Perturbative approach to Markovian open quantum systems
Li, Andy C. Y.; Petruccione, F.; Koch, Jens
2014-01-01
The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical. PMID:24811607
Thermalization in closed quantum systems: Semiclassical approach
NASA Astrophysics Data System (ADS)
Cosme, J. G.; Fialko, O.
2014-11-01
Thermalization in closed quantum systems can be understood either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum-mechanical formalism, such as spectral properties of the eigenstates or entanglement between subsystems, respectively. Here we study instead the onset of thermalization of Bose particles in a two-band double-well potential using the truncated Wigner approximation. This allows us to use the familiar classical formalism to understand quantum thermalization in this system. In particular, we demonstrate that sampling of an initial quantum state mimics a statistical mechanical ensemble, while subsequent chaotic classical evolution turns the initial quantum state into the thermal state.
Open quantum systems approach to atomtronics
Pepino, R. A.; Cooper, J.; Meiser, D.; Anderson, D. Z.; Holland, M. J.
2010-07-15
We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate the atomic transport of bosons across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate and logic gate behavior in an optical lattice.
Approaching infinite temperature upon repeated measurements of a quantum system
Yi, Juyeon; Talkner, Peter; Ingold, Gert-Ludwig
2011-09-15
The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied as a function of the time lag {tau} between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponential in the case of finite Hilbert space dimension. The rate characterizing this approach undergoes a sharp transition from a monotonically increasing to an erratically varying function of the time between subsequent measurements.
Heisenberg picture approach to the stability of quantum Markov systems
Pan, Yu E-mail: zibo.miao@anu.edu.au; Miao, Zibo E-mail: zibo.miao@anu.edu.au; Amini, Hadis; Gough, John; Ugrinovskii, Valery; James, Matthew R.
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Characterization of decohering quantum systems: Machine learning approach
NASA Astrophysics Data System (ADS)
Stenberg, Markku P. V.; Köhn, Oliver; Wilhelm, Frank K.
2016-01-01
Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make adaptive characterization difficult. As an example, we consider two coupled discrete quantum systems. When one of the systems can be controlled and measured, the standard method to characterize another, with an unknown frequency ωr, is swap spectroscopy. Here, adapting measurements can provide estimates whose error decreases exponentially in the number of measurement shots rather than as a power law in conventional swap spectroscopy. However, when the decoherence time is so short that an excitation oscillating between the two systems can only undergo less than a few tens of vacuum Rabi oscillations, this approach can be marred by a severe limit on accuracy unless carefully designed. We adopt machine learning techniques to search for efficient policies for the characterization of decohering quantum systems. We find, for instance, that when the system undergoes more than 2 Rabi oscillations during its relaxation time T1, O (103) measurement shots are sufficient to reduce the squared error of the Bayesian initial prior of the unknown frequency ωr by a factor O (104) or larger. We also develop policies optimized for extreme initial parameter uncertainty and for the presence of imperfections in the readout.
Dissipation equation of motion approach to open quantum systems
NASA Astrophysics Data System (ADS)
Yan, YiJing; Jin, Jinshuang; Xu, Rui-Xue; Zheng, Xiao
2016-08-01
This paper presents a comprehensive account of the dissipaton-equation-of-motion (DEOM) theory for open quantum systems. This newly developed theory treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that are also experimentally measurable. Despite the fact that DEOM recovers the celebrated hierarchical-equations-of-motion (HEOM) formalism, these two approaches have some fundamental differences. To show these differences, we also scrutinize the HEOM construction via its root at the influence functional path integral formalism. We conclude that many unique features of DEOM are beyond the reach of the HEOM framework. The new DEOM approach renders a statistical quasi-particle picture to account for the environment, which can be either bosonic or fermionic. The review covers the DEOM construction, the physical meanings of dynamical variables, the underlying theorems and dissipaton algebra, and recent numerical advancements for efficient DEOM evaluations of various problems. We also address the issue of high-order many-dissipaton truncations with respect to the invariance principle of quantum mechanics of Schrödinger versus Heisenberg prescriptions. DEOM serves as a universal tool for characterizing of stationary and dynamic properties of system-and-bath interferences, as highlighted with its real-time evaluation of both linear and nonlinear current noise spectra of nonequilibrium electronic transport.
