned case, and the interference between initial and final states can be observed in the probability distributions of measurement outcomes as well as in the average values exceeding the conventional range of nonconditioned averages. We develop a proper formalism to compute the distributions of measurement outcomes, and evaluate and discuss the distributions in experimentally relevant setups. We demonstrate the manifestations of the interference between initial and final states in various regimes. We consider analytically simple examples of nontrivial probability distributions. We reveal peaks (or dips) at half-quantized values of the measurement outputs. We discuss in detail the case of zero overlap between initial and final states demonstrating anomalously big average outputs and sudden jump in time-integrated output. We present and discuss the numerical evaluation of the probability distribution aiming at extending the analytical results and describing a realistic experimental situation of a qubit in the regime of resonant fluorescence.

The second law of thermodynamics under unitary evolution and external operations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ikeda, Tatsuhiko N., E-mail: ikeda@cat.phys.s.u-tokyo.ac.jp; Physics Department, Boston University, Boston, MA 02215; Sakumichi, Naoyuki

The von Neumann entropy cannot represent the thermodynamic entropy of equilibrium pure states in isolated quantum systems. The diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, is a natural generalization of the von Neumann entropy and applicable to equilibrium pure states. We show that the diagonal entropy is consistent with the second law of thermodynamics upon arbitrary external unitary operations. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that quantum trajectories under unitary evolution are restricted by the Hamiltonian dynamics and that the external operation is performed withoutmore » reference to the microscopic state of the system.« less

Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

NASA Astrophysics Data System (ADS)

McCaul, G. M. G.; Lorenz, C. D.; Kantorovich, L.

2017-03-01

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the extended stochastic Liouville-von Neumann equation. Our approach generalizes previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.

Transitionless driving on adiabatic search algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oh, Sangchul, E-mail: soh@qf.org.qa; Kais, Sabre, E-mail: kais@purdue.edu; Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907

We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian,more » approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.« less

Long Time Quantum Evolution of Observables on Cusp Manifolds

NASA Astrophysics Data System (ADS)

Bonthonneau, Yannick

2016-04-01

The Eisenstein functions {E(s)} are some generalized eigenfunctions of the Laplacian on manifolds with cusps. We give a version of Quantum Unique Ergodicity for them, for {|{I}s| to ∞} and {R}s to d/2} with {{R}s - d/2 ≥ log log |{I}s| / log |{I}s|}. For the purpose of the proof, we build a semi-classical quantization procedure for finite volume manifolds with hyperbolic cusps, adapted to a geometrical class of symbols. We also prove an Egorov Lemma until Ehrenfest times on such manifolds.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

PubMed

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

PubMed Central

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

Time evolution of complexity in Abelian gauge theories

NASA Astrophysics Data System (ADS)

Hashimoto, Koji; Iizuka, Norihiro; Sugishita, Sotaro

2017-12-01

Quantum complexity is conjectured to probe inside of black hole horizons (or wormholes) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for Abelian pure gauge theories. For this purpose, we discretize the U (1 ) gauge group as ZN and also the continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories and to evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ˜exp (entropy), which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.

On the Time-Dependent Analysis of Gamow Decay

ERIC Educational Resources Information Center

Durr, Detlef; Grummt, Robert; Kolb, Martin

2011-01-01

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

Continuous-variable gate decomposition for the Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Kalajdzievski, Timjan; Weedbrook, Christian; Rebentrost, Patrick

2018-06-01

In this work, we decompose the time evolution of the Bose-Hubbard model into a sequence of logic gates that can be implemented on a continuous-variable photonic quantum computer. We examine the structure of the circuit that represents this time evolution for one-dimensional and two-dimensional lattices. The elementary gates needed for the implementation are counted as a function of lattice size. We also include the contribution of the leading dipole interaction term which may be added to the Hamiltonian and its corresponding circuit.

Reference results for time-like evolution up to

NASA Astrophysics Data System (ADS)

Bertone, Valerio; Carrazza, Stefano; Nocera, Emanuele R.

2015-03-01

We present high-precision numerical results for time-like Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution in the factorisation scheme, for the first time up to next-to-next-to-leading order accuracy in quantum chromodynamics. First, we scrutinise the analytical expressions of the splitting functions available in the literature, in both x and N space, and check their mutual consistency. Second, we implement time-like evolution in two publicly available, entirely independent and conceptually different numerical codes, in x and N space respectively: the already existing APFEL code, which has been updated with time-like evolution, and the new MELA code, which has been specifically developed to perform the study in this work. Third, by means of a model for fragmentation functions, we provide results for the evolution in different factorisation schemes, for different ratios between renormalisation and factorisation scales and at different final scales. Our results are collected in the format of benchmark tables, which could be used as a reference for global determinations of fragmentation functions in the future.

Evolution equation for quantum coherence

PubMed Central

Hu, Ming-Liang; Fan, Heng

2016-01-01

The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933

Quantum rotation gates with controlled nonadiabatic evolutions

NASA Astrophysics Data System (ADS)

Abdelrahim, Abdelrahman A. H.; Benmachiche, Abderrahim; Subhi Mahmoud, Gharib; Messikh, Azeddine

2018-04-01

Quantum gates can be implemented adiabatically and nonadiabatically. Many schemes used at least two sequentially implemented gates to obtain an arbitrary one-qubit gate. Recently, it has been shown that nonadiabatic gates can be realized by single-shot implementation. It has also been shown that quantum gates can be implemented with controlled adiabatic evolutions. In this paper, we combine the advantage of single-shot implementation with controlled adiabatic evolutions to obtain controlled nonadiabatic evolutions. We also investigate the robustness to different types of errors. We find that the fidelity is close to unity for realistic decoherence rates.

Slightly anharmonic systems in quantum optics

NASA Technical Reports Server (NTRS)

Klimov, Andrey B.; Chumakov, Sergey M.

1995-01-01

We consider an arbitrary atomic system (n-level atom or many such atoms) interacting with a strong resonant quantum field. The approximate evolution operator for a quantum field case can be produced from the atomic evolution operator in an external classical field by a 'quantization prescription', passing the operator arguments to Wigner D-functions. Many important phenomena arising from the quantum nature of the field can be described by such a way.

Quantum simulation from the bottom up: the case of rebits

NASA Astrophysics Data System (ADS)

Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

2018-05-01

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Anticipatory dynamics of biological systems: from molecular quantum states to evolution

NASA Astrophysics Data System (ADS)

Igamberdiev, Abir U.

2015-08-01

Living systems possess anticipatory behaviour that is based on the flexibility of internal models generated by the system's embedded description. The idea was suggested by Aristotle and is explicitly introduced to theoretical biology by Rosen. The possibility of holding the embedded internal model is grounded in the principle of stable non-equilibrium (Bauer). From the quantum mechanical view, this principle aims to minimize energy dissipation in expense of long relaxation times. The ideas of stable non-equilibrium were developed by Liberman who viewed living systems as subdivided into the quantum regulator and the molecular computer supporting coherence of the regulator's internal quantum state. The computational power of the cell molecular computer is based on the possibility of molecular rearrangements according to molecular addresses. In evolution, the anticipatory strategies are realized both as a precession of phylogenesis by ontogenesis (Berg) and as the anticipatory search of genetic fixation of adaptive changes that incorporates them into the internal model of genetic system. We discuss how the fundamental ideas of anticipation can be introduced into the basic foundations of theoretical biology.

Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system

NASA Astrophysics Data System (ADS)

Qureshi, Mumnuna A.; Zhong, Johnny; Qureshi, Zihad; Mason, Peter; Betouras, Joseph J.; Zagoskin, Alexandre M.

2018-03-01

We consider the evolution of the quantum states of a Hamiltonian that is parametrically perturbed via a term proportional to the adiabatic parameter λ (t ) . Starting with the Pechukas-Yukawa mapping of the energy eigenvalue evolution in a generalized Calogero-Sutherland model of a one-dimensional classical gas, we consider the adiabatic approximation with two different expansions of the quantum state in powers of d λ /d t and compare them with a direct numerical simulation. We show that one of these expansions (Magnus series) is especially convenient for the description of nonadiabatic evolution of the system. Applying the expansion to the exact cover 3-satisfiability problem, we obtain the occupation dynamics, which provides insight into the population of states and sources of decoherence in a quantum system.

Lorentz quantum mechanics

NASA Astrophysics Data System (ADS)

Zhang, Qi; Wu, Biao

2018-01-01

We present a theoretical framework for the dynamics of bosonic Bogoliubov quasiparticles. We call it Lorentz quantum mechanics because the dynamics is a continuous complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary transformation in Hilbert space. In our Lorentz quantum mechanics, three types of state exist: space-like, light-like and time-like. Fundamental aspects are explored in parallel to the usual quantum mechanics, such as a matrix form of a Lorentz transformation, and the construction of Pauli-like matrices for spinors. We also investigate the adiabatic evolution in these mechanics, as well as the associated Berry curvature and Chern number. Three typical physical systems, where bosonic Bogoliubov quasi-particles and their Lorentz quantum dynamics can arise, are presented. They are a one-dimensional fermion gas, Bose-Einstein condensate (or superfluid), and one-dimensional antiferromagnet.

Quantum nature of the big bang.

PubMed

Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet

2006-04-14

Some long-standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big-bang singularity in loop quantum cosmology are significantly extended as follows: (i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the "emergent time" idea; (ii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously; (iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the nonperturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime.

An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains

NASA Astrophysics Data System (ADS)

Joel, Kira; Kollmar, Davida; Santos, Lea F.

2013-06-01

Quantum spin chains are prototype quantum many-body systems that are employed in the description of various complex physical phenomena. We provide an introduction to this subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.

Minimal Model of Quantum Kinetic Clusters for the Energy-Transfer Network of a Light-Harvesting Protein Complex.

PubMed

Wu, Jianlan; Tang, Zhoufei; Gong, Zhihao; Cao, Jianshu; Mukamel, Shaul

2015-04-02

The energy absorbed in a light-harvesting protein complex is often transferred collectively through aggregated chromophore clusters. For population evolution of chromophores, the time-integrated effective rate matrix allows us to construct quantum kinetic clusters quantitatively and determine the reduced cluster-cluster transfer rates systematically, thus defining a minimal model of energy-transfer kinetics. For Fenna-Matthews-Olson (FMO) and light-havrvesting complex II (LCHII) monomers, quantum Markovian kinetics of clusters can accurately reproduce the overall energy-transfer process in the long-time scale. The dominant energy-transfer pathways are identified in the picture of aggregated clusters. The chromophores distributed extensively in various clusters can assist a fast and long-range energy transfer.

Applicability of transfer tensor method for open quantum system dynamics.

PubMed

Gelzinis, Andrius; Rybakovas, Edvardas; Valkunas, Leonas

2017-12-21

Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand. The possible time-savings thus strongly depend on the ratio of total versus initial evolution lengths. In this work, we investigate the parameter regimes where an application of TTM would be most beneficial in terms of computational time. We identify several promising parameter regimes. Although some of them correspond to cases when perturbative theories could be expected to perform well, we find that the accuracy of such approaches depends on system parameters in a more complex way than it is commonly thought. We propose that the TTM should be applied whenever system evolution is expected to be long and accuracy of perturbative methods cannot be ensured or in cases when the system under consideration does not correspond to any single perturbative regime.

Linear optics only allows every possible quantum operation for one photon or one port

NASA Astrophysics Data System (ADS)

Moyano-Fernández, Julio José; Garcia-Escartin, Juan Carlos

2017-01-01

We study the evolution of the quantum state of n photons in m different modes when they go through a lossless linear optical system. We show that there are quantum evolution operators U that cannot be built with linear optics alone unless the number of photons or the number of modes is equal to one. The evolution for single photons can be controlled with the known realization of any unitary proved by Reck, Zeilinger, Bernstein and Bertani. The evolution for a single mode corresponds to the trivial evolution in a phase shifter. We analyze these two cases and prove that any other combination of the number of photons and modes produces a Hilbert state too large for the linear optics system to give any desired evolution.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

Real time analysis of self-assembled InAs/GaAs quantum dot growth by probing reflection high-energy electron diffraction chevron image

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kudo, Takuya; Inoue, Tomoya; Kita, Takashi

2008-10-01

Self-assembling process of InAs/GaAs quantum dots has been investigated by analyzing reflection high-energy electron diffraction chevron images reflecting the crystal facet structure surrounding the island. The chevron image shows dramatic changes during the island formation. From the temporal evolution of the chevron tail structure, the self-assembling process has been found to consist of four steps. The initial islands do not show distinct facet structures. Then, the island surface is covered by high-index facets, and this is followed by the formation of stable low-index facets. Finally, the flow of In atoms from the islands occurs, which contributes to flatten the wettingmore » layer. Furthermore, we have investigated the island shape evolution during the GaAs capping layer growth by using the same real-time analysis technique.« less

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

NASA Astrophysics Data System (ADS)

Vidanović, Ivana; Bogojević, Aleksandar; Balaž, Antun; Belić, Aleksandar

2009-12-01

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Flat-space quantum gravity in the AdS / CFT correspondence

DOE PAGES

Nomura, Yasunori; Sanches, Fabio; Weinberg, Sean J.

2016-03-22

Motivated by the task of understanding microscopic dynamics of an evolving black hole, we present a scheme describing gauge-fixed continuous time evolution of quantum gravitational processes in asymptotically flat spacetime using the algebra of conformal field theory operators. This allows us to study the microscopic dynamics of the Hawking emission process, although obtaining a full S-matrix may require a modification of the minimal scheme. The role of the operator product expansion is to physically interpret the resulting time evolution by decomposing the Hilbert space of the states for the entire system into those for smaller subsystems. We translate the picturemore » of an evaporating black hole previously proposed by the authors into predictions for nonperturbative properties of the conformal field theories that have weakly coupled dual gravitational descriptions. Finally, we also discuss a possible relationship between the present scheme and a reference frame change in the bulk.« less

Multiple choices of time in quantum cosmology

NASA Astrophysics Data System (ADS)

Małkiewicz, Przemysław

2015-07-01

It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of the gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the meaning of compatibility), we develop suitable tools for determining the relation between quantum theories based on different time functions. First, we discuss how a time function fixes a canonical structure on the constraint surface. The presentation includes both the kinematical and the reduced perspective, and the relation between them. Second, we formulate twin theorems about the existence of two inequivalent maps between any two deparameterizations, a formal canonical and a coordinate one. They are used to separate the effects induced by choice of clock and other factors. We show, in an example, how the spectra of quantum observables are transformed under the change of clock and prove, via a general argument, the existence of choice-of-time-induced semiclassical effects. Finally, we study an example, in which we find that the semiclassical discrepancies can in fact be arbitrarily large for dynamical observables. We conclude that the values of critical energy density or critical volume in the bouncing scenarios of quantum cosmology cannot in general be at the Planck scale, and always need to be given with reference to a specific time function.

Ultimate limits for quantum magnetometry via time-continuous measurements

NASA Astrophysics Data System (ADS)

Albarelli, Francesco; Rossi, Matteo A. C.; Paris, Matteo G. A.; Genoni, Marco G.

2017-12-01

We address the estimation of the magnetic field B acting on an ensemble of atoms with total spin J subjected to collective transverse noise. By preparing an initial spin coherent state, for any measurement performed after the evolution, the mean-square error of the estimate is known to scale as 1/J, i.e. no quantum enhancement is obtained. Here, we consider the possibility of continuously monitoring the atomic environment, and conclusively show that strategies based on time-continuous non-demolition measurements followed by a final strong measurement may achieve Heisenberg-limited scaling 1/{J}2 and also a monitoring-enhanced scaling in terms of the interrogation time. We also find that time-continuous schemes are robust against detection losses, as we prove that the quantum enhancement can be recovered also for finite measurement efficiency. Finally, we analytically prove the optimality of our strategy.

KvN mechanics approach to the time-dependent frequency harmonic oscillator.

PubMed

Ramos-Prieto, Irán; Urzúa-Pineda, Alejandro R; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2018-05-30

Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time. Finally, because the solution of the Ermakov equation is involved in the evolution of the classical state vector, we explore some analytical and numerical solutions.

The Nonlinear Jaynes-Cummings Model for the Multiphoton Transition

NASA Astrophysics Data System (ADS)

Liu, Xiao-Jing; Lu, Jing-Bin; Zhang, Si-Qi; Liu, Ji-Ping; Li, Hong; Liang, Yu; Ma, Ji; Weng, Yi-Jiao; Zhang, Qi-Rui; Liu, Han; Zhang, Xiao-Ru; Wu, Xiang-Yao

2018-01-01

With the nonlinear Jaynes-Cummings model, we have studied the atom and light field quantum entanglement of multiphoton transition in nonlinear medium, and researched the effect of the transition photon number N and the nonlinear coefficient χ on the quantum entanglement degrees. We have given the quantum entanglement degrees curves with time evolution, we find when the transition photon number N increases, the entanglement degrees oscillation get faster. When the nonlinear coefficient α > 0, the entanglement degrees oscillation get quickly, the nonlinear term is disadvantage of the atom and light field entanglement, and when the nonlinear coefficient α < 0, the entanglement degrees oscillation get slow, the nonlinear term is advantage of the atom and light field entanglement. These results will have been used in the quantum communication and quantum information.

Observing single quantum trajectories of a superconducting qubit: ensemble properties and driven dynamics

NASA Astrophysics Data System (ADS)

Weber, Steven; Murch, K. W.; Chantasri, A.; Dressel, J.; Jordan, A. N.; Siddiqi, I.

2014-03-01

We use weak measurements to track individual quantum trajectories of a superconducting qubit embedded in a microwave cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We analyze ensembles of trajectories to determine statistical properties such as the most likely path and most likely time connecting pre and post-selected quantum states. We compare our results with theoretical predictions derived from an action principle for continuous quantum measurement. Furthermore, by introducing a qubit drive, we investigate the interplay between unitary state evolution and non-unitary measurement dynamics. This work was supported by the IARPA CSQ program and the ONR.

State dragging using the quantum Zeno effect

NASA Astrophysics Data System (ADS)

Hacohen-Gourgy, Shay; Martin, Leigh; GarcíA-Pintos, Luis Pedro; Dressel, Justin; Siddiqi, Irfan

The quantum Zeno effect is the suppression of Hamiltonian evolution by continuous measurement. It arises as a consequence of the quantum back-action pushing the state towards an eigenstate of the measurement operator. Rotating the operator at a rate much slower than the measurement rate will effectively drag the state with it. We use our recently developed scheme, which enables dynamic control of the measurement operator, to demonstrate this dragging effect on a superconducting transmon qubit. Since the system is continuously measured, the deterministic trajectory can be monitored, and quantum jumps can be detected in real-time. Furthermore, we perform this with two observables that are set to be either commuting or non-commuting, demonstrating new quantum dynamics. This work was supported by the Army Research Office and the Air Force Research Laboratory.