Linear response theory for open systems: Quantum master equation approach
NASA Astrophysics Data System (ADS)
Ban, Masashi; Kitajima, Sachiko; Arimitsu, Toshihico; Shibata, Fumiaki
2017-02-01
A linear response theory for open quantum systems is formulated by means of the time-local and time-nonlocal quantum master equations, where a relevant quantum system interacts with a thermal reservoir as well as with an external classical field. A linear response function that characterizes how a relaxation process deviates from its intrinsic process by a weak external field is obtained by extracting the linear terms with respect to the external field from the quantum master equation. It consists of four parts. One represents the linear response of a quantum system when system-reservoir correlation at an initial time and correlation between reservoir states at different times are neglected. The others are correction terms due to these effects. The linear response function is compared with the Kubo formula in the usual linear response theory. To investigate the properties of the linear response of an open quantum system, an exactly solvable model for a stochastic dephasing of a two-level system is examined. Furthermore, the method for deriving the linear response function is applied for calculating two-time correlation functions of open quantum systems. It is shown that the quantum regression theorem is not valid for open quantum systems unless their reduced time evolution is Markovian.
Iyengar, Srinivasan S; Jakowski, Jacek
2005-03-15
A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.
Quantum Dynamical Behaviour in Complex Systems - A Semiclassical Approach
Ananth, Nandini
2008-01-01
systems is described. We proposed the use of a semiclassical correction term to a preliminary quantum calculation using, for instance, a variational approach. This allows us to increase the accuracy significantly. Modeling Nonadiabatic dynamics has always been a challenge to classical simulations because the multi-state nature of the dynamics cannot be described accurately by the time evolution on a single average surface, as is the classical approach. We show that using the Meyer-Miller-Stock-Thoss (MMST) representation of the exact vibronic Hamiltonian in combination with the IVR allows us to accurately describe dynamics where the non Born-Oppenheimer regime. One final problem that we address is that of extending this method to the long time regime. We propose the use of a time independent sampling function in the Monte Carlo integration over the phase space of initial trajectory conditions. This allows us to better choose the regions of importance at the various points in time; by using more trajectories in the important regions, we show that the integration can be converged much easier. An algorithm based loosely on the methods of Diffusion Monte Carlo is developed that allows us to carry out this time dependent sampling in a most efficient manner.
Using Quantum Mechanical Approaches to Study Biological Systems
2015-01-01
Conspectus Quantum mechanics (QM) has revolutionized our understanding of the structure and reactivity of small molecular systems. Given the tremendous impact of QM in this research area, it is attractive to believe that this could also be brought into the biological realm where systems of a few thousand atoms and beyond are routine. Applying QM methods to biological problems brings an improved representation to these systems by the direct inclusion of inherently QM effects such as polarization and charge transfer. Because of the improved representation, novel insights can be gleaned from the application of QM tools to biomacromolecules in aqueous solution. To achieve this goal, the computational bottlenecks of QM methods had to be addressed. In semiempirical theory, matrix diagonalization is rate limiting, while in density functional theory or Hartree–Fock theory electron repulsion integral computation is rate-limiting. In this Account, we primarily focus on semiempirical models where the divide and conquer (D&C) approach linearizes the matrix diagonalization step with respect to the system size. Through the D&C approach, a number of applications to biological problems became tractable. Herein, we provide examples of QM studies on biological systems that focus on protein solvation as viewed by QM, QM enabled structure-based drug design, and NMR and X-ray biological structure refinement using QM derived restraints. Through the examples chosen, we show the power of QM to provide novel insights into biological systems, while also impacting practical applications such as structure refinement. While these methods can be more expensive than classical approaches, they make up for this deficiency by the more realistic modeling of the electronic nature of biological systems and in their ability to be broadly applied. Of the tools and applications discussed in this Account, X-ray structure refinement using QM models is now generally available to the community in the
Non-Markovian relaxation of a three-level system: quantum trajectory approach.
Jing, Jun; Yu, Ting
2010-12-10
The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schrödinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.
Group Theoretical Approach for Controlled Quantum Mechanical Systems
2007-11-06
evolution equation with Hamiltonians which may possess discrete , continuous, and mixed spectrum. For such a quantum system, the Hamiltonian operator...study of classical linear and nonlinear systems, which proves to be very useful in understanding the design problems such as disturbance decoupling...developed by Kunita can then be implemented to establish controllability conditions for the original time-dependent Schrodinger control problem. The end
Modified stochastic variational approach to non-Hermitian quantum systems
NASA Astrophysics Data System (ADS)
Kraft, Daniel; Plessas, Willibald
2016-08-01
The stochastic variational method has proven to be a very efficient and accurate tool to calculate especially bound states of quantum-mechanical few-body systems. It relies on the Rayleigh-Ritz variational principle for minimizing real eigenenergies of Hermitian Hamiltonians. From molecular to atomic, nuclear, and particle physics there is actually a great demand of describing also resonant states to a high degree of reliance. This is especially true with regard to hadron resonances, which have to be treated in a relativistic framework. So far standard methods of dealing with quantum chromodynamics have not yet succeeded in describing hadron resonances in a realistic manner. Resonant states can be handled by non-Hermitian quantum Hamiltonians. These states correspond to poles in the lower half of the unphysical sheet of the complex energy plane and are therefore intimately connected with complex eigenvalues. Consequently the Rayleigh-Ritz variational principle cannot be employed in the usual manner. We have studied alternative selection principles for the choice of test functions to treat resonances along the stochastic variational method. We have found that a stationarity principle for the complex energy eigenvalues provides a viable method for selecting test functions for resonant states in a constructive manner. We discuss several variants thereof and exemplify their practical efficiencies.