Experimental creation of quantum Zeno subspaces by repeated multi-spin projections in diamond

NASA Astrophysics Data System (ADS)

Kalb, N.; Cramer, J.; Twitchen, D. J.; Markham, M.; Hanson, R.; Taminiau, T. H.

2016-10-01

Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates quantum Zeno subspaces and simultaneously suppresses the dephasing caused by a quasi-static environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide experimental insight into the interplay between frequent multi-spin measurements and slowly varying noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.

Conformal quantum mechanics and holography in noncommutative space-time

NASA Astrophysics Data System (ADS)

Gupta, Kumar S.; Harikumar, E.; Zuhair, N. S.

2017-09-01

We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the κ-deformed space-time as a prototype. Up to the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The AdS2 / CFT1 duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.

Quantitative conditions for time evolution in terms of the von Neumann equation

NASA Astrophysics Data System (ADS)

Wang, WenHua; Cao, HuaiXin; Chen, ZhengLi; Wang, Lie

2018-07-01

The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schödinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states (unite vectors) and mixed states (density matrices, i.e., positive operators with trace one). Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.

Mapping quantum-classical Liouville equation: projectors and trajectories.

PubMed

Kelly, Aaron; van Zon, Ramses; Schofield, Jeremy; Kapral, Raymond

2012-02-28

The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simulation of an ensemble of entangled trajectories. An approximation to this evolution equation which retains only the Poisson bracket contribution to the evolution operator does admit a solution in an ensemble of independent trajectories but it is shown that this operator does not commute with the projection operators and the dynamics may take the system outside the physical space. The dynamical instabilities, utility, and domain of validity of this approximate dynamics are discussed. The effects are illustrated by simulations on several quantum systems.

Non-local correlations via Wigner-Yanase skew information in two SC-qubit having mutual interaction under phase decoherence

NASA Astrophysics Data System (ADS)

Mohamed, Abdel-Baset A.

2017-10-01

An analytical solution of the master equation that describes a superconducting cavity containing two coupled superconducting charge qubits is obtained. Quantum-mechanical correlations based on Wigner-Yanase skew information, as local quantum uncertainty and uncertainty-induced quantum non-locality, are compared to the concurrence under the effects of the phase decoherence. Local quantum uncertainty exhibits sudden changes during its time evolution and revival process. Sudden death and sudden birth occur only for entanglement, depending on the initial state of the two coupled charge qubits, while the correlations of skew information does not vanish. The quantum correlations of skew information are found to be sensitive to the dephasing rate, the photons number in the cavity, the interaction strength between the two qubits, and the qubit distribution angle of the initial state. With a proper initial state, the stationary correlation of the skew information has a non-zero stationary value for a long time interval under the phase decoherence, that it may be useful in quantum information and computation processes.

Fast non-Abelian geometric gates via transitionless quantum driving.

PubMed

Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan

2015-12-21

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.

Fast non-Abelian geometric gates via transitionless quantum driving

PubMed Central

Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan

2015-01-01

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. PMID:26687580

Understanding the evolution of luminescent gold quantum clusters in protein templates.

PubMed

Chaudhari, Kamalesh; Xavier, Paulrajpillai Lourdu; Pradeep, Thalappil

2011-11-22

We show that the time-dependent biomineralization of Au(3+) by native lactoferrin (NLf) and bovine serum albumin (BSA) resulting in near-infrared (NIR) luminescent gold quantum clusters (QCs) occurs through a protein-bound Au(1+) intermediate and subsequent emergence of free protein. The evolution was probed by diverse tools, principally, using matrix-assisted laser desorption ionization mass spectrometry (MALDI MS), X-ray photoelectron spectroscopy (XPS), and photoluminescence spectroscopy (PL). The importance of alkaline pH in the formation of clusters was probed. At neutral pH, a Au(1+)-protein complex was formed (starting from Au(3+)) with the binding of 13-14 gold atoms per protein. When the pH was increased above 12, these bound gold ions were further reduced to Au(0) and nucleation and growth of cluster commenced, which was corroborated by the beginning of emission; at this point, the number of gold atoms per protein was ~25, suggesting the formation of Au(25). During the cluster evolution, at certain time intervals, for specific molar ratios of gold and protein, occurrence of free protein was noticed in the mass spectra, suggesting a mixture of products and gold ion redistribution. By providing gold ions at specific time of the reaction, monodispersed clusters with enhanced luminescence could be obtained, and the available quantity of free protein could be utilized efficiently. Monodispersed clusters would be useful in obtaining single crystals of protein-protected noble metal quantum clusters where homogeneity of the system is of primary concern. © 2011 American Chemical Society

Simulation of n-qubit quantum systems. III. Quantum operations

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2007-05-01

During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamiołkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Program summaryTitle of program: Feynman Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 processor with ⩾2 GHz or equivalent) and 5-20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems often result in very large symbolic expressions that dramatically slow down the evaluation of measures or other quantities. In these cases, MAPLE's assume facility sometimes helps to reduce the complexity of symbolic expressions, but often only numerical evaluation is possible. Since the complexity of the FEYNMAN commands is very different, no general scaling law for the CPU time and memory usage can be given. No. of bytes in distributed program including test data, etc.: 799 265 No. of lines in distributed program including test data, etc.: 18 589 Distribution format: tar.gz Reasons for new version: While the previous program versions were designed mainly to create and manipulate the state of quantum registers, the present extension aims to support quantum operations as the essential ingredient for studying the effects of noisy environments. Does this version supersede the previous version: Yes Nature of the physical problem: Today, entanglement is identified as the essential resource in virtually all aspects of quantum information theory. In most practical implementations of quantum information protocols, however, decoherence typically limits the lifetime of entanglement. It is therefore necessary and highly desirable to understand the evolution of entanglement in noisy environments. Method of solution: Using the computer algebra system MAPLE, we have developed a set of procedures that support the definition and manipulation of n-qubit quantum registers as well as (unitary) logic gates and (nonunitary) quantum operations that act on the quantum registers. The provided hierarchy of commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems in ideal and nonideal quantum circuits.

Renormalization of the unitary evolution equation for coined quantum walks

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan; Portugal, Renato

2017-03-01

We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.

Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance, and out-of-time-ordered correlator

NASA Astrophysics Data System (ADS)

Torres-Herrera, E. J.; García-García, Antonio M.; Santos, Lea F.

2018-02-01

We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival probability, density imbalance, and out-of-time-ordered correlator. They are compared with numerical results for a one-dimensional-disordered model with two-body interactions and shown to bound the decay rate of this realistic system. Power-law decays are seen at intermediate times, and dips below the infinite time averages (correlation holes) occur at long times for all three quantities when the system exhibits level repulsion. The fact that these features are shared by both the random matrix and the realistic disordered model indicates that they are generic to nonintegrable interacting quantum systems out of equilibrium. Assisted by the random matrix analytical results, we propose expressions that describe extremely well the dynamics of the realistic chaotic system at different time scales.

H-theorem in quantum physics.

PubMed

Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M

2016-09-12

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

Dilepton production from hot hadronic matter in nonequilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schenke, B.; Greiner, C.

2006-03-15

The influence of time-dependent medium modifications of low-mass vector mesons on dilepton production is investigated within a nonequilibrium quantum field-theoretical description on the basis of the Kadanoff-Baym equations. Time scales for the adaption of the spectral properties to changing self-energies are given, and, under use of a model for the fireball evolution, nonequilibrium dilepton yields from the decay of {rho} and {omega} mesons are calculated. In a comparison of these yields, those from calculations that assume instantaneous (Markovian) adaption to the changing-medium quantum-mechanical memory effects turn out to be important.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

Cavity QED implementation of non-adiabatic holonomies for universal quantum gates in decoherence-free subspaces with nitrogen-vacancy centers.

PubMed

Zhou, Jian; Yu, Wei-Can; Gao, Yu-Mei; Xue, Zheng-Yuan

2015-06-01

A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-vacancy centers, can be used to construct a universal set of quantum gates on the encoded logical qubits. Therefore, our scheme opens up the possibility of realizing universal holonomic quantum computation with cavity assisted interaction on solid-state spins characterized by long coherence times.

High-Fidelity Single-Shot Toffoli Gate via Quantum Control.

PubMed

Zahedinejad, Ehsan; Ghosh, Joydip; Sanders, Barry C

2015-05-22

A single-shot Toffoli, or controlled-controlled-not, gate is desirable for classical and quantum information processing. The Toffoli gate alone is universal for reversible computing and, accompanied by the Hadamard gate, forms a universal gate set for quantum computing. The Toffoli gate is also a key ingredient for (nontopological) quantum error correction. Currently Toffoli gates are achieved by decomposing into sequentially implemented single- and two-qubit gates, which require much longer times and yields lower overall fidelities compared to a single-shot implementation. We develop a quantum-control procedure to construct a single-shot Toffoli gate for three nearest-neighbor-coupled superconducting transmon systems such that the fidelity is 99.9% and is as fast as an entangling two-qubit gate under the same realistic conditions. The gate is achieved by a nongreedy quantum control procedure using our enhanced version of the differential evolution algorithm.

Zeno subspace in quantum-walk dynamics

NASA Astrophysics Data System (ADS)

Chandrashekar, C. M.

2010-11-01

We investigate discrete-time quantum-walk evolution under the influence of periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace P(0,t) is compared with the survival probability after frequent (n) measurements at interval τ=t/n, P(0,τ)n. We show that P(0,τ)n>P(0,t) leads to the quantum Zeno effect in position subspace when a parameter θ in the quantum coin operations and frequency of measurements is greater than the critical value, θ>θc and n>nc. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has the potential to play a significant role in quantum tasks such as preserving the quantum state of the particle at any particular position, and to understand the Zeno dynamics in a multidimensional system that is highly transient in nature.

Dynamics and thermodynamics of linear quantum open systems.

PubMed

Martinez, Esteban A; Paz, Juan Pablo

2013-03-29

We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

SEMICONDUCTOR PHYSICS: Properties of the two- and three-dimensional quantum dot qubit

NASA Astrophysics Data System (ADS)

Shihua, Chen

2010-05-01

On the condition of electric-longitudinal-optical (LO) phonon strong coupling in both two- and three-dimensional parabolic quantum dots (QDs), we obtain the eigenenergies of the ground state (GS) and the first excited state (ES), the eigenfunctions of the GS and the first ES by using a variational method of Pekar type. This system in QD may be employed as a quantum system-quantum bit (qubit). When the electron is in the superposition state of the GS and the first ES, we obtain the time evolution of the electron density. The relations of both the electron probability density and the period of oscillation with the electric-LO phonon coupling strength and confinement length are discussed.

Solving the quantum many-body problem with artificial neural networks

NASA Astrophysics Data System (ADS)

Carleo, Giuseppe; Troyer, Matthias

2017-02-01

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.

Dicke states in multiple quantum dots

NASA Astrophysics Data System (ADS)

Sitek, Anna; Manolescu, Andrei

2013-10-01

We present a theoretical study of the collective optical effects which can occur in groups of three and four quantum dots. We define conditions for stable subradiant (dark) states, rapidly decaying super-radiant states, and spontaneous trapping of excitation. Each quantum dot is treated like a two-level system. The quantum dots are, however, realistic, meaning that they may have different transition energies and dipole moments. The dots interact via a short-range coupling which allows excitation transfer across the dots, but conserves the total population of the system. We calculate the time evolution of single-exciton and biexciton states using the Lindblad equation. In the steady state the individual populations of each dot may have permanent oscillations with frequencies given by the energy separation between the subradiant eigenstates.

Quantum Dynamics of Solitons in Strongly Interacting Systems on Optical Lattices

NASA Astrophysics Data System (ADS)

Rubbo, Chester; Balakrishnan, Radha; Reinhardt, William; Satija, Indubala; Rey, Ana; Manmana, Salvatore

2012-06-01

We present results of the quantum dynamics of solitons in XXZ spin-1/2 systems which in general can be derived from a system of spinless fermions or hard-core bosons (HCB) with nearest neighbor interaction on a lattice. A mean-field treatment using spin-coherent states revealed analytic solutions of both bright and dark solitons [1]. We take these solutions and apply a full quantum evolution using the adaptive time-dependent density matrix renormalization group method (adaptive t-DMRG), which takes into account the effect of strong correlations. We use local spin observables, correlations functions, and entanglement entropies as measures for the stability of these soliton solutions over the simulation times. [4pt] [1] R. Balakrishnan, I.I. Satija, and C.W. Clark, Phys. Rev. Lett. 103, 230403 (2009).

Quantum Time Evolution in a Qubit Readout Process with a Josephson Bifurcation Amplifier

NASA Astrophysics Data System (ADS)

Nakano, Hayato; Saito, Shiro; Semba, Kouichi; Takayanagi, Hideaki

2009-06-01

We analyzed the Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit quantum mechanically by calculating the dynamics of the density operator of a driven nonlinear oscillator and a qubit coupled system during the measurement process. In purely quantum cases, bifurcation is impossible. Introducing decoherence enables us to reproduce the bifurcation with a finite hysteresis. When a qubit is initially in a superposition state, we have observed the qubit-probe (JBA) entangled state, and it is divided into two separable states at the moment the JBA transition begins. This corresponds to “projection.” To readout the measurement result, however, we must wait until the two JBA states are macroscopically well separated. The waiting time is determined by the strength of the decoherence in the JBA.

Hybrid Quantum-Classical Approach to Quantum Optimal Control.

PubMed

Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

2017-04-14

A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

On One Possible Generalization of the Regression Theorem

NASA Astrophysics Data System (ADS)

Bogolubov, N. N.; Soldatov, A. V.

2018-03-01

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.

A full quantum analysis of the Stern-Gerlach experiment using the evolution operator method: analyzing current issues in teaching quantum mechanics

NASA Astrophysics Data System (ADS)

Benítez Rodríguez, E.; Arévalo Aguilar, L. M.; Piceno Martínez, E.

2017-03-01

To the quantum mechanics specialists community it is a well-known fact that the famous original Stern-Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community.

Global coherence of quantum evolutions based on decoherent histories: Theory and application to photosynthetic quantum energy transport

NASA Astrophysics Data System (ADS)

Allegra, Michele; Giorda, Paolo; Lloyd, Seth

2016-04-01

Assessing the role of interference in natural and artificial quantum dynamical processes is a crucial task in quantum information theory. To this aim, an appropriate formalism is provided by the decoherent histories framework. While this approach has been deeply explored from different theoretical perspectives, it still lacks of a comprehensive set of tools able to concisely quantify the amount of coherence developed by a given dynamics. In this paper, we introduce and test different measures of the (average) coherence present in dissipative (Markovian) quantum evolutions, at various time scales and for different levels of environmentally induced decoherence. In order to show the effectiveness of the introduced tools, we apply them to a paradigmatic quantum process where the role of coherence is being hotly debated: exciton transport in photosynthetic complexes. To spot out the essential features that may determine the performance of the transport, we focus on a relevant trimeric subunit of the Fenna-Matthews-Olson complex and we use a simplified (Haken-Strobl) model for the system-bath interaction. Our analysis illustrates how the high efficiency of environmentally assisted transport can be traced back to a quantum recoil avoiding effect on the exciton dynamics, that preserves and sustains the benefits of the initial fast quantum delocalization of the exciton over the network. Indeed, for intermediate levels of decoherence, the bath is seen to selectively kill the negative interference between different exciton pathways, while retaining the initial positive one. The concepts and tools here developed show how the decoherent histories approach can be used to quantify the relation between coherence and efficiency in quantum dynamical processes.

Berry phase and Hannay's angle in a quantum-classical hybrid system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, H. D.; Wu, S. L.; Yi, X. X.

2011-06-15

The Berry phase, which was discovered more than two decades ago, provides very deep insight into the geometric structure of quantum mechanics. Its classical counterpart, Hannay's angle, is defined if closed curves of action variables return to the same curves in phase space after a time evolution. In this paper we study the Berry phase and Hannay's angle in a quantum-classical hybrid system under the Born-Oppenheimer approximation. By the term quantum-classical hybrid system, we mean a composite system consists of a quantum subsystem and a classical subsystem. The effects of subsystem-subsystem couplings on the Berry phase and Hannay's angle aremore » explored. The results show that the Berry phase has been changed sharply by the couplings, whereas the couplings have a small effect on the Hannay's angle.« less

Finite-Temperature Entanglement Dynamics in an Anisotropic Two-Qubit Heisenberg Spin Chain

NASA Astrophysics Data System (ADS)

Chen, Tao; Shan, Chuanjia; Li, Jinxing; Liu, Tangkun; Huang, Yanxia; Li, Hong

2010-07-01

This paper investigates the entanglement dynamics of an anisotropic two-qubit Heisenberg spin chain in the presence of decoherence at finite temperature. The time evolution of the concurrence is studied for different initial Werner states. The influences of initial purity, finite temperature, spontaneous decay and Hamiltonian on the entanglement evolution are analyzed in detail. Our calculations show that the finite temperature restricts the evolution of the entanglement all the time when the Hamiltonian improves it and the spontaneous decay to the reservoirs can produce quantum entanglement with the anisotropy of spin-spin interaction. Finally, the steady-state concurrence which may remain non-zero for low temperature is also given.

Chaos in quantum channels

DOE PAGES

Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; ...

2016-02-01

For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back upmore » our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.« less

Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i

NASA Astrophysics Data System (ADS)

Palenik, Mark C.

2014-07-01

Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations F=\\frac{dP}{dt}, P=m\\frac{dV}{dt}, and [X, P] = i. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantum mechanics and the motion of a classical particle under Newton's laws. The propagator is solved for three cases where an exact solution is possible: (1) the free particle; (2) the harmonic oscillator; and (3) a constant force, or linear potential in the standard interpretation. We then show that for a general for a general force F(X), by Taylor expanding X(t) in time, we can use this methodology to reproduce the Feynman path integral formula for the propagator. Such a picture may be useful for students as they make the transition from classical to quantum mechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds.

Fundamental limits on quantum dynamics based on entropy change

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Khatri, Sumeet; Siopsis, George; Wilde, Mark M.