Numerical approaches to isolated many-body quantum systems
NASA Astrophysics Data System (ADS)
Kolodrubetz, Michael H.
Ultracold atoms have revolutionized atomic and condensed matter physics. In addition to having clean, controllable Hamiltonians, ultracold atoms are near-perfect realizations of isolated quantum systems, in which weak environmental coupling can be neglected on experimental time scales. This opens new opportunities to explore these systems not just in thermal equilibrium, but out of equilibrium as well. In this dissertation, we investigate some properties of closed quantum systems, utilizing a combination of numerical and analytical techniques. We begin by applying full configuration-interaction quantum Monte Carlo (FCIQMC) to the Fermi polaron, which we use as a test bed to improve the algorithm. In addition to adapting standard QMC techniques, we introduce novel controlled approximations that allow mitigation of the sign problem and simulation directly in the thermodynamic limit. We also contrast the sign problem of FCIQMC with that of more standard techniques, focusing on FCIQMC's capacity to work in a second quantized determinant space. Next, we discuss nonequilibrium dynamics near a quantum critical point, focusing on the one-dimensional transverse-field Ising (TFI) chain. We show that the TFI dynamics exhibit critical scaling, within which the spin correlations exhibit qualitatively athermal behavior. We provide strong numerical evidence for the universality of dynamic scaling by utilizing time-dependent matrix product states to simulate a non-integrable model in the same equilibrium universality class. As this non-integrable model has been realized experimentally, we investigate the robustness of our predictions against the presence of open boundary conditions and disorder. We find that the qualitatively athermal correlations remain visible, although other phenomena such as even/odd effects become relevant within the finite size scaling theory. Finally, we investigate the properties of the integrable TFI model upon varying the strength of a non
Quantum thermal transport through anharmonic systems: A self-consistent approach
NASA Astrophysics Data System (ADS)
He, Dahai; Thingna, Juzar; Wang, Jian-Sheng; Li, Baowen
2016-10-01
We propose a feasible and effective approach to study quantum thermal transport through anharmonic systems. The main idea is to obtain an effective harmonic Hamiltonian for the anharmonic system by applying the self-consistent phonon theory. By using the effective harmonic Hamiltonian, we study thermal transport within the framework of the nonequilibrium Green's function method using the celebrated Caroli formula. We corroborate our quantum self-consistent approach by using the quantum master equation that can deal with anharmonicity exactly, but is limited to the weak system-bath coupling regime. Finally, in order to demonstrate its strength, we apply the quantum self-consistent approach to study thermal rectification in a weakly coupled two-segment anharmonic system.
General approach to quantum-classical hybrid systems and geometric forces.
Zhang, Qi; Wu, Biao
2006-11-10
We present a general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem. We approach such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart, which is commonly the case in hybrid systems. Moreover, this canonical transformation generates a vector potential which, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics and, on the other hand, yields a Lorentz-like geometric force in the slow classical dynamics.
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Werner, A. H.; Jaschke, D.; Silvi, P.; Kliesch, M.; Calarco, T.; Eisert, J.; Montangero, S.
2016-06-01
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems.
Werner, A H; Jaschke, D; Silvi, P; Kliesch, M; Calarco, T; Eisert, J; Montangero, S
2016-06-10
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2009-03-01
Preface; Part I. Fundamental Ideas and General Formalisms: 1. Unfinished revolution C. Rovelli; 2. The fundamental nature of space and time G. 't Hooft; 3. Does locality fail at intermediate length scales R. Sorkin; 4. Prolegomena to any future quantum gravity J. Stachel; 5. Spacetime symmetries in histories canonical gravity N. Savvidou; 6. Categorical geometry and the mathematical foundations of quantum gravity L. Crane; 7. Emergent relativity O. Dreyer; 8. Asymptotic safety R. Percacci; 9. New directions in background independent quantum gravity F. Markopoulou; Questions and answers; Part II: 10. Gauge/gravity duality G. Horowitz and J. Polchinski; 11. String theory, holography and quantum gravity T. Banks; 12. String field theory W. Taylor; Questions and answers; Part III: 13. Loop Quantum Gravity T. Thiemann; 14. Covariant loop quantum gravity? E. LIvine; 15. The spin foam representation of loop quantum gravity A. Perez; 16. 3-dimensional spin foam quantum gravity L. Freidel; 17. The group field theory approach to quantum gravity D. Oriti; Questions and answers; Part IV. Discrete Quantum Gravity: 18. Quantum gravity: the art of building spacetime J. Ambjørn, J. Jurkiewicz and R. Loll; 19. Quantum Regge calculations R. Williams; 20. Consistent discretizations as a road to quantum gravity R. Gambini and J. Pullin; 21. The causal set approach to quantum gravity J. Henson; Questions and answers; Part V. Effective Models and Quantum Gravity Phenomenology: 22. Quantum gravity phenomenology G. Amelino-Camelia; 23. Quantum gravity and precision tests C. Burgess; 24. Algebraic approach to quantum gravity II: non-commutative spacetime F. Girelli; 25. Doubly special relativity J. Kowalski-Glikman; 26. From quantum reference frames to deformed special relativity F. Girelli; 27. Lorentz invariance violation and its role in quantum gravity phenomenology J. Collins, A. Perez and D. Sudarsky; 28. Generic predictions of quantum theories of gravity L. Smolin; Questions and
Dynamics of open quantum spin systems: An assessment of the quantum master equation approach.
Zhao, P; De Raedt, H; Miyashita, S; Jin, F; Michielsen, K
2016-08-01
Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation.
Galitski, Victor
2011-07-15
We propose a Lie-algebraic duality approach to analyze nonequilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first part of the paper utilizes a geometric Hilbert-space-invariant formulation of unitary time evolution, where a quantum Hamiltonian is viewed as a trajectory in an abstract Lie algebra, while the sought-after evolution operator is a trajectory in a dynamic group, generated by the algebra via exponentiation. The evolution operator is uniquely determined by the time-dependent dual generators that satisfy a system of differential equations, dubbed here dual Schroedinger-Bloch equations, which represent a viable alternative to the conventional Schroedinger formulation. These dual Schroedinger-Bloch equations are derived and analyzed on a number of specific examples. It is shown that deterministic dynamics of a closed classical dynamical system occurs as action of a symmetry group on a classical manifold and is driven by the same dual generators as in the corresponding quantum problem. This represents quantum-to-classical correspondence. In the second part of the paper, we further extend the Lie-algebraic approach to a wide class of interacting many-particle lattice models. A generalized Hubbard-Stratonovich transform is proposed and it is used to show that the thermodynamic partition function of a generic many-body quantum lattice model can be expressed in terms of traces of single-particle evolution operators governed by the dynamic Hubbard-Stratonovich fields. The corresponding Hubbard-Stratonovich dynamical systems are generally nonunitary, which yields a number of notable complications, including breakdown of the global exponential representation. Finally, we derive Hubbard-Stratonovich dynamical systems for the Bose-Hubbard model and a quantum spin model and use the Lie-algebraic approach to obtain new nonperturbative dual
Quantum Approach to Informatics
NASA Astrophysics Data System (ADS)
Stenholm, Stig; Suominen, Kalle-Antti
2005-08-01
An essential overview of quantum information Information, whether inscribed as a mark on a stone tablet or encoded as a magnetic domain on a hard drive, must be stored in a physical object and thus made subject to the laws of physics. Traditionally, information processing such as computation occurred in a framework governed by laws of classical physics. However, information can also be stored and processed using the states of matter described by non-classical quantum theory. Understanding this quantum information, a fundamentally different type of information, has been a major project of physicists and information theorists in recent years, and recent experimental research has started to yield promising results. Quantum Approach to Informatics fills the need for a concise introduction to this burgeoning new field, offering an intuitive approach for readers in both the physics and information science communities, as well as in related fields. Only a basic background in quantum theory is required, and the text keeps the focus on bringing this theory to bear on contemporary informatics. Instead of proofs and other highly formal structures, detailed examples present the material, making this a uniquely accessible introduction to quantum informatics. Topics covered include: * An introduction to quantum information and the qubit * Concepts and methods of quantum theory important for informatics * The application of information concepts to quantum physics * Quantum information processing and computing * Quantum gates * Error correction using quantum-based methods * Physical realizations of quantum computing circuits A helpful and economical resource for understanding this exciting new application of quantum theory to informatics, Quantum Approach to Informatics provides students and researchers in physics and information science, as well as other interested readers with some scientific background, with an essential overview of the field.