2018-01-01

It is well known in the realm of quantum mechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde [Phys. Rev. A 93(6), 062314 (2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characterize quantum dynamics. In particular, we derive a lower limit on the rate of entropy change for memoryless quantum dynamics, and we argue that it provides a witness of non-unitality. This limit on the rate of entropy change leads to definitions of several witnesses for testing memory effects in quantum dynamics. Furthermore, from the aforementioned lower bound on entropy change, we obtain a measure of non-unitarity for unital evolutions.

Architectures for Quantum Simulation Showing a Quantum Speedup

NASA Astrophysics Data System (ADS)

Bermejo-Vega, Juan; Hangleiter, Dominik; Schwarz, Martin; Raussendorf, Robert; Eisert, Jens

2018-04-01

One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy," referring to the experimental realization of a quantum device that computationally outperforms classical computers. In this work, we show that one can devise versatile and feasible schemes of two-dimensional, dynamical, quantum simulators showing such a quantum speedup, building on intermediate problems involving nonadaptive, measurement-based, quantum computation. In each of the schemes, an initial product state is prepared, potentially involving an element of randomness as in disordered models, followed by a short-time evolution under a basic translationally invariant Hamiltonian with simple nearest-neighbor interactions and a mere sampling measurement in a fixed basis. The correctness of the final-state preparation in each scheme is fully efficiently certifiable. We discuss experimental necessities and possible physical architectures, inspired by platforms of cold atoms in optical lattices and a number of others, as well as specific assumptions that enter the complexity-theoretic arguments. This work shows that benchmark settings exhibiting a quantum speedup may require little control, in contrast to universal quantum computing. Thus, our proposal puts a convincing experimental demonstration of a quantum speedup within reach in the near term.

Exploring quantum thermodynamics in continuous measurement of superconducting qubits

NASA Astrophysics Data System (ADS)

Murch, Kater

The extension of thermodynamics into the realm of quantum mechanics, where quantum fluctuations dominate and systems need not occupy definite states, poses unique challenges. Superconducting quantum circuits offer exquisite control over the environment of simple quantum systems allowing the exploration of thermodynamics at the quantum level through measurement and feedback control. We use a superconducting transmon qubit that is resonantly coupled to a waveguide cavity as an effectively one-dimensional quantum emitter. By driving the emitter and detecting the fluorescence with a near-quantum-limited Josephson parametric amplifier, we track the evolution of the quantum state and characterize the work and heat along single quantum trajectories. By using quantum feedback control to compensate for heat exchanged with the emitter's environment we are able to extract the work statistics associated with the quantum evolution and examine fundamental fluctuation theorems in non-equilibrium thermodynamics. This work was supported by the Alfred P. Sloan Foundation, the National Science Foundation, and the Office of Naval Research.

H-theorem in quantum physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less

H-theorem in quantum physics

PubMed Central

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.

2016-01-01

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571

H-theorem in quantum physics

DOE PAGES

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; ...

2016-09-12

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less

Molecular recognition of the environment and mechanisms of the origin of species in quantum-like modeling of evolution.

PubMed

Melkikh, Alexey V; Khrennikov, Andrei

2017-11-01

A review of the mechanisms of speciation is performed. The mechanisms of the evolution of species, taking into account the feedback of the state of the environment and mechanisms of the emergence of complexity, are considered. It is shown that these mechanisms, at the molecular level, cannot work steadily in terms of classical mechanics. Quantum mechanisms of changes in the genome, based on the long-range interaction potential between biologically important molecules, are proposed as one of possible explanation. Different variants of interactions of the organism and environment based on molecular recognition and leading to new species origins are considered. Experiments to verify the model are proposed. This bio-physical study is completed by the general operational model of based on quantum information theory. The latter is applied to model of epigenetic evolution. We briefly present the basics of the quantum-like approach to modeling of bio-informational processes. This approach is illustrated by the quantum-like model of epigenetic evolution. Copyright © 2017 Elsevier Ltd. All rights reserved.

Production of a sterile species: Quantum kinetics

NASA Astrophysics Data System (ADS)

Boyanovsky, D.; Ho, C. M.

2007-10-01

Production of a sterile species is studied within an effective model of active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum kinetic equations for the distribution functions and coherences are obtained from two independent methods: the effective action and the quantum master equation. The decoherence time scale for active-sterile oscillations is τdec=2/Γaa, but the evolution of the distribution functions is determined by the two different time scales associated with the damping rates of the quasiparticle modes in the medium: Γ1=Γaacos⁡2θm; Γ2=Γaasin⁡2θm where Γaa is the interaction rate of the active species in the absence of mixing and θm the mixing angle in the medium. These two time scales are widely different away from Mikheyev-Smirnov-Wolfenstein resonances and preclude the kinetic description of active-sterile production in terms of a simple rate equation. We give the complete set of quantum kinetic equations for the active and sterile populations and coherences and discuss in detail the various approximations. A generalization of the active-sterile transition probability in a medium is provided via the quantum master equation. We derive explicitly the usual quantum kinetic equations in terms of the “polarization vector” and show their equivalence to those obtained from the quantum master equation and effective action.

Entangling two unequal atoms through a common bath

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benatti, F.; Marzolino, U.; Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34014 Trieste

The evolution of two, noninteracting, two-level atoms immersed in a weakly coupled bath can be described by a refined, time-coarse-grained Markovian evolution, still preserving complete positivity. We find that this improved, reduced dynamics is able to entangle the two atoms even when their internal frequencies are unequal, an effect that appears impossible in the standard weak-coupling-limit approach. We study in detail this phenomenon for an environment made of quantum fields.

Quantum many-body dynamics of dark solitons in optical lattices

NASA Astrophysics Data System (ADS)

Mishmash, R. V.; Danshita, I.; Clark, Charles W.; Carr, L. D.

2009-11-01

We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [R. V. Mishmash and L. D. Carr, Phys. Rev. Lett. 103, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system’s natural orbitals.

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits

PubMed Central

Chiesa, Alessandro; Santini, Paolo; Gerace, Dario; Raftery, James; Houck, Andrew A.; Carretta, Stefano

2015-01-01

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model and we numerically simulate the scheme by including the main sources of decoherence. PMID:26563516

Observation of photonic states dynamics in 3-D integrated Fourier circuits

NASA Astrophysics Data System (ADS)

Flamini, Fulvio; Viggianiello, Niko; Giordani, Taira; Bentivegna, Marco; Spagnolo, Nicolò; Crespi, Andrea; Corrielli, Giacomo; Osellame, Roberto; Martin-Delgado, Miguel Angel; Sciarrino, Fabio

2018-07-01

Entanglement is a fundamental resource at the basis of quantum-enhanced performances in several applications, such as quantum algorithms and quantum metrology. In these contexts, Fourier interferometers implement a relevant class of unitary evolutions which can be embedded in a large variety of protocols. For instance, in the single-particle regime it can be adopted to implement the quantum Fourier transform, while in the multi-particle scenario it can be employed to generate quantum states possessing useful entanglement for quantum phase estimation purposes, or as a tool to verify genuine multi-photon interference. In this article, we study experimentally the dynamics of single-photon and two-photon input states during the evolution provided by a 8-mode Fourier transformation, implemented by exploiting a three-dimensional architecture enabled by the femtosecond laser micromachining technology. In such a way, we fabricated three devices to study the evolution after each step of the decomposition. We observe that the probability distributions obey a step-by-step majorization relationship, where the quantum state occupies a progressively larger portion of the Hilbert space. Such behaviour can be related to the majorization principle, which has been conjectured as a necessary condition for quantum speedup.

Dynamic symmetries and quantum nonadiabatic transitions

DOE PAGES

Li, Fuxiang; Sinitsyn, Nikolai A.

2016-05-30

Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between anmore » arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.« less

Time rescaling and pattern formation in biological evolution.

PubMed

Igamberdiev, Abir U

2014-09-01

Biological evolution is analyzed as a process of continuous measurement in which biosystems interpret themselves in the environment resulting in changes of both. This leads to rescaling of internal time (heterochrony) followed by spatial reconstructions of morphology (heterotopy). The logical precondition of evolution is the incompleteness of biosystem's internal description, while the physical precondition is the uncertainty of quantum measurement. The process of evolution is based on perpetual changes in interpretation of information in the changing world. In this interpretation the external biospheric gradients are used for establishment of new features of organization. It is concluded that biological evolution involves the anticipatory epigenetic changes in the interpretation of genetic symbolism which cannot generally be forecasted but can provide canalization of structural transformations defined by the existing organization and leading to predictable patterns of form generation. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Reconstructing quantum entropy production to probe irreversibility and correlations

NASA Astrophysics Data System (ADS)

Gherardini, Stefano; Müller, Matthias M.; Trombettoni, Andrea; Ruffo, Stefano; Caruso, Filippo

2018-07-01

One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state of-the-art trapped-ion platforms.

Universal bounds on the time evolution of entanglement entropy.

PubMed

Avery, Steven G; Paulos, Miguel F

2014-12-05

Using relative entropy, we derive bounds on the time rate of change of geometric entanglement entropy for any relativistic quantum field theory in any dimension. The bounds apply to both mixed and pure states, and may be extended to curved space. We illustrate the bounds in a few examples and comment on potential applications and future extensions.

Quantization of systems with temporally varying discretization. II. Local evolution moves

NASA Astrophysics Data System (ADS)

Höhn, Philipp A.

2014-10-01

Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the Pachner evolution moves of simplicial gravity models, (2) update only a small subset of the dynamical data, (3) change the number of kinematical and physical degrees of freedom, and (4) generate a dynamical (or canonical) coarse graining or refining of the underlying discretization. To systematically explore such local moves and their implications in the quantum theory, this article suitably expands the quantum formalism for global evolution moves, constructed in Paper I [P. A. Höhn, "Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces," J. Math. Phys. 55, 083508 (2014); e-print arXiv:1401.6062 [gr-qc

Watching the Real-time Evolution of a Laser Modified Atom Using Attosecond Pulses

NASA Astrophysics Data System (ADS)

Shivaram, Niranjan; Timmers, Henry; Tong, Xiao-Min; Sandhu, Arvinder

2011-10-01

In the presence of even moderately strong laser fields, atomic states are heavily modified and develop rich structure. Such a laser dressed atom can be described using the Floquet theory in which the laser dressed states called Floquet states are composed of different Fourier components. In this work we use XUV attosecond pulses to excite a He atom from its ground state to near-infrared (NIR) laser dressed Floquet states, which are ionized by the dressing laser field. Quantum interferences between Fourier components of these Floquet states lead to oscillations in He ion yield as a function of time-delay between the XUV and NIR pulses. From the ion yield signal we measure the quantum phase difference between transition matrix elements to two different Fourier components as a function of both time-delay (instantaneous NIR intensity) and NIR pulse peak intensity. These measurements along with information from time-dependent Schrodinger equation simulations enable us to observe the real-time evolution of the laser modified atom as the dominant Floquet state mediating the ionization changes from the 5p Floquet state to the 2p Floquet state with increasing NIR intensity.

New class of photonic quantum error correction codes

NASA Astrophysics Data System (ADS)

Silveri, Matti; Michael, Marios; Brierley, R. T.; Salmilehto, Juha; Albert, Victor V.; Jiang, Liang; Girvin, S. M.

We present a new class of quantum error correction codes for applications in quantum memories, communication and scalable computation. These codes are constructed from a finite superposition of Fock states and can exactly correct errors that are polynomial up to a specified degree in creation and destruction operators. Equivalently, they can perform approximate quantum error correction to any given order in time step for the continuous-time dissipative evolution under these errors. The codes are related to two-mode photonic codes but offer the advantage of requiring only a single photon mode to correct loss (amplitude damping), as well as the ability to correct other errors, e.g. dephasing. Our codes are also similar in spirit to photonic ''cat codes'' but have several advantages including smaller mean occupation number and exact rather than approximate orthogonality of the code words. We analyze how the rate of uncorrectable errors scales with the code complexity and discuss the unitary control for the recovery process. These codes are realizable with current superconducting qubit technology and can increase the fidelity of photonic quantum communication and memories.

Entanglement evolution across a conformal interface

NASA Astrophysics Data System (ADS)

Wen, Xueda; Wang, Yuxuan; Ryu, Shinsei

2018-05-01

For two-dimensional conformal field theories (CFTs) in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from to , where L is the length of the subsystem A, and is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e. a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with , where is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state.

Time evolution of linearized gauge field fluctuations on a real-time lattice

NASA Astrophysics Data System (ADS)

Kurkela, A.; Lappi, T.; Peuron, J.

2016-12-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law.

Morphological evolution of Ge/Si(001) quantum dot rings formed at the rim of wet-etched pits.

PubMed

Grydlik, Martyna; Brehm, Moritz; Schäffler, Friedrich

2012-10-30

We demonstrate the formation of Ge quantum dots in ring-like arrangements around predefined {111}-faceted pits in the Si(001) substrate. We report on the complex morphological evolution of the single quantum dots contributing to the rings by means of atomic force microscopy and demonstrate that by careful adjustment of the epitaxial growth parameters, such rings containing densely squeezed islands can be grown with large spatial distances of up to 5 μm without additional nucleation of randomly distributed quantum dots between the rings.

Quantum speed limit constraints on a nanoscale autonomous refrigerator

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Chiranjib; Misra, Avijit; Bhattacharya, Samyadeb; Pati, Arun Kumar

2018-06-01

Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, however, have attracted a great deal of attention in the past few years. In this paper, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a tradeoff relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called "bounding second order cooling rate" and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second-order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second-order cooling rate. We study the efficiency of the refrigerator at maximum bounding second-order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second-order cooling rate is given by a simple formula resembling the Curzon-Ahlborn relation.

Quantum hydrodynamics: capturing a reactive scattering resonance.

PubMed

Derrickson, Sean W; Bittner, Eric R; Kendrick, Brian K

2005-08-01

The hydrodynamic equations of motion associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a meshless method based upon a moving least-squares approach. An arbitrary Lagrangian-Eulerian frame of reference and a regridding algorithm which adds and deletes computational points are used to maintain a uniform and nearly constant interparticle spacing. The methodology also uses averaged fields to maintain unitary time evolution. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. A new and more robust artificial viscosity algorithm is presented which gives accurate scattering results and is capable of capturing quantum resonances. The methodology is applied to a one-dimensional model chemical reaction that is known to exhibit a quantum resonance. The correlation function approach is used to compute the reactive scattering matrix, reaction probability, and time delay as a function of energy. Excellent agreement is obtained between the scattering results based upon the quantum hydrodynamic approach and those based upon standard quantum mechanics. This is the first clear demonstration of the ability of moving grid approaches to accurately and robustly reproduce resonance structures in a scattering system.

Quench dynamics of a dissipative Rydberg gas in the classical and quantum regimes

NASA Astrophysics Data System (ADS)

Gribben, Dominic; Lesanovsky, Igor; Gutiérrez, Ricardo

2018-01-01

Understanding the nonequilibrium behavior of quantum systems is a major goal of contemporary physics. Much research is currently focused on the dynamics of many-body systems in low-dimensional lattices following a quench, i.e., a sudden change of parameters. Already such a simple setting poses substantial theoretical challenges for the investigation of the real-time postquench quantum dynamics. In classical many-body systems, the Kolmogorov-Mehl-Johnson-Avrami model describes the phase transformation kinetics of a system that is quenched across a first-order phase transition. Here, we show that a similar approach can be applied for shedding light on the quench dynamics of an interacting gas of Rydberg atoms, which has become an important experimental platform for the investigation of quantum nonequilibrium effects. We are able to gain an analytical understanding of the time evolution following a sudden quench from an initial state devoid of Rydberg atoms and identify strikingly different behaviors of the excitation growth in the classical and quantum regimes. Our approach allows us to describe quenches near a nonequilibrium phase transition and provides an approximate analytical solution deep in the quantum domain.

Synergistically enhanced photocatalytic hydrogen evolution performance of ZnCdS by co-loading graphene quantum dots and PdS dual cocatalysts under visible light

NASA Astrophysics Data System (ADS)

Wang, Fang; Su, Yanhong; Min, Shixiong; Li, Yanan; Lei, Yonggang; Hou, Jianhua

2018-04-01

Here, we report that the co-loading of graphene quantum dots (GQDs) and PdS dual cocatalysts on ZnCdS surface achieves a high efficiency photocatalytic H2 evolution under visible light (≥420 nm). The GQDs/ZnCdS/PdS photocatalyst was prepared by a facile two steps: hydrothermal coupling of GQDs on ZnCdS surface followed by an in-situ chemical deposition of PdS. The resulted GQDs/ZnCdS/PdS exhibits a H2 evolution rate of 517 μmol h-1, which is 15, 7, and 1.7 times higher than that of pure ZnCdS, GQDs/ZnCdS, and ZnCdS/PdS, respectively, demonstrating the synergistic effects of GQDs and PdS dual cocatalysts. A high apparent quantum efficiency (AQE) up to 22.4% can be achieved over GQDs/ZnCdS/PdS at 420 nm. GQDs/ZnCdS/PdS also has a relatively good stability. Such a considerable enhancement of photocatalytic activity was attributable to the co-loading of the GQDs and PdS as respective reduction and oxidation cocatalysts, leading to an efficient charge separation and surface reactions.

Separation of Time Scales in a Quantum Newton’s Cradle

DOE PAGES

van den Berg, R.; Wouters, B.; Eliëns, S.; ...

2016-06-01

For strongly repulsive bosons in one dimension, we provide detailed modeling of the Bragg pulse used in quantum Newton's cradle-like settings or in Bragg spectroscopy experiments. By employing the Fermi-Bose mapping for a nite harmonically trapped gas and the Quench Action approach for a thermodynamic system on a ring, we reconstruct the exact post-pulse many-body time evolution of Lieb-Liniger gases in the Tonks-Girardeau limit, together with their changing local density pro le and momentum distribution. Our results display a clear separation of timescales between rapid and trap-insensitive relaxation immediately after the pulse, followed by slow in-trap periodic behaviour.

Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method

NASA Astrophysics Data System (ADS)

Hayata, Tomoya; Hidaka, Yoshimasa; Noumi, Toshifumi; Hongo, Masaru

2015-09-01

We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

Berman, P. R.