A sum-over-paths approach to one-dimensional time-independent quantum systems
NASA Astrophysics Data System (ADS)
Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna
2016-09-01
We present an alternative treatment for simple time-independent quantum systems in one dimension, which can be used in the context of an elementary introduction to quantum physics using the Feynman approach. The method is based on representation of the energy-dependent propagator (or Green function) as a sum of complex amplitudes over all possible paths, classical and non-classical, at fixed energy. We treat both confined and open systems with piecewise-constant potentials, obtaining exact results. We introduce an approximation scheme to extend the method to smooth potentials, recovering the Van Vleck-Gutzwiller propagator. Finally, we discuss the educational application of the method.
NASA Astrophysics Data System (ADS)
Foerster, A.; Leymann, H. A. M.; Wiersig, J.
2017-03-01
We introduce an equation of motion approach that allows for an approximate evaluation of the time evolution of a quantum system, where the algebraic work to derive the equations of motion is done by the computer. The introduced procedures offer a variety of different types of approximations applicable for finite systems with strong coupling as well as for arbitrary large systems where augmented mean-field theories like the cluster expansion can be applied.
Operational approach to fluctuations of thermodynamic variables in finite quantum systems.
Jahnke, T; Lanéry, S; Mahler, G
2011-01-01
In this paper we present a quantum approach to the old problem of temperature fluctuations. We start by observing that according to quantum thermodynamics, fluctuations of intensive parameters like temperature cannot exist. Furthermore, such parameters are not observables, so their estimation has to be done indirectly. The respective temperature estimate based on quantum measurements of the energy is shown to fluctuate according to the well-known formula ΔT(2)=k(B)T(2)/C, but only within a certain temperature range and if the system is not too small. We also calculate the fourth-order correction term, becoming important at higher temperatures. Finally we illustrate our results with a concrete model of n spins.
Quantum noise in the mirror-field system: A field theoretic approach
Hsiang, Jen-Tsung; Wu, Tai-Hung; Lee, Da-Shin; King, Sun-Kun; Wu, Chun-Hsien
2013-02-15
We revisit the quantum noise problem in the mirror-field system by a field-theoretic approach. Here a perfectly reflecting mirror is illuminated by a single-mode coherent state of the massless scalar field. The associated radiation pressure is described by a surface integral of the stress-tensor of the field. The read-out field is measured by a monopole detector, from which the effective distance between the detector and mirror can be obtained. In the slow-motion limit of the mirror, this field-theoretic approach allows to identify various sources of quantum noise that all in all leads to uncertainty of the read-out measurement. In addition to well-known sources from shot noise and radiation pressure fluctuations, a new source of noise is found from field fluctuations modified by the mirror's displacement. Correlation between different sources of noise can be established in the read-out measurement as the consequence of interference between the incident field and the field reflected off the mirror. In the case of negative correlation, we found that the uncertainty can be lowered than the value predicted by the standard quantum limit. Since the particle-number approach is often used in quantum optics, we compared results obtained by both approaches and examine its validity. We also derive a Langevin equation that describes the stochastic dynamics of the mirror. The underlying fluctuation-dissipation relation is briefly mentioned. Finally we discuss the backreaction induced by the radiation pressure. It will alter the mean displacement of the mirror, but we argue this backreaction can be ignored for a slowly moving mirror. - Highlights: Black-Right-Pointing-Pointer The quantum noise problem in the mirror-field system is re-visited by a field-theoretic approach. Black-Right-Pointing-Pointer Other than the shot noise and radiation pressure noise, we show there are new sources of noise and correlation between them. Black-Right-Pointing-Pointer The noise correlations can
When do perturbative approaches accurately capture the dynamics of complex quantum systems?
Fruchtman, Amir; Lambert, Neill; Gauger, Erik M.
2016-01-01
Understanding the dynamics of higher-dimensional quantum systems embedded in a complex environment remains a significant theoretical challenge. While several approaches yielding numerically converged solutions exist, these are computationally expensive and often provide only limited physical insight. Here we address the question: when do more intuitive and simpler-to-compute second-order perturbative approaches provide adequate accuracy? We develop a simple analytical criterion and verify its validity for the case of the much-studied FMO dynamics as well as the canonical spin-boson model. PMID:27335176
Scheme of thinking quantum systems
NASA Astrophysics Data System (ADS)
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
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.
Control of noisy quantum systems: Field-theory approach to error mitigation
NASA Astrophysics Data System (ADS)
Hipolito, Rafael; Goldbart, Paul M.
2016-04-01
We consider the basic quantum-control task of obtaining a target unitary operation (i.e., a quantum gate) via control fields that couple to the quantum system and are chosen to best mitigate errors resulting from time-dependent noise, which frustrate this task. We allow for two sources of noise: fluctuations in the control fields and fluctuations arising from the environment. We address the issue of control-error mitigation by means of a formulation rooted in the Martin-Siggia-Rose (MSR) approach to noisy, classical statistical-mechanical systems. To do this, we express the noisy control problem in terms of a path integral, and integrate out the noise to arrive at an effective, noise-free description. We characterize the degree of success in error mitigation via a fidelity metric, which characterizes the proximity of the sought-after evolution to ones that are achievable in the presence of noise. Error mitigation is then best accomplished by applying the optimal control fields, i.e., those that maximize the fidelity subject to any constraints obeyed by the control fields. To make connection with MSR, we reformulate the fidelity in terms of a Schwinger-Keldysh (SK) path integral, with the added twist that the "forward" and "backward" branches of the time contour are inequivalent with respect to the noise. The present approach naturally and readily allows the incorporation of constraints on the control fields—a useful feature in practice, given that constraints feature in all real experiments. In addition to addressing the noise average of the fidelity, we consider its full probability distribution. The information content present in this distribution allows one to address more complex questions regarding error mitigation, including, in principle, questions of extreme value statistics, i.e., the likelihood and impact of rare instances of the fidelity and how to harness or cope with their influence. We illustrate this MSR-SK reformulation by considering a model
Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach
NASA Astrophysics Data System (ADS)
Chen, Yusui; You, J. Q.; Yu, Ting
2014-11-01
A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.
First-Principles Approach to Transient Heat Flow in Quantum Systems
NASA Astrophysics Data System (ADS)
Walczak, Kamil; Yerkes, Kirk; Nanoscale Physics Division Team; Thermal Management Center Collaboration
2015-03-01
We examine heat transfer via quantum advection modes (coherently correlated quantum states) between two thermal baths of different temperatures mediated by quantum system with discrete spectrum of accessible energy levels. Nanoscale transport is treated within the first-principles method by including the superposed wave functions into the quantum expression for heat flux. Our results show the specific modifications of heat transport characteristics due to the dynamics of quantum systems under consideration. Such dynamics is captured by non-steady-state solutions to time-dependent Schrödinger wave equation or by specific solutions of interrelated Pauli rate equations. Since the applicability of Fourier's law is questionable at nanoscale and in the case of transient heat conduction, we pay particular attention to the new physics of post-Fourier heat transport and its further consequences. For instance, the non-equilibrium conditions may establish and maintain certain degree of coherence between correlated quantum states which are involved into the energy conduction process. Understanding and gaining control of coherent manipulations of qubits (two-level quantum systems) is crucial for further development of quantum informatics. This work was supported by Pace University Start-up Grant and the Air Force Office of Scientific Research (AFOSR).
A quantum annealing approach for fault detection and diagnosis of graph-based systems
NASA Astrophysics Data System (ADS)
Perdomo-Ortiz, A.; Fluegemann, J.; Narasimhan, S.; Biswas, R.; Smelyanskiy, V. N.
2015-02-01
Diagnosing the minimal set of faults capable of explaining a set of given observations, e.g., from sensor readouts, is a hard combinatorial optimization problem usually tackled with artificial intelligence techniques. We present the mapping of this combinatorial problem to quadratic unconstrained binary optimization (QUBO), and the experimental results of instances embedded onto a quantum annealing device with 509 quantum bits. Besides being the first time a quantum approach has been proposed for problems in the advanced diagnostics community, to the best of our knowledge this work is also the first research utilizing the route Problem → QUBO → Direct embedding into quantum hardware, where we are able to implement and tackle problem instances with sizes that go beyond previously reported toy-model proof-of-principle quantum annealing implementations; this is a significant leap in the solution of problems via direct-embedding adiabatic quantum optimization. We discuss some of the programmability challenges in the current generation of the quantum device as well as a few possible ways to extend this work to more complex arbitrary network graphs.
Asplund, Erik; Kluener, Thorsten
2012-03-28
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.
Asplund, Erik; Klüner, Thorsten
2012-03-28
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated.
Roadmap on quantum optical systems
NASA Astrophysics Data System (ADS)
Dumke, Rainer; Lu, Zehuang; Close, John; Robins, Nick; Weis, Antoine; Mukherjee, Manas; Birkl, Gerhard; Hufnagel, Christoph; Amico, Luigi; Boshier, Malcolm G.; Dieckmann, Kai; Li, Wenhui; Killian, Thomas C.