1972-01-01

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

The set of triple-resonance sequences with a multiple quantum coherence evolution period

NASA Astrophysics Data System (ADS)

Koźmiński, Wiktor; Zhukov, Igor

2004-12-01

The new pulse sequence building block that relies on evolution of heteronuclear multiple quantum coherences is proposed. The particular chemical shifts are obtained in multiple quadrature, using linear combinations of frequencies taken from spectra measured at different quantum levels. The pulse sequences designed in this way consist of small number of RF-pulses, are as short as possible, and could be applied for determination of coupling constants. The examples presented involve 2D correlations H NCO, H NCA, H N(CO) CA, and H(N) COCA via heteronuclear zero and double coherences, as well as 2D H NCOCA technique with simultaneous evolution of triple and three distinct single quantum coherences. Applications of the new sequences are presented for 13C, 15N-labeled ubiquitin.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tian, Zehua, E-mail: zehuatian@126.com; Wang, Jieci; Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081

We show how the use of entanglement can enhance the precision of the detection of the Unruh effect with an accelerated probe. We use a two-level atom interacting relativistically with a quantum field as the probe, and treat it as an open quantum system to derive the master equation governing its evolution. By means of quantum state discrimination, we detect the accelerated motion of the atom by examining its time evolving state. It turns out that the optimal strategy for the detection of the Unruh effect, to which the accelerated atom is sensitive, involves letting the atom-thermometer equilibrate with themore » thermal bath. However, introducing initial entanglement between the detector and an external degree of freedom leads to an enhancement of the sensitivity of the detector. Also, the maximum precision is attained within finite time, before equilibration takes place.« less

Deterministic Squeezed States with Collective Measurements and Feedback.

PubMed

Cox, Kevin C; Greve, Graham P; Weiner, Joshua M; Thompson, James K

2016-03-04

We demonstrate the creation of entangled, spin-squeezed states using a collective, or joint, measurement and real-time feedback. The pseudospin state of an ensemble of N=5×10^{4} laser-cooled ^{87}Rb atoms is deterministically driven to a specified population state with angular resolution that is a factor of 5.5(8) [7.4(6) dB] in variance below the standard quantum limit for unentangled atoms-comparable to the best enhancements using only unitary evolution. Without feedback, conditioning on the outcome of the joint premeasurement, we directly observe up to 59(8) times [17.7(6) dB] improvement in quantum phase variance relative to the standard quantum limit for N=4×10^{5}  atoms. This is one of the largest reported entanglement enhancements to date in any system.

Photonic simulation of entanglement growth and engineering after a spin chain quench.

PubMed

Pitsios, Ioannis; Banchi, Leonardo; Rab, Adil S; Bentivegna, Marco; Caprara, Debora; Crespi, Andrea; Spagnolo, Nicolò; Bose, Sougato; Mataloni, Paolo; Osellame, Roberto; Sciarrino, Fabio

2017-11-17

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices.

Coherent Optical Memory with High Storage Efficiency and Large Fractional Delay

NASA Astrophysics Data System (ADS)

Chen, Yi-Hsin; Lee, Meng-Jung; Wang, I.-Chung; Du, Shengwang; Chen, Yong-Fan; Chen, Ying-Cheng; Yu, Ite A.

2013-02-01

A high-storage efficiency and long-lived quantum memory for photons is an essential component in long-distance quantum communication and optical quantum computation. Here, we report a 78% storage efficiency of light pulses in a cold atomic medium based on the effect of electromagnetically induced transparency. At 50% storage efficiency, we obtain a fractional delay of 74, which is the best up-to-date record. The classical fidelity of the recalled pulse is better than 90% and nearly independent of the storage time, as confirmed by the direct measurement of phase evolution of the output light pulse with a beat-note interferometer. Such excellent phase coherence between the stored and recalled light pulses suggests that the current result may be readily applied to single photon wave packets. Our work significantly advances the technology of electromagnetically induced transparency-based optical memory and may find practical applications in long-distance quantum communication and optical quantum computation.

Coherent optical memory with high storage efficiency and large fractional delay.

PubMed

Chen, Yi-Hsin; Lee, Meng-Jung; Wang, I-Chung; Du, Shengwang; Chen, Yong-Fan; Chen, Ying-Cheng; Yu, Ite A

2013-02-22

A high-storage efficiency and long-lived quantum memory for photons is an essential component in long-distance quantum communication and optical quantum computation. Here, we report a 78% storage efficiency of light pulses in a cold atomic medium based on the effect of electromagnetically induced transparency. At 50% storage efficiency, we obtain a fractional delay of 74, which is the best up-to-date record. The classical fidelity of the recalled pulse is better than 90% and nearly independent of the storage time, as confirmed by the direct measurement of phase evolution of the output light pulse with a beat-note interferometer. Such excellent phase coherence between the stored and recalled light pulses suggests that the current result may be readily applied to single photon wave packets. Our work significantly advances the technology of electromagnetically induced transparency-based optical memory and may find practical applications in long-distance quantum communication and optical quantum computation.

Adiabatic approximation with exponential accuracy for many-body systems and quantum computation

NASA Astrophysics Data System (ADS)

Lidar, Daniel A.; Rezakhani, Ali T.; Hamma, Alioscia

2009-10-01

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.

Quantum regression theorem and non-Markovianity of quantum dynamics

NASA Astrophysics Data System (ADS)

Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano

2014-08-01

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.

Quantum correlation dynamics in photosynthetic processes assisted by molecular vibrations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giorgi, G.L., E-mail: g.giorgi@inrim.it; Roncaglia, M.; Raffa, F.A.

2015-10-15

During the long course of evolution, nature has learnt how to exploit quantum effects. In fact, recent experiments reveal the existence of quantum processes whose coherence extends over unexpectedly long time and space ranges. In particular, photosynthetic processes in light-harvesting complexes display a typical oscillatory dynamics ascribed to quantum coherence. Here, we consider the simple model where a dimer made of two chromophores is strongly coupled with a quasi-resonant vibrational mode. We observe the occurrence of wide oscillations of genuine quantum correlations, between electronic excitations and the environment, represented by vibrational bosonic modes. Such a quantum dynamics has been unveiledmore » through the calculation of the negativity of entanglement and the discord, indicators widely used in quantum information for quantifying the resources needed to realize quantum technologies. We also discuss the possibility of approximating additional weakly-coupled off-resonant vibrational modes, simulating the disturbances induced by the rest of the environment, by a single vibrational mode. Within this approximation, one can show that the off-resonant bath behaves like a classical source of noise.« less

Development of efficient time-evolution method based on three-term recurrence relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akama, Tomoko, E-mail: a.tomo---s-b-l-r@suou.waseda.jp; Kobayashi, Osamu; Nanbu, Shinkoh, E-mail: shinkoh.nanbu@sophia.ac.jp

The advantage of the real-time (RT) propagation method is a direct solution of the time-dependent Schrödinger equation which describes frequency properties as well as all dynamics of a molecular system composed of electrons and nuclei in quantum physics and chemistry. Its applications have been limited by computational feasibility, as the evaluation of the time-evolution operator is computationally demanding. In this article, a new efficient time-evolution method based on the three-term recurrence relation (3TRR) was proposed to reduce the time-consuming numerical procedure. The basic formula of this approach was derived by introducing a transformation of the operator using the arcsine function.more » Since this operator transformation causes transformation of time, we derived the relation between original and transformed time. The formula was adapted to assess the performance of the RT time-dependent Hartree-Fock (RT-TDHF) method and the time-dependent density functional theory. Compared to the commonly used fourth-order Runge-Kutta method, our new approach decreased computational time of the RT-TDHF calculation by about factor of four, showing the 3TRR formula to be an efficient time-evolution method for reducing computational cost.« less

Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall

DOE Office of Scientific and Technical Information (OSTI.GOV)

Messina, Riccardo; Vasile, Ruggero; Passante, Roberto

2010-12-15

We study the time evolution of the Casimir-Polder force acting on a neutral atom in front of a perfectly conducting plate, when the system starts its unitary evolution from a partially dressed state. We solve the Heisenberg equations for both atomic and field quantum operators, exploiting a series expansion with respect to the electric charge and an iterative technique. After discussing the behavior of the time-dependent force on an initially partially dressed atom, we analyze a possible experimental scheme to prepare the partially dressed state and the observability of this new dynamical effect.

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph

2015-09-01

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension . We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the -faces of the -dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the -faces.

Generalized speed and cost rate in transitionless quantum driving

NASA Astrophysics Data System (ADS)

Xu, Zhen-Yu; You, Wen-Long; Dong, Yu-Li; Zhang, Chengjie; Yang, W. L.

2018-03-01

Transitionless quantum driving, also known as counterdiabatic driving, is a unique shortcut technique to adiabaticity, enabling a fast-forward evolution to the same target quantum states as those in the adiabatic case. However, as nothing is free, the fast evolution is obtained at the cost of stronger driving fields. Here, given the system initially gets prepared in equilibrium states, we construct relations between the dynamical evolution speed and the cost rate of transitionless quantum driving in two scenarios: one that preserves the transitionless evolution for a single energy eigenstate (individual driving), and the other that maintains all energy eigenstates evolving transitionlessly (collective driving). Remarkably, we find that individual driving may cost as much as collective driving, in contrast to the common belief that individual driving is more economical than collective driving in multilevel systems. We then present a potentially practical proposal to demonstrate the above phenomena in a three-level Landau-Zener model using the electronic spin system of a single nitrogen-vacancy center in diamond.

Variety of (d + 1) dimensional cosmological evolutions with and without bounce in a class of LQC-inspired models

NASA Astrophysics Data System (ADS)

Rama, S. Kalyana

2017-08-01

The bouncing evolution of an universe in Loop Quantum Cosmology can be described very well by a set of effective equations, involving a function sin x. Recently, we have generalised these effective equations to (d + 1) dimensions and to any function f( x). Depending on f( x) in these models inspired by Loop Quantum Cosmology, a variety of cosmological evolutions are possible, singular as well as non singular. In this paper, we study them in detail. Among other things, we find that the scale factor a(t) ∝ t^{ 2 q/(2 q - 1) (1 + w) d} for f(x) = x^q, and find explicit Kasner-type solutions if w = 2 q - 1 also. A result which we find particularly fascinating is that, for f(x) = √{x}, the evolution is non singular and the scale factor a( t) grows exponentially at a rate set, not by a constant density, but by a quantum parameter related to the area quantum.

Non-Markovian continuous-time quantum walks on lattices with dynamical noise

NASA Astrophysics Data System (ADS)

Benedetti, Claudia; Buscemi, Fabrizio; Bordone, Paolo; Paris, Matteo G. A.

2016-04-01

We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites, and attention is focused on non-Gaussian telegraph noise, going beyond the usual assumption of fast Gaussian noise. We observe the emergence of two different dynamical behaviors for the walker, corresponding to two opposite noise regimes: slow noise (i.e., strong coupling with the environment) confines the walker into few lattice nodes, while fast noise (weak coupling) induces a transition between quantum and classical diffusion over the lattice. A phase transition between the two dynamical regimes may be observed by tuning the ratio between the autocorrelation time of the noise and the coupling between the walker and the external environment generating the noise. We also address the non-Markovianity of the quantum map by assessing its memory effects, as well as evaluating the information backflow to the system. Our results suggest that the non-Markovian character of the evolution is linked to the dynamical behavior in the slow noise regime, and that fast noise induces a Markovian dynamics for the walker.

Quantum steering and entanglement in three-mode triangle Bose-Hubbard system

NASA Astrophysics Data System (ADS)

Kalaga, J. K.; Leoński, W.; Szczȩśniak, R.

2017-11-01

We consider the possibility of generation steerable states in Bose-Hubbard system composed of three interacting wells in the form of a triangle. We show that although our system still fulfills the monogamy relations, the presence of additional coupling which transforms a chain of wells onto triangle gives a variety of new possibilities for the generation of steerable quantum states. Deriving analytical formulas for the parameters describing steering and bipartite entanglement, we show that interplay between two couplings influences quantum correlations of various types. We compare the time evolution of steering parameters to those describing bipartite entanglement and find the relations between the appearance of maximal entanglement and disappearance of steering effect.

Efficient state initialization by a quantum spectral filtering algorithm

NASA Astrophysics Data System (ADS)

Fillion-Gourdeau, François; MacLean, Steve; Laflamme, Raymond

2017-04-01

An algorithm that initializes a quantum register to a state with a specified energy range is given, corresponding to a quantum implementation of the celebrated Feit-Fleck method. This is performed by introducing a nondeterministic quantum implementation of a standard spectral filtering procedure combined with an apodization technique, allowing for accurate state initialization. It is shown that the implementation requires only two ancilla qubits. A lower bound for the total probability of success of this algorithm is derived, showing that this scheme can be realized using a finite, relatively low number of trials. Assuming the time evolution can be performed efficiently and using a trial state polynomially close to the desired states, it is demonstrated that the number of operations required scales polynomially with the number of qubits. Tradeoffs between accuracy and performance are demonstrated in a simple example: the harmonic oscillator. This algorithm would be useful for the initialization phase of the simulation of quantum systems on digital quantum computers.

Anisotropy-Induced Quantum Interference and Population Trapping between Orthogonal Quantum Dot Exciton States in Semiconductor Cavity Systems

NASA Astrophysics Data System (ADS)

Hughes, Stephen; Agarwal, Girish S.

2017-02-01

We describe how quantum dot semiconductor cavity systems can be engineered to realize anisotropy-induced dipole-dipole coupling between orthogonal dipole states in a single quantum dot. Quantum dots in single-mode cavity structures as well as photonic crystal waveguides coupled to spin states or linearly polarized excitons are considered. We demonstrate how the dipole-dipole coupling can control the radiative decay rate of excitons and form pure entangled states in the long time limit. We investigate both field-free entanglement evolution and coherently pumped exciton regimes, and show how a double-field pumping scenario can completely eliminate the decay of coherent Rabi oscillations and lead to population trapping. In the Mollow triplet regime, we explore the emitted spectra from the driven dipoles and show how a nonpumped dipole can take on the form of a spectral triplet, quintuplet, or a singlet, which has applications for producing subnatural linewidth single photons and more easily accessing regimes of high-field quantum optics and cavity-QED.

Anisotropy-Induced Quantum Interference and Population Trapping between Orthogonal Quantum Dot Exciton States in Semiconductor Cavity Systems.

PubMed

Hughes, Stephen; Agarwal, Girish S

2017-02-10

We describe how quantum dot semiconductor cavity systems can be engineered to realize anisotropy-induced dipole-dipole coupling between orthogonal dipole states in a single quantum dot. Quantum dots in single-mode cavity structures as well as photonic crystal waveguides coupled to spin states or linearly polarized excitons are considered. We demonstrate how the dipole-dipole coupling can control the radiative decay rate of excitons and form pure entangled states in the long time limit. We investigate both field-free entanglement evolution and coherently pumped exciton regimes, and show how a double-field pumping scenario can completely eliminate the decay of coherent Rabi oscillations and lead to population trapping. In the Mollow triplet regime, we explore the emitted spectra from the driven dipoles and show how a nonpumped dipole can take on the form of a spectral triplet, quintuplet, or a singlet, which has applications for producing subnatural linewidth single photons and more easily accessing regimes of high-field quantum optics and cavity-QED.

Fractional quantum mechanics on networks: Long-range dynamics and quantum transport

NASA Astrophysics Data System (ADS)

Riascos, A. P.; Mateos, José L.

2015-11-01

In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schrödinger equation. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. By using the fractional Laplacian matrix of a network, we establish a formalism that combines a long-range dynamics with the quantum superposition of states; this general approach applies to any type of connected undirected networks, including regular, random, and complex networks, and can be implemented from the spectral properties of the Laplacian matrix. We study the fractional dynamics and its capacity to explore the network by means of the transition probability, the average probability of return, and global quantities that characterize the efficiency of this quantum process. As a particular case, we explore analytically these quantities for circulant networks such as rings, interacting cycles, and complete graphs.

Fractional quantum mechanics on networks: Long-range dynamics and quantum transport.

PubMed

Riascos, A P; Mateos, José L

2015-11-01

In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schrödinger equation. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. By using the fractional Laplacian matrix of a network, we establish a formalism that combines a long-range dynamics with the quantum superposition of states; this general approach applies to any type of connected undirected networks, including regular, random, and complex networks, and can be implemented from the spectral properties of the Laplacian matrix. We study the fractional dynamics and its capacity to explore the network by means of the transition probability, the average probability of return, and global quantities that characterize the efficiency of this quantum process. As a particular case, we explore analytically these quantities for circulant networks such as rings, interacting cycles, and complete graphs.

Loop quantum cosmology and singularities.

PubMed

Struyve, Ward

2017-08-15

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

Quantum trilogy: discrete Toda, Y-system and chaos

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-02-01

We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra G, generalizing the previous construction of discrete quantum Liouville theory for the case G  =  A 1. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length L. In addition we also find a ‘discretized extra dimension’ whose width is given by the rank r of G, which decompactifies in the large r limit. For the case of G  =  A N or AN-1(1) , we find a symmetry exchanging L and N under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is quantizations of the so-called Y-system, and the theory can be well described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmüller theory of type A N .

Recoverability in quantum information theory

NASA Astrophysics Data System (ADS)

Wilde, Mark

The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This is based on arXiv:1505.04661, now accepted for publication in Proceedings of the Royal Society A. I acknowledge support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.

Nucleation versus instability race in strained films

NASA Astrophysics Data System (ADS)

Liu, Kailang; Berbezier, Isabelle; David, Thomas; Favre, Luc; Ronda, Antoine; Abbarchi, Marco; Voorhees, Peter; Aqua, Jean-Noël

2017-10-01

Under the generic term "Stranski-Krastanov" are grouped two different growth mechanisms of SiGe quantum dots. They result from the self-organized Asaro-Tiller-Grinfel'd (ATG) instability at low strain, while at high strain, from a stochastic nucleation. While these regimes are well known, we elucidate here the origin of the transition between these two pathways thanks to a joint theoretical and experimental work. Nucleation is described within the master equation framework. By comparing the time scales for ATG instability development and three-dimensional (3D) nucleation onset, we demonstrate that the transition between these two regimes is simply explained by the crossover between their divergent evolutions. Nucleation exhibits a strong exponential deviation at low strain while ATG behaves only algebraically. The associated time scale varies with exp(1 /x4) for nucleation, while it only behaves as 1 /x8 for the ATG instability. Consequently, at high (low) strain, nucleation (instability) occurs faster and inhibits the alternate evolution. It is then this different kinetic evolution which explains the transition from one regime to the other. Such a kinetic view of the transition between these two 3D growth regimes was not provided before. The crossover between nucleation and ATG instability is found to occur both experimentally and theoretically at a Ge composition around 50% in the experimental conditions used here. Varying the experimental conditions and/or the system parameters does not allow us to suppress the transition. This means that the SiGe quantum dots always grow via ATG instability at low strain and nucleation at high strain. This result is important for the self-organization of quantum dots.

Detecting Non-Markovianity of Quantum Evolution via Spectra of Dynamical Maps.

PubMed

Chruściński, Dariusz; Macchiavello, Chiara; Maniscalco, Sabrina

2017-02-24

We provide an analysis on non-Markovian quantum evolution based on the spectral properties of dynamical maps. We introduce the dynamical analog of entanglement witness to detect non-Markovianity and we illustrate its behavior with several instructive examples. It is shown that for several important classes of dynamical maps the corresponding evolution of singular values and/or eigenvalues of the map provides a simple non-Markovianity witness.

Out-of-time-order correlators in finite open systems

NASA Astrophysics Data System (ADS)

Syzranov, S. V.; Gorshkov, A. V.; Galitski, V.

2018-04-01

We study out-of-time-order correlators (OTOCs) of the form for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝∑aie-t /τi+const to a constant value at t →∞ , in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focusing on the case of a two-level system, we calculate microscopically the decay times τi and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

Space and time renormalization in phase transition dynamics

DOE PAGES

Francuz, Anna; Dziarmaga, Jacek; Gardas, Bartłomiej; ...

2016-02-18

Here, when a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time τ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length ξˆ set at the time tˆ=τˆ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigatingmore » an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.« less

Holonomic Quantum Control by Coherent Optical Excitation in Diamond.

PubMed

Zhou, Brian B; Jerger, Paul C; Shkolnikov, V O; Heremans, F Joseph; Burkard, Guido; Awschalom, David D

2017-10-06

Although geometric phases in quantum evolution are historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary single-qubit holonomic gates from a single cycle of nonadiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.

Holonomic Quantum Control by Coherent Optical Excitation in Diamond

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Brian B.; Jerger, Paul C.; Shkolnikov, V. O.

Although geometric phases in quantum evolution are historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary singlequbit holonomic gates from a single cycle of nonadiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.

Use of non-adiabatic geometric phase for quantum computing by NMR.

PubMed

Das, Ranabir; Kumar, S K Karthick; Kumar, Anil

2005-12-01

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.

Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.

PubMed

Belenchia, Alessio; Benincasa, Dionigi M T; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello

2016-04-22

Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.

Stability of Local Quantum Dissipative Systems

NASA Astrophysics Data System (ADS)

Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David

2015-08-01

Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time that scales logarithmically with the system size. The proof relies on Lieb-Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates, which may not preserve detailed balance.

Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe

NASA Astrophysics Data System (ADS)

Moriconi, Riccardo; Montani, Giovanni; Capozziello, Salvatore

2016-07-01

We analyze the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach, the cosmological singularity is removed in correspondence to a positive defined value of the dust energy density. Furthermore, the quantum big bounce is connected to the Universe's turning point via a well-defined semiclassical limit. Then we can reliably infer that the proposed scenario is compatible with a cyclical universe picture. We also show how, when the contribution of the dust energy density is sufficiently high, the proposed scenario can be extended to the Bianchi IX cosmology and therefore how it can be regarded as a paradigm for the generic cosmological model. Finally, we investigate the origin of the observed cutoff on the cosmological dynamics, demonstrating how the big-bounce evolution can be mimicked by the same semiclassical scenario, where the negative cosmological constant is replaced via a polymer discretization of the Universe's volume. A direct proportionality law between these two parameters is then established.

Adiabatic quantum computing with spin qubits hosted by molecules.

PubMed

Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji

2015-01-28

A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.

Spin-electron acoustic soliton and exchange interaction in separate spin evolution quantum plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru

Separate spin evolution quantum hydrodynamics is generalized to include the Coulomb exchange interaction, which is considered as interaction between the spin-down electrons being in quantum states occupied by one electron. The generalized model is applied to study the non-linear spin-electron acoustic waves. Existence of the spin-electron acoustic soliton is demonstrated. Contributions of concentration, spin polarization, and exchange interaction to the properties of the spin electron acoustic soliton are studied.

Quantum Metropolis sampling.

PubMed

Temme, K; Osborne, T J; Vollbrecht, K G; Poulin, D; Verstraete, F

2011-03-03

The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.

Quantum microbiology.

PubMed

Trevors, J T; Masson, L

2011-01-01

During his famous 1943 lecture series at Trinity College Dublin, the reknown physicist Erwin Schrodinger discussed the failure and challenges of interpreting life by classical physics alone and that a new approach, rooted in Quantum principles, must be involved. Quantum events are simply a level of organization below the molecular level. This includes the atomic and subatomic makeup of matter in microbial metabolism and structures, as well as the organic, genetic information code of DNA and RNA. Quantum events at this time do not elucidate, for example, how specific genetic instructions were first encoded in an organic genetic code in microbial cells capable of growth and division, and its subsequent evolution over 3.6 to 4 billion years. However, due to recent technological advances, biologists and physicists are starting to demonstrate linkages between various quantum principles like quantum tunneling, entanglement and coherence in biological processes illustrating that nature has exerted some level quantum control to optimize various processes in living organisms. In this article we explore the role of quantum events in microbial processes and endeavor to show that after nearly 67 years, Schrödinger was prophetic and visionary in his view of quantum theory and its connection with some of the fundamental mechanisms of life.

Underwater sonar image detection: A combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm.

PubMed

Wang, Xingmei; Liu, Shu; Liu, Zhipeng

2017-01-01

This paper proposes a combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm to detect underwater objects in sonar images. Specifically, for the first time, the problem of inappropriate filtering degree parameter which commonly occurs in non-local spatial information and seriously affects the denoising performance in sonar images, was solved with the method utilizing a novel filtering degree parameter. Then, a quantum-inspired shuffled frog leaping algorithm based on new search mechanism (QSFLA-NSM) is proposed to precisely and quickly detect sonar images. Each frog individual is directly encoded by real numbers, which can greatly simplify the evolution process of the quantum-inspired shuffled frog leaping algorithm (QSFLA). Meanwhile, a fitness function combining intra-class difference with inter-class difference is adopted to evaluate frog positions more accurately. On this basis, recurring to an analysis of the quantum-behaved particle swarm optimization (QPSO) and the shuffled frog leaping algorithm (SFLA), a new search mechanism is developed to improve the searching ability and detection accuracy. At the same time, the time complexity is further reduced. Finally, the results of comparative experiments using the original sonar images, the UCI data sets and the benchmark functions demonstrate the effectiveness and adaptability of the proposed method.

Underwater sonar image detection: A combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm

PubMed Central

Liu, Zhipeng

2017-01-01

This paper proposes a combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm to detect underwater objects in sonar images. Specifically, for the first time, the problem of inappropriate filtering degree parameter which commonly occurs in non-local spatial information and seriously affects the denoising performance in sonar images, was solved with the method utilizing a novel filtering degree parameter. Then, a quantum-inspired shuffled frog leaping algorithm based on new search mechanism (QSFLA-NSM) is proposed to precisely and quickly detect sonar images. Each frog individual is directly encoded by real numbers, which can greatly simplify the evolution process of the quantum-inspired shuffled frog leaping algorithm (QSFLA). Meanwhile, a fitness function combining intra-class difference with inter-class difference is adopted to evaluate frog positions more accurately. On this basis, recurring to an analysis of the quantum-behaved particle swarm optimization (QPSO) and the shuffled frog leaping algorithm (SFLA), a new search mechanism is developed to improve the searching ability and detection accuracy. At the same time, the time complexity is further reduced. Finally, the results of comparative experiments using the original sonar images, the UCI data sets and the benchmark functions demonstrate the effectiveness and adaptability of the proposed method. PMID:28542266

Optical vortex knots – one photon at a time

PubMed Central

Tempone-Wiltshire, Sebastien J.; Johnstone, Shaun P.; Helmerson, Kristian

2016-01-01

Feynman described the double slit experiment as “a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which has in it the heart of quantum mechanics”. The double-slit experiment, performed one photon at a time, dramatically demonstrates the particle-wave duality of quantum objects by generating a fringe pattern corresponding to the interference of light (a wave phenomenon) from two slits, even when there is only one photon (a particle) at a time passing through the apparatus. The particle-wave duality of light should also apply to complex three dimensional optical fields formed by multi-path interference, however, this has not been demonstrated. Here we observe particle-wave duality of a three dimensional field by generating a trefoil optical vortex knot – one photon at a time. This result demonstrates a fundamental physical principle, that particle-wave duality implies interference in both space (between spatially distinct modes) and time (through the complex evolution of the superposition of modes), and has implications for topologically entangled single photon states, orbital angular momentum multiplexing and topological quantum computing. PMID:27087642

Entropic uncertainty relation of a two-qutrit Heisenberg spin model in nonuniform magnetic fields and its dynamics under intrinsic decoherence

NASA Astrophysics Data System (ADS)

Zhang, Zuo-Yuan; Wei, DaXiu; Liu, Jin-Ming

2018-06-01

The precision of measurements for two incompatible observables in a physical system can be improved with the assistance of quantum memory. In this paper, we investigate the quantum-memory-assisted entropic uncertainty relation for a spin-1 Heisenberg model in the presence of external magnetic fields, the systemic quantum entanglement (characterized by the negativity) is analyzed as contrast. Our results show that for the XY spin chain in thermal equilibrium, the entropic uncertainty can be reduced by reinforcing the coupling between the two particles or decreasing the temperature of the environment. At zero-temperature, the strong magnetic field can result in the growth of the entropic uncertainty. Moreover, in the Ising case, the variation trends of the uncertainty are relied on the choices of anisotropic parameters. Taking the influence of intrinsic decoherence into account, we find that the strong coupling accelerates the inflation of the uncertainty over time, whereas the high magnetic field contributes to its reduction during the temporal evolution. Furthermore, we also verify that the evolution behavior of the entropic uncertainty is roughly anti-correlated with that of the entanglement in the whole dynamical process. Our results could offer new insights into quantum precision measurement for the high spin solid-state systems.

The quantum matrix and information from the hydrocarbon oil molecule

NASA Astrophysics Data System (ADS)

Seyful-Mulyukov, R. B.

2016-03-01

The quantum matrix of the hydrocarbon (HC) molecule is substantiated. On the basis of its properties and behavior, the genesis of oil is explained as a process of self-evolution of oil and preservation of molecules of different composition and generation time. Individual HC molecules are generated in nanoseconds, and the period of the genesis of oil is comparable with that of migration of the HC fluid from the mantle to the deposit. A model of subatomic abiogenic genesis of oil is presented. Hydrocarbon (HC) molecules of various structure and composition are formed due to interaction of the valency electron orbitals of C and H atoms, the elemental particles of which are quantum objects and carriers of information. On the basis of this, the term quantum matrix of the HC molecule, the properties and behavior of which explain the genesis of oil as a process of its self-evolution and preservation of the molecules of various composition and the period of generation of oil, is substantiated. It is proved that individual HC molecules are generated within nanoseconds and the period of origin of the entire assemblage of more than 500 molecules of oil of various types is comparable with the period of migration of the HC fluid from the mantle to the deposit.

Applications of fidelity measures to complex quantum systems

PubMed Central

2016-01-01

We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular–chaotic phase space. PMID:27140967

Implementation and characterization of active feed-forward for deterministic linear optics quantum computing

NASA Astrophysics Data System (ADS)

Böhi, P.; Prevedel, R.; Jennewein, T.; Stefanov, A.; Tiefenbacher, F.; Zeilinger, A.

2007-12-01

In general, quantum computer architectures which are based on the dynamical evolution of quantum states, also require the processing of classical information, obtained by measurements of the actual qubits that make up the computer. This classical processing involves fast, active adaptation of subsequent measurements and real-time error correction (feed-forward), so that quantum gates and algorithms can be executed in a deterministic and hence error-free fashion. This is also true in the linear optical regime, where the quantum information is stored in the polarization state of photons. The adaptation of the photon’s polarization can be achieved in a very fast manner by employing electro-optical modulators, which change the polarization of a trespassing photon upon appliance of a high voltage. In this paper we discuss techniques for implementing fast, active feed-forward at the single photon level and we present their application in the context of photonic quantum computing. This includes the working principles and the characterization of the EOMs as well as a description of the switching logics, both of which allow quantum computation at an unprecedented speed.

Hidden edge Dirac point and robust quantum edge transport in InAs/GaSb quantum wells

NASA Astrophysics Data System (ADS)

Li, Chang-An; Zhang, Song-Bo; Shen, Shun-Qing

2018-01-01

The robustness of quantum edge transport in InAs/GaSb quantum wells in the presence of magnetic fields raises an issue on the fate of topological phases of matter under time-reversal symmetry breaking. A peculiar band structure evolution in InAs/GaSb quantum wells is revealed: the electron subbands cross the heavy hole subbands but anticross the light hole subbands. The topologically protected band crossing point (Dirac point) of the helical edge states is pulled to be close to and even buried in the bulk valence bands when the system is in a deeply inverted regime, which is attributed to the existence of the light hole subbands. A sizable Zeeman energy gap verified by the effective g factors of edge states opens at the Dirac point by an in-plane or perpendicular magnetic field; however, it can also be hidden in the bulk valance bands. This provides a plausible explanation for the recent observation on the robustness of quantum edge transport in InAs/GaSb quantum wells subjected to strong magnetic fields.

Black holes as parts of entangled systems

NASA Astrophysics Data System (ADS)

Basini, G.; Capozziello, S.; Longo, G.

A possible link between EPR-type quantum phenomena and astrophysical objects like black holes, under a new general definition of entanglement, is established. A new approach, involving backward time evolution and topology changes, is presented bringing to a definition of the system black hole-worm hole-white hole as an entangled system.

Quantum and classical ripples in graphene

NASA Astrophysics Data System (ADS)

Hašík, Juraj; Tosatti, Erio; MartoÅák, Roman

2018-04-01

Thermal ripples of graphene are well understood at room temperature, but their quantum counterparts at low temperatures are in need of a realistic quantitative description. Here we present atomistic path-integral Monte Carlo simulations of freestanding graphene, which show upon cooling a striking classical-quantum evolution of height and angular fluctuations. The crossover takes place at ever-decreasing temperatures for ever-increasing wavelengths so that a completely quantum regime is never attained. Zero-temperature quantum graphene is flatter and smoother than classical graphene at large scales yet rougher at short scales. The angular fluctuation distribution of the normals can be quantitatively described by coexistence of two Gaussians, one classical strongly T -dependent and one quantum about 2° wide, of zero-point character. The quantum evolution of ripple-induced height and angular spread should be observable in electron diffraction in graphene and other two-dimensional materials, such as MoS2, bilayer graphene, boron nitride, etc.

Quantum robots and environments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, P.

1998-08-01

Quantum robots and their interactions with environments of quantum systems are described, and their study justified. A quantum robot is a mobile quantum system that includes an on-board quantum computer and needed ancillary systems. Quantum robots carry out tasks whose goals include specified changes in the state of the environment, or carrying out measurements on the environment. Each task is a sequence of alternating computation and action phases. Computation phase activites include determination of the action to be carried out in the next phase, and recording of information on neighborhood environmental system states. Action phase activities include motion of themore » quantum robot and changes in the neighborhood environment system states. Models of quantum robots and their interactions with environments are described using discrete space and time. A unitary step operator T that gives the single time step dynamics is associated with each task. T=T{sub a}+T{sub c} is a sum of action phase and computation phase step operators. Conditions that T{sub a} and T{sub c} should satisfy are given along with a description of the evolution as a sum over paths of completed phase input and output states. A simple example of a task{emdash}carrying out a measurement on a very simple environment{emdash}is analyzed in detail. A decision tree for the task is presented and discussed in terms of the sums over phase paths. It is seen that no definite times or durations are associated with the phase steps in the tree, and that the tree describes the successive phase steps in each path in the sum over phase paths. {copyright} {ital 1998} {ital The American Physical Society}« less

Understanding Hawking radiation in the framework of open quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu Hongwei; Zhang Jialin

2008-01-15

We study the Hawking radiation in the framework of open quantum systems by examining the time evolution of a detector (modeled by a two-level atom) interacting with vacuum massless scalar fields. The dynamics of the detector is governed by a master equation obtained by tracing over the field degrees of freedom from the complete system. The nonunitary effects are studied by analyzing the time behavior of a particular observable of the detector, i.e., its admissible state, in the Unruh, Hartle-Hawking, as well as Boulware vacua outside a Schwarzschild black hole. We find that the detector in both the Unruh andmore » Hartle-Hawking vacua would spontaneously excite with a nonvanishing probability the same as what one would obtain if there is thermal radiation at the Hawking temperature from the black hole, thus reproducing the basic results concerning the Hawking effect in the framework of open quantum systems.« less

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

NASA Astrophysics Data System (ADS)

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin

2018-03-01

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter ɛ. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

Finite-size effect on optimal efficiency of heat engines.

PubMed

Tajima, Hiroyasu; Hayashi, Masahito

2017-07-01

The optimal efficiency of quantum (or classical) heat engines whose heat baths are n-particle systems is given by the strong large deviation. We give the optimal work extraction process as a concrete energy-preserving unitary time evolution among the heat baths and the work storage. We show that our optimal work extraction turns the disordered energy of the heat baths to the ordered energy of the work storage, by evaluating the ratio of the entropy difference to the energy difference in the heat baths and the work storage, respectively. By comparing the statistical mechanical optimal efficiency with the macroscopic thermodynamic bound, we evaluate the accuracy of the macroscopic thermodynamics with finite-size heat baths from the statistical mechanical viewpoint. We also evaluate the quantum coherence effect on the optimal efficiency of the cycle processes without restricting their cycle time by comparing the classical and quantum optimal efficiencies.

Real-Time Reciprocal Space Mapping of Nano-Islands Induced by Quantum Confinement

NASA Astrophysics Data System (ADS)

Hong, Hawoong; Gray, Aaron; Chiang, T.-C.

2011-01-01

The effects of quantum confinement have been observed pronouncedly in the island morphology of Pb thin films. The evolution of these nano-islands on Si (111)-(7 × 7) and sapphire (001) surfaces has been studied with a new X-ray diffraction method. A charge-coupled device (CCD) camera was used to collect two- and three-dimensional (2-D and 3-D, respectively) maps of the surface X-ray diffraction in real time. Large ranges of the reflectivity curves, with rocking curves at every point on the reflectivity curves, could be measured continuously in a relatively short amount of time. The abundance of information from 2-D k-space maps reveals clear changes in the growth modes of these thin Pb films. With the 3-D extension of this method, it was possible to observe the ordering of the islands. The islands maintain a nearly uniform interisland distance but lack any angular correlation. The interisland ordering is correlated well with the development of "magic" island heights caused by quantum confinement.