2016-09-01
This roadmap bundles fast developing topics in experimental optical quantum sciences, addressing current challenges as well as potential advances in future research. We have focused on three main areas: quantum assisted high precision measurements, quantum information/simulation, and quantum gases. Quantum assisted high precision measurements are discussed in the first three sections, which review optical clocks, atom interferometry, and optical magnetometry. These fields are already successfully utilized in various applied areas. We will discuss approaches to extend this impact even further. In the quantum information/simulation section, we start with the traditionally successful employed systems based on neutral atoms and ions. In addition the marvelous demonstrations of systems suitable for quantum information is not progressing, unsolved challenges remain and will be discussed. We will also review, as an alternative approach, the utilization of hybrid quantum systems based on superconducting quantum devices and ultracold atoms. Novel developments in atomtronics promise unique access in exploring solid-state systems with ultracold gases and are investigated in depth. The sections discussing the continuously fast-developing quantum gases include a review on dipolar heteronuclear diatomic gases, Rydberg gases, and ultracold plasma. Overall, we have accomplished a roadmap of selected areas undergoing rapid progress in quantum optics, highlighting current advances and future challenges. These exciting developments and vast advances will shape the field of quantum optics in the future.
Jin, Jinshuang; Zheng, Xiao; Yan, YiJing
2008-06-21
A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.
NASA Astrophysics Data System (ADS)
Jin, Jinshuang; Zheng, Xiao; Yan, Yijing
2008-06-01
A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schön and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Büttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.
Engineering quantum communication systems
NASA Astrophysics Data System (ADS)
Pinto, Armando N.; Almeida, Álvaro J.; Silva, Nuno A.; Muga, Nelson J.; Martins, Luis M.
2012-06-01
Quantum communications can provide almost perfect security through the use of quantum laws to detect any possible leak of information. We discuss critical issues in the implementation of quantum communication systems over installed optical fibers. We use stimulated four-wave mixing to generate single photons inside optical fibers, and by tuning the separation between the pump and the signal we adjust the average number of photons per pulse. We report measurements of the source statistics and show that it goes from a thermal to Poisson distribution with the increase of the pump power. We generate entangled photons pairs through spontaneous four-wave mixing. We report results for different type of fibers to approach the maximum value of the Bell inequality. We model the impact of polarization rotation, attenuation and Raman scattering and present optimum configurations to increase the degree of entanglement. We encode information in the photons polarization and assess the use of wavelength and time division multiplexing based control systems to compensate for the random rotation of the polarization during transmission. We show that time division multiplexing systems provide a more robust solution considering the values of PMD of nowadays installed fibers. We evaluate the impact on the quantum channel of co-propagating classical channels, and present guidelines for adding quantum channels to installed WDM optical communication systems without strongly penalizing the performance of the quantum channel. We discuss the process of retrieving information from the photons polarization. We identify the major impairments that limit the speed and distance of the quantum channel. Finally, we model theoretically the QBER and present results of an experimental performance assessment of the system quality through QBER measurements.
Open quantum system approach to the Gibbons-Hawking effect of de Sitter space-time.
Yu, Hongwei
2011-02-11
We analyze, in the paradigm of open quantum systems, the reduced dynamics of a freely falling two-level detector in de Sitter space-time in weak interaction with a reservoir of fluctuating quantized conformal scalar fields in the de Sitter-invariant vacuum. We find that the detector is asymptotically driven to a thermal state at the Gibbons-Hawking temperature, regardless of its initial state. Our discussion, therefore, shows that the Gibbons-Hawking effect of de Sitter space-time can be understood as a manifestation of thermalization phenomena that involves decoherence and dissipation in open quantum systems.
2013-02-15
Universiti Teknikal Malaysia Melaka in Malaysia. The project was then used to partially support a new PhD student, Mr Shanon Vuglar (who is a former...method based on cascade realization of quantum systems is used and a conference and journal paper have been produced. In another approach, a method...based on singular perturbation is used and a conference and journal paper have resulted. This work was extended by the graduate student Shanon Vuglar to
A unified approach to quantum and classical TTW systems based on factorizations
Celeghini, E.; Kuru, Ş.; Negro, J.; Olmo, M.A. del
2013-05-15
A unifying method based on factorization properties is introduced for finding symmetries of quantum and classical superintegrable systems using the example of the Tremblay–Turbiner–Winternitz (TTW) model. It is shown that the symmetries of the quantum system can be implemented in a natural way to its classical version. Besides, by this procedure we get also other type of constants of motion depending explicitly on time that allow to find directly the motion of the system whose corresponding trajectories coincide with those obtained previously by using its symmetries. -- Highlights: ► A unified method is given to find symmetries of classical and quantum systems. ► Ladder–shift operators and functions have analog expressions and relations. ► This method is applied to the TTW system to obtain its symmetries. ► For the classical cases a set of time dependent constants of motion are obtained. ► They allow us to find directly the motion and trajectories.