Single particle nonlocality, geometric phases and time-dependent boundary conditions

NASA Astrophysics Data System (ADS)

Matzkin, A.

2018-03-01

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

Real time evolution at finite temperatures with operator space matrix product states

NASA Astrophysics Data System (ADS)

Pižorn, Iztok; Eisler, Viktor; Andergassen, Sabine; Troyer, Matthias

2014-07-01

We propose a method to simulate the real time evolution of one-dimensional quantum many-body systems at finite temperature by expressing both the density matrices and the observables as matrix product states. This allows the calculation of expectation values and correlation functions as scalar products in operator space. The simulations of density matrices in inverse temperature and the local operators in the Heisenberg picture are independent and result in a grid of expectation values for all intermediate temperatures and times. Simulations can be performed using real arithmetics with only polynomial growth of computational resources in inverse temperature and time for integrable systems. The method is illustrated for the XXZ model and the single impurity Anderson model.

Electron quantum dynamics in atom-ion interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sabzyan, H., E-mail: sabzyan@sci.ui.ac.ir; Jenabi, M. J.

2016-04-07

Electron transfer (ET) process and its dependence on the system parameters are investigated by solving two-dimensional time-dependent Schrödinger equation numerically using split operator technique. Evolution of the electron wavepacket occurs from the one-electron species hydrogen atom to another bare nucleus of charge Z > 1. This evolution is quantified by partitioning the simulation box and defining regional densities belonging to the two nuclei of the system. It is found that the functional form of the time-variations of these regional densities and the extent of ET process depend strongly on the inter-nuclear distance and relative values of the nuclear charges, whichmore » define the potential energy surface governing the electron wavepacket evolution. Also, the initial electronic state of the single-electron atom has critical effect on this evolution and its consequent (partial) electron transfer depending on its spreading extent and orientation with respect to the inter-nuclear axis.« less

Better late than never: information retrieval from black holes.

PubMed

Braunstein, Samuel L; Pirandola, Stefano; Życzkowski, Karol

2013-03-08

We show that, in order to preserve the equivalence principle until late times in unitarily evaporating black holes, the thermodynamic entropy of a black hole must be primarily entropy of entanglement across the event horizon. For such black holes, we show that the information entering a black hole becomes encoded in correlations within a tripartite quantum state, the quantum analogue of a one-time pad, and is only decoded into the outgoing radiation very late in the evaporation. This behavior generically describes the unitary evaporation of highly entangled black holes and requires no specially designed evolution. Our work suggests the existence of a matter-field sum rule for any fundamental theory.

Computational Role of Tunneling in a Programmable Quantum Annealer

NASA Technical Reports Server (NTRS)

Boixo, Sergio; Smelyanskiy, Vadim; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Amin, Mohammad; Mohseni, Masoud; Denchev, Vasil S.; Neven, Hartmut

2016-01-01

Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

The weak coupling limit as a quantum functional central limit

NASA Astrophysics Data System (ADS)

Accardi, L.; Frigerio, A.; Lu, Y. G.

1990-08-01

We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.

Linear Optics Simulation of Quantum Non-Markovian Dynamics

PubMed Central

Chiuri, Andrea; Greganti, Chiara; Mazzola, Laura; Paternostro, Mauro; Mataloni, Paolo

2012-01-01

The simulation of open quantum dynamics has recently allowed the direct investigation of the features of system-environment interaction and of their consequences on the evolution of a quantum system. Such interaction threatens the quantum properties of the system, spoiling them and causing the phenomenon of decoherence. Sometimes however a coherent exchange of information takes place between system and environment, memory effects arise and the dynamics of the system becomes non-Markovian. Here we report the experimental realisation of a non-Markovian process where system and environment are coupled through a simulated transverse Ising model. By engineering the evolution in a photonic quantum simulator, we demonstrate the role played by system-environment correlations in the emergence of memory effects. PMID:23236588

Quantum gates with controlled adiabatic evolutions

NASA Astrophysics Data System (ADS)

Hen, Itay

2015-02-01

We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building blocks in the construction of arbitrary "adiabatic circuits," analogously to the manner in which gates are used in the circuit model. One implication of the above construction is that arbitrary classical boolean circuits as well as gate model circuits may be directly translated to adiabatic algorithms with no additional resources or complexities. We show that while these adiabatic algorithms fail to exhibit certain aspects of the inherent fault tolerance of traditional quantum adiabatic algorithms, they may have certain other experimental advantages acting as quantum gates.

Quantum adiabatic computation with a constant gap is not useful in one dimension.

PubMed

Hastings, M B

2009-07-31

We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state. The proof relies on a recently proven area law for such systems, implying the existence of a good matrix product representation of the ground state, combined with an appropriate algorithm to update the matrix product state as the Hamiltonian is changed. This implies that adiabatic evolution with such Hamiltonians is not useful for universal quantum computation. Therefore, adiabatic algorithms which are useful for universal quantum computation either require a spectral gap tending to zero or need to be implemented in more than one dimension (we leave open the question of the computational power of adiabatic simulation with a constant gap in more than one dimension).

Quantum dynamics of thermalizing systems

NASA Astrophysics Data System (ADS)

White, Christopher David; Zaletel, Michael; Mong, Roger S. K.; Refael, Gil

2018-01-01

We introduce a method "DMT" for approximating density operators of 1D systems that, when combined with a standard framework for time evolution (TEBD), makes possible simulation of the dynamics of strongly thermalizing systems to arbitrary times. We demonstrate that the method performs well for both near-equilibrium initial states (Gibbs states with spatially varying temperatures) and far-from-equilibrium initial states, including quenches across phase transitions and pure states.

Controllable continuous evolution of electronic states in a single quantum ring

NASA Astrophysics Data System (ADS)

Chakraborty, Tapash; Manaselyan, Aram; Barseghyan, Manuk; Laroze, David

2018-02-01

An intense terahertz laser field is shown to have a profound effect on the electronic and optical properties of quantum rings where the isotropic and anisotropic quantum rings can now be treated on equal footing. We have demonstrated that in isotropic quantum rings the laser field creates unusual Aharonov-Bohm oscillations that are usually expected in anisotropic rings. Furthermore, we have shown that intense laser fields can restore the isotropic physical properties in anisotropic quantum rings. In principle, all types of anisotropies (structural, effective masses, defects, etc.) can evolve as in isotropic rings in our present approach. Most importantly, we have found a continuous evolution of the energy spectra and intraband optical characteristics of structurally anisotropic quantum rings to those of isotropic rings in a controlled manner with the help of a laser field.

From Classical to Quantum: New Canonical Tools for the Dynamics of Gravity

NASA Astrophysics Data System (ADS)

Höhn, P. A.

2012-05-01

In a gravitational context, canonical methods offer an intuitive picture of the dynamics and simplify an identification of the degrees of freedom. Nevertheless, extracting dynamical information from background independent approaches to quantum gravity is a highly non-trivial challenge. In this thesis, the conundrum of (quantum) gravitational dynamics is approached from two different directions by means of new canonical tools. This thesis is accordingly divided into two parts: In the first part, a general canonical formalism for discrete systems featuring a variational action principle is developed which is equivalent to the covariant formulation following directly from the action. This formalism can handle evolving phase spaces and is thus appropriate for describing evolving lattices. Attention will be devoted to a characterization of the constraints, symmetries and degrees of freedom appearing in such discrete systems which, in the case of evolving phase spaces, is time step dependent. The advantage of this formalism is that it does not depend on the particular discretization and, hence, is suitable for coarse graining procedures. This formalism is applicable to discrete mechanics, lattice field theories and discrete gravity models---underlying some approaches to quantum gravity---and, furthermore, may prove useful for numerical imple mentations. For concreteness, these new tools are employed to formulate Regge Calculus canonically as a theory of the dynamics of discrete hypersurfaces in discrete spacetimes, thereby removing a longstanding obstacle to connecting covariant simplicial gravity models with canonical frameworks. This result is interesting in view of several background independent approaches to quantum gravity. In addition, perturbative expansions around symmetric background solutions of Regge Calculus are studied up to second order. Background gauge modes generically become propagating at second order as a consequence of a symmetry breaking. In the second part of this thesis, the paradigm of relational dynamics is considered. Dynamical observables in gravity are relational. Unfortunately, their construction and evaluation is notoriously difficult, especially in the quantum theory. An effective canonical framework is devised which permits to evaluate the semiclassical relational dynamics of constrained quantum systems by sidestepping technical problems associated with explicit constructions of physical Hilbert spaces. This effective approach is well-geared for addressing the concept of relational evolution in general quantum cosmological models since it (i) allows to depart from idealized relational `clock references’ and, instead, to employ generic degrees of freedom as imperfect relational `clocks’, (ii) enables one to systematically switch between different such `clocks’ and (iii) yields a consistent (temporally) local time evolution with transient observables so long as semiclassicality holds. These techniques are illustrated by toy models and, finally, are applied to a non-integrable cosmological model. It is argued that relational evolution is generically only a transient and semiclassical phenomenon

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free

PubMed Central

Bianconi, Ginestra; Rahmede, Christoph

2015-01-01

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension . We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the -faces of the -dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the -faces. PMID:26356079

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free.

PubMed

Bianconi, Ginestra; Rahmede, Christoph

2015-09-10

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension d. We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the δ-faces of the d-dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the δ-faces.

Dynamical maps, quantum detailed balance, and the Petz recovery map

NASA Astrophysics Data System (ADS)

Alhambra, Álvaro M.; Woods, Mischa P.

2017-08-01

Markovian master equations (formally known as quantum dynamical semigroups) can be used to describe the evolution of a quantum state ρ when in contact with a memoryless thermal bath. This approach has had much success in describing the dynamics of real-life open quantum systems in the laboratory. Such dynamics increase the entropy of the state ρ and the bath until both systems reach thermal equilibrium, at which point entropy production stops. Our main result is to show that the entropy production at time t is bounded by the relative entropy between the original state and the state at time 2 t . The bound puts strong constraints on how quickly a state can thermalize, and we prove that the factor of 2 is tight. The proof makes use of a key physically relevant property of these dynamical semigroups, detailed balance, showing that this property is intimately connected with the field of recovery maps from quantum information theory. We envisage that the connections made here between the two fields will have further applications. We also use this connection to show that a similar relation can be derived when the fixed point is not thermal.

Two-walker discrete-time quantum walks on the line with percolation

NASA Astrophysics Data System (ADS)

Rigovacca, L.; di Franco, C.

2016-02-01

One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles performing a quantum walk on the line when the possibility of lattice imperfections, in the form of missing links, is considered. We investigate two regimes, statical and dynamical percolation, that correspond to different time scales for the imperfections evolution with respect to the quantum-walk one. By studying the qualitative behaviour of three two-particle quantities for different probabilities of having missing bonds, we argue that the chosen symmetry under particle-exchange of the input state strongly affects the output of the walk, even in noisy and highly non-ideal regimes. We provide evidence against the possibility of gathering information about the walkers indistinguishability from the observation of bunching phenomena in the output distribution, in all those situations that require a comparison between averaged quantities. Although the spread of the walk is not substantially changed by the addition of a second particle, we show that the presence of multiple walkers can be beneficial for a procedure to estimate the probability of having a broken link.

Tachyon field in loop quantum cosmology: Inflation and evolution picture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xiong Huaui; Zhu Jianyang

2007-04-15

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universne through a bounce in the high energy region. We show that this is always true in tachyon matter LQC. Differing from the classical Friedman-Robertson-Walker (FRW) cosmology, the super inflation can appear in the tachyon matter LQC; furthermore, the inflation can be extended to the region where classical inflation stops. Using the numerical method, we give an evolution picture of the tachyon field with an exponential potential in the context of LQC. It indicates that the quantum dynamical solutions have the same attractive behavior as the classical solutions do. Themore » whole evolution of the tachyon field is that in the distant past, the tachyon field--being in the contracting cosmology--accelerates to climb up the potential hill with a negative velocity; then at the boundary the tachyon field is bounced into an expanding universe with positive velocity rolling down to the bottom of the potential. In the slow roll limit, we compare the quantum inflation with the classical case in both an analytic and a numerical way.« less

Quantum Tunnelling to the Origin and Evolution of Life

PubMed Central

Trixler, Frank

2013-01-01

Quantum tunnelling is a phenomenon which becomes relevant at the nanoscale and below. It is a paradox from the classical point of view as it enables elementary particles and atoms to permeate an energetic barrier without the need for sufficient energy to overcome it. Tunnelling might seem to be an exotic process only important for special physical effects and applications such as the Tunnel Diode, Scanning Tunnelling Microscopy (electron tunnelling) or Near-field Optical Microscopy operating in photon tunnelling mode. However, this review demonstrates that tunnelling can do far more, being of vital importance for life: physical and chemical processes which are crucial in theories about the origin and evolution of life can be traced directly back to the effects of quantum tunnelling. These processes include the chemical evolution in stellar interiors and within the cold interstellar medium, prebiotic chemistry in the atmosphere and subsurface of planetary bodies, planetary habitability via insolation and geothermal heat as well as the function of biomolecular nanomachines. This review shows that quantum tunnelling has many highly important implications to the field of molecular and biological evolution, prebiotic chemistry and astrobiology. PMID:24039543

Consequences of elastic anisotropy in patterned substrate heteroepitaxy.

PubMed

Dixit, Gopal Krishna; Ranganathan, Madhav

2018-06-13

The role of elastic anisotropy on quantum dot formation and evolution on a pre-patterned substrate is evaluated within the framework of a continuum model. We first extend the formulation for surface evolution to take elastic anisotropy into account. Using a small slope approximation, we derive the evolution equation and show how it can be numerically implemented up to linear and second order for stripe and egg-carton patterned substrates using an accurate and efficient procedure. The semi--infinite nature of the substrate is used to solve the elasticity problem subject to other boundary conditions at the free surface and at the film--substrate interface. The positioning of the quantum dots with respect to the peaks and valleys of the pattern is explained by a competition between the length scale of the pattern and the wavelength of the Asaro--Tiller--Grinfeld instability, which is also affected by the elastic anisotropy. The alignment of dots is affected by a competition between the elastic anisotropy of the film and the pattern orientation. A domain of pattern inversion, wherein the quantum dots form exclusively in the valleys of the patterns is identified as a function of the average film thickness and the elastic anisotropy, and the time--scale for this inversion as function of height is analyzed. © 2018 IOP Publishing Ltd.

Variational mixed quantum/semiclassical simulation of dihalogen guest and rare-gas solid host dynamics

NASA Astrophysics Data System (ADS)

Cheng, Xiaolu; Cina, Jeffrey A.

2014-07-01

A variational mixed quantum-semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested, and used to simulate the temporal evolution of nonstationary states of the internal molecular and surrounding medium degrees of freedom. In this theory, termed the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) method, the system is treated fully quantum mechanically while Gaussian wave packets are used for the bath degrees of freedom. An approximate time-dependent wave function of the entire model is obtained instead of just a reduced system density matrix, so the theory enables the analysis of the entangled system and bath dynamics that ensues following initial displacement of the internal-molecular (system) coordinate from its equilibrium position. The norm- and energy-conserving properties of the propagation of our trial wave function are natural consequences of the Dirac-Frenkel-McLachlan variational principle. The variational approach also stabilizes the time evolution in comparison to the same ansatz propagated under a previously employed locally quadratic approximation to the bath potential and system-bath interaction terms in the bath-parameter equations of motion. Dynamics calculations are carried out for molecular iodine in a 2D krypton lattice that reveal both the time-course of vibrational decoherence and the details of host-atom motion accompanying energy dissipation and dephasing. This work sets the stage for the comprehensive simulation of ultrafast time-resolved optical experiments on small molecules in low-temperature solids.

Environment-Assisted Speed-up of the Field Evolution in Cavity Quantum Electrodynamics

DOE PAGES

Cimmarusti, A. D.; Yan, Z.; Patterson, B. D.; ...

2015-06-11

We measure the quantum speed of the state evolution of the field in a weakly-driven optical cavity QED system. To this end, the mode of the electromagnetic field is considered as a quantum system of interest with a preferential coupling to a tunable environment: the atoms. By controlling the environment, i.e., changing the number of atoms coupled to the optical cavity mode, an environment assisted speed-up is realized: the quantum speed of the state re-population in the optical cavity increases with the coupling strength between the optical cavity mode and this non-Markovian environment (the number of atoms).

Wave packet dynamics, time scales and phase diagram in the IBM-Lipkin-Meshkov-Glick model

NASA Astrophysics Data System (ADS)

Castaños, Octavio; de los Santos, Francisco; Yáñez, Rafael; Romera, Elvira

2018-02-01

We derive the phase diagram of a scalar two-level boson model by studying the equilibrium and stability properties of its energy surface. The plane of control parameters is enlarged with respect to previous studies. We then analyze the time evolution of wave packets centered around the ground state at various quantum phase transition boundary lines. In particular, classical and revival times are computed numerically.

On the theory of Brownian motion with the Alder-Wainwright effect

NASA Astrophysics Data System (ADS)

Okabe, Yasunori

1986-12-01

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

Compiling Planning into Quantum Optimization Problems: A Comparative Study

DTIC Science & Technology

2015-06-07

and Sipser, M. 2000. Quantum computation by adiabatic evolution. arXiv:quant- ph/0001106. Fikes, R. E., and Nilsson, N. J. 1972. STRIPS: A new...become available: quantum annealing. Quantum annealing is one of the most accessible quantum algorithms for a computer sci- ence audience not versed...in quantum computing because of its close ties to classical optimization algorithms such as simulated annealing. While large-scale universal quantum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Apel, V.M.; Curilef, S.; Plastino, A.R., E-mail: arplastino@unnoba.edu.ar

We explore the entanglement-related features exhibited by the dynamics of a composite quantum system consisting of a particle and an apparatus (here referred to as the “pointer”) that measures the position of the particle. We consider measurements of finite duration, and also the limit case of instantaneous measurements. We investigate the time evolution of the quantum entanglement between the particle and the pointer, with special emphasis on the final entanglement associated with the limit case of an impulsive interaction. We consider entanglement indicators based on the expectation values of an appropriate family of observables, and also an entanglement measure computedmore » on particular exact analytical solutions of the particle–pointer Schrödinger equation. The general behavior exhibited by the entanglement indicators is consistent with that shown by the entanglement measure evaluated on particular analytical solutions of the Schrödinger equation. In the limit of instantaneous measurements the system’s entanglement dynamics corresponds to that of an ideal quantum measurement process. On the contrary, we show that the entanglement evolution corresponding to measurements of finite duration departs in important ways from the behavior associated with ideal measurements. In particular, highly localized initial states of the particle lead to highly entangled final states of the particle–pointer system. This indicates that the above mentioned initial states, in spite of having an arbitrarily small position uncertainty, are not left unchanged by a finite-duration position measurement process. - Highlights: • We explore entanglement features of a quantum position measurement. • We consider instantaneous and finite-duration measurements. • We evaluate the entanglement of exact time-dependent particle–pointer states.« less

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

NASA Technical Reports Server (NTRS)

Deutsch, Ivan H.; Garrison, John C.

1992-01-01

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Array of nanoparticles coupling with quantum-dot: Lattice plasmon quantum features

NASA Astrophysics Data System (ADS)

Salmanogli, Ahmad; Gecim, H. Selcuk

2018-06-01

In this study, we analyze the interaction of lattice plasmon with quantum-dot in order to mainly examine the quantum features of the lattice plasmon containing the photonic/plasmonic properties. Despite optical properties of the localized plasmon, the lattice plasmon severely depends on the array geometry, which may influence its quantum features such as uncertainty and the second-order correlation function. To investigate this interaction, we consider a closed system containing an array of the plasmonic nanoparticles and quantum-dot. We analyze this system with full quantum theory by which the array electric far field is quantized and the strength coupling of the quantum-dot array is analytically calculated. Moreover, the system's dynamics are evaluated and studied via the Heisenberg-Langevin equations to attain the system optical modes. We also analytically examine the Purcell factor, which shows the effect of the lattice plasmon on the quantum-dot spontaneous emission. Finally, the lattice plasmon uncertainty and its time evolution of the second-order correlation function at different spatial points are examined. These parameters are dramatically affected by the retarded field effect of the array nanoparticles. We found a severe quantum fluctuation at points where the lattice plasmon occurs, suggesting that the lattice plasmon photons are correlated.

Equilibration in one-dimensional quantum hydrodynamic systems

NASA Astrophysics Data System (ADS)

Sotiriadis, Spyros

2017-10-01

We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time steady state is inherently connected to the presence of ballistically moving localised excitations. When such excitations are present, the system retains memory of initial correlations up to infinite times, thus evading decoherence. We demonstrate this connection in the context of the Luttinger model, the simplest quantum hydrodynamic model, and in the quantum KdV equation. In the standard Luttinger model, memory of all initial correlations is preserved throughout the time evolution up to infinitely large times, as a result of the purely ballistic dynamics. However nonlinear dispersion or interactions, when separately present, lead to spreading and delocalisation that suppress the above effect by eliminating the memory of non-Gaussian correlations. We show that, for any initial state that satisfies sufficient clustering of correlations, the steady state is Gaussian in terms of the bosonised or fermionised fields in the dispersive or interacting case respectively. On the other hand, when dispersion and interaction are simultaneously present, a semiclassical approximation suggests that localisation is restored as the two effects compensate each other and solitary waves are formed. Solitary waves, or simply solitons, are experimentally observed in quantum gases and theoretically predicted based on semiclassical approaches, but the question of their stability at the quantum level remains to a large extent an open problem. We give a general overview on the subject and discuss the relevance of our findings to general out of equilibrium problems. Dedicated to John Cardy on the occasion of his 70th birthday.

Fully Quantum Fluctuation Theorems

NASA Astrophysics Data System (ADS)

Åberg, Johan

2018-02-01

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

Probing quantumness with joint continuous measurements of non-commuting qubit observables

NASA Astrophysics Data System (ADS)

Garcia-Pintos, Luis Pedro; Dressel, Justin

In this talk we consider continuous weak measurements as a means to probe foundational issues in quantum mechanics. We consider the simultaneous monitoring of two noncommuting observables-as recently implemented by the Siddiqi group at UC Berkeley. Contrary to naive expectation, the output of such experiment can be used to simultaneously track the approximate observable dynamics. Despite this seeming realism, we also show that the readouts violate macrorealistic Leggett-Garg inequalities for arbitrarily short temporal correlations, and that the derived inequalities are manifestly violated even in the absence of Hamiltonian evolution. Such violations should indicate the failure of at least one postulate of macrorealism: either physical quantities do not have well defined values at all times, or the measurement process itself disturbs what is being measured. Despite this macrorealism violation, we construct a realistic, but epistemically restricted, model that perfectly emulates both the qubit evolution and the observed noisy signals, thus also emulating the violations.

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Vlijm, R.; Ganahl, M.; Fioretto, D.; Brockmann, M.; Haque, M.; Evertz, H. G.; Caux, J.-S.

2015-12-01

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time-evolution fits on the displacements. The time-evolved block decimation algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

Floquet Supersymmetry

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Hsieh, Timothy H.

2018-05-01

We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical supersymmetry. In particular, we find Floquet analogs of the Witten index that place lower bounds on the degeneracies of states with quasienergies 0 and π . Moreover, we show that in some cases time-reflection symmetry can also interchange fermions and bosons, leading to fermion-boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies 0 and π , which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.

Entanglement loss in molecular quantum-dot qubits due to interaction with the environment.

PubMed

Blair, Enrique P; Tóth, Géza; Lent, Craig S

2018-05-16

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunković-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots.

Entanglement loss in molecular quantum-dot qubits due to interaction with the environment

NASA Astrophysics Data System (ADS)

Blair, Enrique P.; Tóth, Géza; Lent, Craig S.

2018-05-01

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser–Horne–Shimony–Holt (CHSH) and Brukner–Paunković–Rudolph–Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots.

Relaxation versus adiabatic quantum steady-state preparation

NASA Astrophysics Data System (ADS)

Venuti, Lorenzo Campos; Albash, Tameem; Marvian, Milad; Lidar, Daniel; Zanardi, Paolo

2017-04-01

Adiabatic preparation of the ground states of many-body Hamiltonians in the closed-system limit is at the heart of adiabatic quantum computation, but in reality systems are always open. This motivates a natural comparison between, on the one hand, adiabatic preparation of steady states of Lindbladian generators and, on the other hand, relaxation towards the same steady states subject to the final Lindbladian of the adiabatic process. In this work we thus adopt the perspective that the goal is the most efficient possible preparation of such steady states, rather than ground states. Using known rigorous bounds for the open-system adiabatic theorem and for mixing times, we are then led to a disturbing conclusion that at first appears to doom efforts to build physical quantum annealers: relaxation seems to always converge faster than adiabatic preparation. However, by carefully estimating the adiabatic preparation time for Lindbladians describing thermalization in the low-temperature limit, we show that there is, after all, room for an adiabatic speedup over relaxation. To test the analytically derived bounds for the adiabatic preparation time and the relaxation time, we numerically study three models: a dissipative quasifree fermionic chain, a single qubit coupled to a thermal bath, and the "spike" problem of n qubits coupled to a thermal bath. Via these models we find that the answer to the "which wins" question depends for each model on the temperature and the system-bath coupling strength. In the case of the "spike" problem we find that relaxation during the adiabatic evolution plays an important role in ensuring a speedup over the final-time relaxation procedure. Thus, relaxation-assisted adiabatic preparation can be more efficient than both pure adiabatic evolution and pure relaxation.

The Emergence of Temporal Structures in Dynamical Systems

NASA Astrophysics Data System (ADS)

Mainzer, Klaus

2010-10-01

Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

NASA Astrophysics Data System (ADS)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

The Madelung Picture as a Foundation of Geometric Quantum Theory

NASA Astrophysics Data System (ADS)

Reddiger, Maik

2017-10-01

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.

The role of internal dynamics in the coherent evolution of indirect excitons

NASA Astrophysics Data System (ADS)

Grasselli, Federico; Bertoni, Andrea; Goldoni, Guido

2017-08-01

We study the time-dependent quantum scattering of a spatially indirect exciton by an external potential, taking fully into account the relative quantum dynamics of the electron-hole (e-h) pair. Exact calculations for an e-h wave packet show that transfer of energy between centre-of-mass (c.m.) and relative degrees of freedom may result in a genuine correction to the evolution during the scattering and eventually at asymptotic times. We show in experimentally relevant regimes and device configurations, that transmission resonances, tunnelling probabilities, diffraction patterns and wave packet fragmentation of indirect excitons are largely determined by the internal dynamics, and could not be reproduced by point-like dipole models or mean-field calculations. We show that a properly-designed local self-energy potential to be added to the c.m. Hamiltonian embeds the effects of the c.m.-internal motion correlation at a small fraction of the computation load needed for full-propagation calculations. The explicit form of this self-energy emphasises the dominant role of internal virtual transitions in determining scattering coefficients of indirect excitons.

Gradient optimization of finite projected entangled pair states

NASA Astrophysics Data System (ADS)

Liu, Wen-Yuan; Dong, Shao-Jun; Han, Yong-Jian; Guo, Guang-Can; He, Lixin

2017-05-01

Projected entangled pair states (PEPS) methods have been proven to be powerful tools to solve strongly correlated quantum many-body problems in two dimensions. However, due to the high computational scaling with the virtual bond dimension D , in a practical application, PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, frustrated systems. Optimization of the ground state using the imaginary time evolution method with a simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that by combining the imaginary time evolution method with a simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking advantage of massive parallel computing, we can study quantum systems with larger bond dimensions up to D =10 without resorting to any symmetry. Benchmark tests of the method on the J1-J2 model give impressive accuracy compared with exact results.

Composite pulses for interferometry in a thermal cold atom cloud

NASA Astrophysics Data System (ADS)

Dunning, Alexander; Gregory, Rachel; Bateman, James; Cooper, Nathan; Himsworth, Matthew; Jones, Jonathan A.; Freegarde, Tim

2014-09-01

Atom interferometric sensors and quantum information processors must maintain coherence while the evolving quantum wave function is split, transformed, and recombined, but suffer from experimental inhomogeneities and uncertainties in the speeds and paths of these operations. Several error-correction techniques have been proposed to isolate the variable of interest. Here we apply composite pulse methods to velocity-sensitive Raman state manipulation in a freely expanding thermal atom cloud. We compare several established pulse sequences, and follow the state evolution within them. The agreement between measurements and simple predictions shows the underlying coherence of the atom ensemble, and the inversion infidelity in a ˜80μK atom cloud is halved. Composite pulse techniques, especially if tailored for atom interferometric applications, should allow greater interferometer areas, larger atomic samples, and longer interaction times, and hence improve the sensitivity of quantum technologies from inertial sensing and clocks to quantum information processors and tests of fundamental physics.

Single photon detection of 1.5 THz radiation with the quantum capacitance detector

NASA Astrophysics Data System (ADS)

Echternach, P. M.; Pepper, B. J.; Reck, T.; Bradford, C. M.

2018-01-01

Far-infrared spectroscopy can reveal secrets of galaxy evolution and heavy-element enrichment throughout cosmic time, prompting astronomers worldwide to design cryogenic space telescopes for far-infrared spectroscopy. The most challenging aspect is a far-infrared detector that is both exquisitely sensitive (limited by the zodiacal-light noise in a narrow wavelength band, λ/Δλ 1,000) and array-able to tens of thousands of pixels. We present the quantum capacitance detector, a superconducting device adapted from quantum computing applications in which photon-produced free electrons in a superconductor tunnel into a small capacitive island embedded in a resonant circuit. The quantum capacitance detector has an optically measured noise equivalent power below 10-20 W Hz-1/2 at 1.5 THz, making it the most sensitive far-infrared detector ever demonstrated. We further demonstrate individual far-infrared photon counting, confirming the excellent sensitivity and suitability for cryogenic space astrophysics.

A new and trustworthy formalism to compute entropy in quantum systems

NASA Astrophysics Data System (ADS)

Ansari, Mohammad

Entropy is nonlinear in density matrix and as such its evaluation in open quantum system has not been fully understood. Recently a quantum formalism was proposed by Ansari and Nazarov that evaluates entropy using parallel time evolutions of multiple worlds. We can use this formalism to evaluate entropy flow in a photovoltaic cells coupled to thermal reservoirs and cavity modes. Recently we studied the full counting statistics of energy transfers in such systems. This rigorously proves a nontrivial correspondence between energy exchanges and entropy changes in quantum systems, which only in systems without entanglement can be simplified to the textbook second law of thermodynamics. We evaluate the flow of entropy using this formalism. In the presence of entanglement, however, interestingly much less information is exchanged than what we expected. This increases the upper limit capacity for information transfer and its conversion to energy for next generation devices in mesoscopic physics.

The Measurement Process in Local Quantum Physics and the EPR Paradox

NASA Astrophysics Data System (ADS)

Doplicher, Sergio

2018-01-01

We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account the finite and non zero time duration T of the interaction between the observed system and the microscopic part of the measurement apparatus; the finite space size R of that apparatus; and the fact that the macroscopic part of the measurement apparatus, having the role of amplifying the effect of that interaction to a macroscopic scale, is composed by a very large but finite number N of particles. The Schrödinger evolution of the composed system can be expected to deform into the conventional picture of the measurement, as an instantaneous action turning a pure state into a mixture, only in the limit {N → ∞, T → 0, R → ∞}. Our main point is to discuss this picture for the measurement of local observables in Quantum Field Theory, where the dynamics of the theory and the measurement itself are described by the same time evolution complying with the Principle of Locality. We comment on the Einstein Podolski Rosen thought experiment, reformulated here only in terms of local observables (rather than global ones, as one particle or polarization observables).The local picture of the measurement process helps to make it clear that there is no conflict with the Principle of Locality.

Optimal Synthesis of the Joint Unitary Evolutions

NASA Astrophysics Data System (ADS)

Wei, Hai-Rui; Alsaedi, Ahmed; Hobiny, Aatef; Deng, Fu-Guo; Hu, Hui; Zhang, Dun

2018-07-01

Joint unitary operations play a central role in quantum communication and computation. We give a quantum circuit for implementing a type of unconstructed useful joint unitary evolutions in terms of controlled-NOT (CNOT) gates and single-qubit rotations. Our synthesis is optimal and possible in experiment. Two CNOT gates and seven R x , R y or R z rotations are required for our synthesis, and the arbitrary parameter contained in the evolutions can be controlled by local Hamiltonian or external fields.

Optimal Synthesis of the Joint Unitary Evolutions

NASA Astrophysics Data System (ADS)

Wei, Hai-Rui; Alsaedi, Ahmed; Hobiny, Aatef; Deng, Fu-Guo; Hu, Hui; Zhang, Dun

2018-03-01

Joint unitary operations play a central role in quantum communication and computation. We give a quantum circuit for implementing a type of unconstructed useful joint unitary evolutions in terms of controlled-NOT (CNOT) gates and single-qubit rotations. Our synthesis is optimal and possible in experiment. Two CNOT gates and seven R x , R y or R z rotations are required for our synthesis, and the arbitrary parameter contained in the evolutions can be controlled by local Hamiltonian or external fields.

Random unitary evolution model of quantum Darwinism with pure decoherence

NASA Astrophysics Data System (ADS)

Balanesković, Nenad

2015-10-01

We study the behavior of Quantum Darwinism [W.H. Zurek, Nat. Phys. 5, 181 (2009)] within the iterative, random unitary operations qubit-model of pure decoherence [J. Novotný, G. Alber, I. Jex, New J. Phys. 13, 053052 (2011)]. We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system S from the point of view of its environment E, is not a generic phenomenon, but depends on the specific form of input states and on the type of S-E-interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial input states of environment E that allow to store information about an open system S of interest with maximal efficiency.

Implementation and characterization of a controllable dephasing channel based on coupling polarization and spatial degrees of freedom of light.

PubMed

Urrego, Daniel F; Álvarez, Juan-Rafael; Calderón-Losada, Omar; Svozilík, Jiří; Nuñez, Mayerlin; Valencia, Alejandra

2018-04-30

We present the experimental implementation and theoretical model of a controllable dephasing quantum channel using photonic systems. The channel is implemented by coupling the polarization and the spatial distribution of light that play, in the perspective of open quantum systems, the role of quantum system and environment, respectively. The capability of controlling our channel allows us to visualize its effects in a quantum system. Different from standard dephasing channels, our channel presents an exotic behavior in the sense that the evolution of a state, from a pure to a mixed state, shows an oscillatory behavior if tracked in the Bloch sphere. Additionally, we report the evolution of the purity and perform a quantum process tomography to obtain the χ matrix associated to our channel.

Quantum adiabatic machine learning

NASA Astrophysics Data System (ADS)

Pudenz, Kristen L.; Lidar, Daniel A.

2013-05-01

We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. This approach consists of two quantum phases, with some amount of classical preprocessing to set up the quantum problems. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. All quantum processing is strictly limited to two-qubit interactions so as to ensure physical feasibility. We apply and illustrate this approach in detail to the problem of software verification and validation, with a specific example of the learning phase applied to a problem of interest in flight control systems. Beyond this example, the algorithm can be used to attack a broad class of anomaly detection problems.

Quantum coherence and entanglement control for atom-cavity systems

NASA Astrophysics Data System (ADS)

Shu, Wenchong

Coherence and entanglement play a significant role in the quantum theory. Ideal quantum systems, "closed" to the outside world, remain quantum forever and thus manage to retain coherence and entanglement. Real quantum systems, however, are open to the environment and are therefore susceptible to the phenomenon of decoherence and disentanglement which are major hindrances to the effectiveness of quantum information processing tasks. In this thesis we have theoretically studied the evolution of coherence and entanglement in quantum systems coupled to various environments. We have also studied ways and means of controlling the decay of coherence and entanglement. We have studied the exact qubit entanglement dynamics of some interesting initial states coupled to a high-Q cavity containing zero photon, one photon, two photons and many photons respectively. We have found that an initially correlated environmental state can serve as an enhancer for entanglement decay or generation processes. More precisely, we have demonstrated that the degree of entanglement, including its collapse as well as its revival times, can be significantly modified by the correlated structure of the environmental modes. We have also studied dynamical decoupling (DD) technique --- a prominent strategy of controlling decoherence and preserving entanglement in open quantum systems. We have analyzed several DD control methods applied to qubit systems that can eliminate the system-environment coupling and prolong the quantum coherence time. Particularly, we have proposed a new DD sequence consisting a set of designed control operators that can universally protected an unknown qutrit state against colored phase and amplitude environment noises. In addition, in a non-Markovian regime, we have reformulated the quantum state diffusion (QSD) equation to incorporate the effect of the external control fields. Without any assumptions on the system-environment coupling and the size of environment, we have consistently solved the control dynamics of open quantum systems using this stochastic QSD approach. By implementing the QSD equation, our numerical results have revealed that how the control efficacy depends on the designed time points and shapes of the applied control pulses, and the environment memory time scale.

Graphene quantum dots to enhance the photocatalytic hydrogen evolution efficiency of anatase TiO2 with exposed {001} facet.

PubMed

Yu, Shan; Zhong, Yun-Qian; Yu, Bao-Quan; Cai, Shi-Yi; Wu, Li-Zhu; Zhou, Ying

2016-07-27

Hydrogen evolution through photocatalysis is promising with respect to the environmental problems and challenges of energy shortage that we encounter today. In this paper, we have combined graphene quantum dots (GQDs) and {001} faceted anatase TiO2 (with an exposed percentage of 65-75%) together for effective photocatalytic hydrogen evolution. A series of characterizations including X-ray diffraction, transmission electron microscopy, X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy and UV-visible absorption spectroscopy have been carried out to study the structure of the as-prepared GQDs/{001}TiO2 composite. It turns out that GQDs could be effectively decorated on {001}TiO2 sheet without changing its intrinsic structure. With an optimum loading amount of GQDs (0.5 wt% to {001}TiO2), GQDs/{001}TiO2 exhibits a hydrogen evolution efficiency 8 times higher than that of bare {001}TiO2, which is a significantly more obvious improvement than many other photocatalytic systems relevant to GQDs and TiO2 hybrids. In addition, GQDs/{001}TiO2 could stand long-term photocatalytic experiments. Photocurrent tests show that such an improvement of the photocatalytic efficiency over GQDs/{001}TiO2 may originate from a higher charge separation efficiency. The present study could offer reference for the construction of photocatalytic hydrogen evolution systems with low cost and long term stability.

Multitime correlators in continuous measurement of qubit observables

NASA Astrophysics Data System (ADS)

Atalaya, Juan; Hacohen-Gourgy, Shay; Martin, Leigh S.; Siddiqi, Irfan; Korotkov, Alexander N.

2018-02-01

We consider multitime correlators for output signals from linear detectors, continuously measuring several qubit observables at the same time. Using the quantum Bayesian formalism, we show that for unital (symmetric) evolution in the absence of phase backaction, an N -time correlator can be expressed as a product of two-time correlators when N is even. For odd N , there is a similar factorization, which also includes a single-time average. Theoretical predictions agree well with experimental results for two detectors, which simultaneously measure noncommuting qubit observables.

Quantum Information Processing with Large Nuclear Spins in GaAs Semiconductors

NASA Astrophysics Data System (ADS)

Leuenberger, Michael N.; Loss, Daniel; Poggio, M.; Awschalom, D. D.

2002-10-01

We propose an implementation for quantum information processing based on coherent manipulations of nuclear spins I=3/2 in GaAs semiconductors. We describe theoretically an NMR method which involves multiphoton transitions and which exploits the nonequidistance of nuclear spin levels due to quadrupolar splittings. Starting from known spin anisotropies we derive effective Hamiltonians in a generalized rotating frame, valid for arbitrary I, which allow us to describe the nonperturbative time evolution of spin states generated by magnetic rf fields. We identify an experimentally observable regime for multiphoton Rabi oscillations. In the nonlinear regime, we find Berry phase interference.

Did God create our universe? Theological reflections on the Big Bang, inflation, and quantum cosmologies.

PubMed

Russell, R J

2001-12-01

The sciences and the humanities, including theology, form an epistemic hierarchy that ensures both constraint and irreducibility. At the same time, theological methodology is analogous to scientific methodology, though with several important differences. This model of interaction between science and theology can be seen illustrated in a consideration of the relation between contemporary cosmology (Big Bang cosmology, cosmic inflation, and quantum cosmology) and Christian systematic and natural theology. In light of developments in cosmology, the question of origins has become theologically less interesting than that of the cosmic evolution of a contingent universe.

Spacetime topology change and black hole information

NASA Astrophysics Data System (ADS)

Hsu, Stephen D. H.

2007-01-01

Topology change-the creation of a disconnected baby universe-due to black hole collapse may resolve the information loss paradox. Evolution from an early time Cauchy surface to a final surface which includes a slice of the disconnected region can be unitary and consistent with conventional quantum mechanics. We discuss the issue of cluster decomposition, showing that any violations thereof are likely to be unobservably small. Topology change is similar to the black hole remnant scenario and only requires assumptions about the behavior of quantum gravity in Planckian regimes. It does not require non-locality or any modification of low-energy physics.

Analog quantum simulation of the Rabi model in the ultra-strong coupling regime.

PubMed

Braumüller, Jochen; Marthaler, Michael; Schneider, Andre; Stehli, Alexander; Rotzinger, Hannes; Weides, Martin; Ustinov, Alexey V

2017-10-03

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.

C++QEDv2: The multi-array concept and compile-time algorithms in the definition of composite quantum systems

NASA Astrophysics Data System (ADS)

Vukics, András

2012-06-01

C++QED is a versatile framework for simulating open quantum dynamics. It allows to build arbitrarily complex quantum systems from elementary free subsystems and interactions, and simulate their time evolution with the available time-evolution drivers. Through this framework, we introduce a design which should be generic for high-level representations of composite quantum systems. It relies heavily on the object-oriented and generic programming paradigms on one hand, and on the other hand, compile-time algorithms, in particular C++ template-metaprogramming techniques. The core of the design is the data structure which represents the state vectors of composite quantum systems. This data structure models the multi-array concept. The use of template metaprogramming is not only crucial to the design, but with its use all computations pertaining to the layout of the simulated system can be shifted to compile time, hence cutting on runtime. Program summaryProgram title: C++QED Catalogue identifier: AELU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:http://cpc.cs.qub.ac.uk/licence/aelu_v1_0.html. The C++QED package contains other software packages, Blitz, Boost and FLENS, all of which may be distributed freely but have individual license requirements. Please see individual packages for license conditions. No. of lines in distributed program, including test data, etc.: 597 974 No. of bytes in distributed program, including test data, etc.: 4 874 839 Distribution format: tar.gz Programming language: C++ Computer: i386-i686, x86_64 Operating system: In principle cross-platform, as yet tested only on UNIX-like systems (including Mac OS X). RAM: The framework itself takes about 60 MB, which is fully shared. The additional memory taken by the program which defines the actual physical system (script) is typically less than 1 MB. The memory storing the actual data scales with the system dimension for state-vector manipulations, and the square of the dimension for density-operator manipulations. This might easily be GBs, and often the memory of the machine limits the size of the simulated system. Classification: 4.3, 4.13, 6.2, 20 External routines: Boost C++ libraries (http://www.boost.org/), GNU Scientific Library (http://www.gnu.org/software/gsl/), Blitz++ (http://www.oonumerics.org/blitz/), Linear Algebra Package - Flexible Library for Efficient Numerical Solutions (http://flens.sourceforge.net/). Nature of problem: Definition of (open) composite quantum systems out of elementary building blocks [1]. Manipulation of such systems, with emphasis on dynamical simulations such as Master-equation evolution [2] and Monte Carlo wave-function simulation [3]. Solution method: Master equation, Monte Carlo wave-function method. Restrictions: Total dimensionality of the system. Master equation - few thousands. Monte Carlo wave-function trajectory - several millions. Unusual features: Because of the heavy use of compile-time algorithms, compilation of programs written in the framework may take a long time and much memory (up to several GBs). Additional comments: The framework is not a program, but provides and implements an application-programming interface for developing simulations in the indicated problem domain. Supplementary information: http://cppqed.sourceforge.net/. Running time: Depending on the magnitude of the problem, can vary from a few seconds to weeks.

Time-reversal symmetric resolution of unity without background integrals in open quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hatano, Naomichi, E-mail: hatano@iis.u-tokyo.ac.jp; Ordonez, Gonzalo, E-mail: gordonez@butler.edu

2014-12-15

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green’s function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schrödinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the centralmore » scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly, the exponential decays due to the resonance poles.« less

Time-invariant PT product and phase locking in PT -symmetric lattice models

NASA Astrophysics Data System (ADS)

Joglekar, Yogesh N.; Onanga, Franck Assogba; Harter, Andrew K.

2018-01-01

Over the past decade, non-Hermitian, PT -symmetric Hamiltonians have been investigated as candidates for both a fundamental, unitary, quantum theory and open systems with a nonunitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the PT (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of PT -symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave-function phases at adjacent sites occurs in the PT -symmetry-broken region. Our results pave the way towards understanding the physically observable implications of time invariants in the nonunitary dynamics produced by PT -symmetric Hamiltonians.

Quantum Bio-Informatics II From Quantum Information to Bio-Informatics

NASA Astrophysics Data System (ADS)

Accardi, L.; Freudenberg, Wolfgang; Ohya, Masanori

2009-02-01

The problem of quantum-like representation in economy cognitive science, and genetics / L. Accardi, A. Khrennikov and M. Ohya -- Chaotic behavior observed in linea dynamics / M. Asano, T. Yamamoto and Y. Togawa -- Complete m-level quantum teleportation based on Kossakowski-Ohya scheme / M. Asano, M. Ohya and Y. Tanaka -- Towards quantum cybernetics: optimal feedback control in quantum bio informatics / V. P. Belavkin -- Quantum entanglement and circulant states / D. Chruściński -- The compound Fock space and its application in brain models / K. -H. Fichtner and W. Freudenberg -- Characterisation of beam splitters / L. Fichtner and M. Gäbler -- Application of entropic chaos degree to a combined quantum baker's map / K. Inoue, M. Ohya and I. V. Volovich -- On quantum algorithm for multiple alignment of amino acid sequences / S. Iriyama and M. Ohya --Quantum-like models for decision making in psychology and cognitive science / A. Khrennikov -- On completely positive non-Markovian evolution of a d-level system / A. Kossakowski and R. Rebolledo -- Measures of entanglement - a Hilbert space approach / W. A. Majewski -- Some characterizations of PPT states and their relation / T. Matsuoka -- On the dynamics of entanglement and characterization ofentangling properties of quantum evolutions / M. Michalski -- Perspective from micro-macro duality - towards non-perturbative renormalization scheme / I. Ojima -- A simple symmetric algorithm using a likeness with Introns behavior in RNA sequences / M. Regoli -- Some aspects of quadratic generalized white noise functionals / Si Si and T. Hida -- Analysis of several social mobility data using measure of departure from symmetry / K. Tahata ... [et al.] -- Time in physics and life science / I. V. Volovich -- Note on entropies in quantum processes / N. Watanabe -- Basics of molecular simulation and its application to biomolecules / T. Ando and I. Yamato -- Theory of proton-induced superionic conduction in hydrogen-bonded systems / H. Kamimura -- Massive collection of full-length complementary DNA clones and microarray analyses: keys to rice transcriptome analysis / S. Kikuchi -- Changes of influenza A(H5) viruses by means of entropic chaos degree / K. Sato and M. Ohya -- Basics of genome sequence analysis in bioinformatics - its fundamental ideas and problems / T. Suzuki and S. Miyazaki -- A basic introduction to gene expression studies using microarray expression data analysis / D. Wanke and J. Kilian -- Integrating biological perspectives: a quantum leap for microarray expression analysis / D. Wanke ... [et al.].

Squeezing effects applied in nonclassical superposition states for quantum nanoelectronic circuits

NASA Astrophysics Data System (ADS)

Choi, Jeong Ryeol

2017-06-01

Quantum characteristics of a driven series RLC nanoelectronic circuit whose capacitance varies with time are studied using an invariant operator method together with a unitary transformation approach. In particular, squeezing effects and nonclassical properties of a superposition state composed of two displaced squeezed number states of equal amplitude, but 180° out of phase, are investigated in detail. We applied our developments to a solvable specific case obtained from a suitable choice of time-dependent parameters. The pattern of mechanical oscillation of the amount of charges stored in the capacitor, which are initially displaced, has exhibited more or less distortion due to the influence of the time-varying parameters of the system. We have analyzed squeezing effects of the system from diverse different angles and such effects are illustrated for better understanding. It has been confirmed that the degree of squeezing is not constant, but varies with time depending on specific situations. We have found that quantum interference occurs whenever the two components of the superposition meet together during the time evolution of the probability density. This outcome signifies the appearance of nonclassical features of the system. Nonclassicality of dynamical systems can be a potential resource necessary for realizing quantum information technique. Indeed, such nonclassical features of superposition states are expected to play a key role in upcoming information science which has attracted renewed attention recently.

The Liouville equation for flavour evolution of neutrinos and neutrino wave packets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Rasmus Sloth Lundkvist; Smirnov, Alexei Yu., E-mail: rasmus@mpi-hd.mpg.de, E-mail: smirnov@mpi-hd.mpg.de

We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over amore » trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.« less

Topological Rényi Entropy after a Quantum Quench

NASA Astrophysics Data System (ADS)

Halász, Gábor B.; Hamma, Alioscia

2013-04-01

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.

Topological Rényi entropy after a quantum quench.

PubMed

Halász, Gábor B; Hamma, Alioscia

2013-04-26

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.

Can observations look back to the beginning of inflation?

NASA Astrophysics Data System (ADS)

Wetterich, C.

2016-03-01

The cosmic microwave background can measure the inflaton potential only if inflation lasts sufficiently long before the time of horizon crossing of observable fluctuations, such that non-linear effects in the time evolution of Green's functions lead to a loss of memory of initial conditions for the ultraviolet tail of the spectrum. Within a derivative expansion of the quantum effective action for an interacting scalar field we discuss the most general solution for the correlation function, including arbitrary pure and mixed quantum states. In this approximation no loss of memory occurs - cosmic microwave observations see the initial spectrum at the beginning of inflation, processed only mildly by the scale-violating effects at horizon crossing induced by the inflaton potential.

Critical quench dynamics in confined systems.

PubMed

Collura, Mario; Karevski, Dragi

2010-05-21

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the nonadiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field.

New Class of Quantum Error-Correcting Codes for a Bosonic Mode

NASA Astrophysics Data System (ADS)

Michael, Marios H.; Silveri, Matti; Brierley, R. T.; Albert, Victor V.; Salmilehto, Juha; Jiang, Liang; Girvin, S. M.

2016-07-01

We construct a new class of quantum error-correcting codes for a bosonic mode, which are advantageous for applications in quantum memories, communication, and scalable computation. These "binomial quantum codes" are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the time step between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes, but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to "cat codes" based on superpositions of the coherent states but offer several advantages such as smaller mean boson number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology, and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up- and down-conversion.

Astronomical constraints on the cosmic evolution of the fine structure constant and possible quantum dimensions.

PubMed

Carilli, C L; Menten, K M; Stocke, J T; Perlman, E; Vermeulen, R; Briggs, F; de Bruyn , A G; Conway, J; Moore, C P

2000-12-25

We present measurements of absorption by the 21 cm hyperfine transition of neutral hydrogen toward radio sources at substantial look-back times. These data are used in combination with observations of rotational transitions of common interstellar molecules to set limits on the evolution of the fine structure constant: alpha/ alpha<3.5x10(-15) yr(-1), to a look-back time of 4.8 Gyr. In the context of string theory, the limit on the secular evolution of the scale factor of the compact dimensions, R, is &Rdot/ R<10(-15) yr(-1). Including terrestrial and other astronomical measurements places 2sigma limits on slow oscillations of R from the present to the epoch of cosmic nucleosynthesis, just seconds after the big bang, of DeltaR /R<10(-5).

Dynamics of entropic uncertainty for atoms immersed in thermal fluctuating massless scalar field

NASA Astrophysics Data System (ADS)

Huang, Zhiming

2018-04-01

In this article, the dynamics of quantum memory-assisted entropic uncertainty relation for two atoms immersed in a thermal bath of fluctuating massless scalar field is investigated. The master equation that governs the system evolution process is derived. It is found that the mixedness is closely associated with entropic uncertainty. For equilibrium state, the tightness of uncertainty vanishes. For the initial maximum entangled state, the tightness of uncertainty undergoes a slight increase and then declines to zero with evolution time. It is found that temperature can increase the uncertainty, but two-atom separation does not always increase the uncertainty. The uncertainty evolves to different relatively stable values for different temperatures and converges to a fixed value for different two-atom distances with evolution time. Furthermore, weak measurement reversal is employed to control the entropic uncertainty.

Epistemic Primacy vs. Ontological Elusiveness of Spatial Extension: Is There an Evolutionary Role for the Quantum?

NASA Astrophysics Data System (ADS)

Pauri, Massimo

2011-11-01

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein "giving up the extensional continuum … is like to breathe in airless space"). On the other hand, Planck's discovery of the atomization of action leads to the fundamental recognition of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations ( measurements). The elementary quantum act (measured by Planck's constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: "Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind". An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a `primary spatial' reduction is `continually' taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the `primary reduction' has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant's Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, "space can well be transcendental without the axioms being so", in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even `leave the ground', vindicating Bohr's viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible.

Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal

NASA Astrophysics Data System (ADS)

Yannouleas, Constantine; Landman, Uzi

2017-10-01

A constructive theoretical platform for the description of quantum space-time crystals uncovers for N interacting and ring-confined rotating particles the existence of low-lying states with proper space-time crystal behavior. The construction of the corresponding many-body trial wave functions proceeds first via symmetry breaking at the mean-field level followed by symmetry restoration using projection techniques. The ensuing correlated many-body wave functions are stationary states and preserve the rotational symmetries, and at the same time they reflect the point-group symmetries of the mean-field crystals. This behavior results in the emergence of sequences of select magic angular momenta Lm. For angular-momenta away from the magic values, the trial functions vanish. Symmetry breaking beyond the mean-field level can be induced by superpositions of such good-Lm many-body stationary states. We show that superposing a pair of adjacent magic angular momenta states leads to formation of special broken-symmetry states exhibiting quantum space-time-crystal behavior. In particular, the corresponding particle densities rotate around the ring, showing undamped and nondispersed periodic crystalline evolution in both space and time. The experimental synthesis of such quantum space-time-crystal wave packets is predicted to be favored in the vicinity of ground-state energy crossings of the Aharonov-Bohm-type spectra accessed via an externally applied, natural or synthetic, magnetic field. These results are illustrated here for Coulomb-repelling fermionic ions and for a lump of contact-interaction attracting bosons.

Early universe with modified scalar-tensor theory of gravity

NASA Astrophysics Data System (ADS)

Mandal, Ranajit; Sarkar, Chandramouli; Sanyal, Abhik Kumar

2018-05-01

Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.