NASA Astrophysics Data System (ADS)
Agarwalla, Bijay Kumar; Kulkarni, Manas; Mukamel, Shaul; Segal, Dvira
2016-07-01
We investigate gain in microwave photonic cavities coupled to voltage-biased double quantum dot systems with an arbitrarily strong dot-lead coupling and with a Holstein-like light-matter interaction, by employing the diagrammatic Keldysh nonequilibrium Green's function approach. We compute out-of-equilibrium properties of the cavity: its transmission, phase response, mean photon number, power spectrum, and spectral function. We show that by the careful engineering of these hybrid light-matter systems, one can achieve a significant amplification of the optical signal with the voltage-biased electronic system serving as a gain medium. We also study the steady-state current across the device, identifying elastic and inelastic tunneling processes which involve the cavity mode. Our results show how recent advances in quantum electronics can be exploited to build hybrid light-matter systems that behave as microwave amplifiers and photon source devices. The diagrammatic Keldysh approach is primarily discussed for a cavity-coupled double quantum dot architecture, but it is generalizable to other hybrid light-matter systems.
Advanced quantum communication systems
NASA Astrophysics Data System (ADS)
Jeffrey, Evan Robert
Quantum communication provides several examples of communication protocols which cannot be implemented securely using only classical communication. Currently, the most widely known of these is quantum cryptography, which allows secure key exchange between parties sharing a quantum channel subject to an eavesdropper. This thesis explores and extends the realm of quantum communication. Two new quantum communication protocols are described. The first is a new form of quantum cryptography---relativistic quantum cryptography---which increases communication efficiency by exploiting a relativistic bound on the power of an eavesdropper, in addition to the usual quantum mechanical restrictions intrinsic to quantum cryptography. By doing so, we have observed over 170% improvement in communication efficiency over a similar protocol not utilizing relativity. A second protocol, Quantum Orienteering, allows two cooperating parties to communicate a specific direction in space. This application shows the possibility of using joint measurements, or projections onto an entangled state, in order to extract the maximum useful information from quantum bits. For two-qubit communication, the maximal fidelity of communication using only separable operations is 73.6%, while joint measurements can improve the efficiency to 78.9%. In addition to implementing these protocols, we have improved several resources for quantum communication and quantum computing. Specifically, we have developed improved sources of polarization-entangled photons, a low-loss quantum memory for polarization qubits, and a quantum random number generator. These tools may be applied to a wide variety of future quantum and classical information systems.
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
2007-07-20
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Natural approach to quantum dissipation
NASA Astrophysics Data System (ADS)
Taj, David; Öttinger, Hans Christian
2015-12-01
The dissipative dynamics of a quantum system weakly coupled to one or several reservoirs is usually described in terms of a Lindblad generator. The popularity of this approach is certainly due to the linear character of the latter. However, while such linearity finds justification from an underlying Hamiltonian evolution in some scaling limit, it does not rely on solid physical motivations at small but finite values of the coupling constants, where the generator is typically used for applications. The Markovian quantum master equations we propose are instead supported by very natural thermodynamic arguments. They themselves arise from Markovian master equations for the system and the environment which preserve factorized states and mean energy and generate entropy at a non-negative rate. The dissipative structure is driven by an entropic map, called modular, which introduces nonlinearity. The generated modular dynamical semigroup (MDS) guarantees for the positivity of the time evolved state the correct steady state properties, the positivity of the entropy production, and a positive Onsager matrix with symmetry relations arising from Green-Kubo formulas. We show that the celebrated Davies Lindblad generator, obtained through the Born and the secular approximations, generates a MDS. In doing so we also provide a nonlinear MDS which is supported by a weak coupling argument and is free from the limitations of the Davies generator.
NASA Astrophysics Data System (ADS)
Cahill, Reginald T.
2002-10-01
So far proposed quantum computers use fragile and environmentally sensitive natural quantum systems. Here we explore the new notion that synthetic quantum systems suitable for quantum computation may be fabricated from smart nanostructures using topological excitations of a stochastic neural-type network that can mimic natural quantum systems. These developments are a technological application of process physics which is an information theory of reality in which space and quantum phenomena are emergent, and so indicates the deep origins of quantum phenomena. Analogous complex stochastic dynamical systems have recently been proposed within neurobiology to deal with the emergent complexity of biosystems, particularly the biodynamics of higher brain function. The reasons for analogous discoveries in fundamental physics and neurobiology are discussed.
Numerical approach of the quantum circuit theory
NASA Astrophysics Data System (ADS)
Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.
2017-03-01
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Sorting quantum systems efficiently
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
NASA Astrophysics Data System (ADS)
Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert
Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.
Dressed coherent states in finite quantum systems: A cooperative game theory approach
NASA Astrophysics Data System (ADS)
Vourdas, A.
2017-01-01
A quantum system with variables in Z(d) is considered. Coherent density matrices and coherent projectors of rank n are introduced, and their properties (e.g., the resolution of the identity) are discussed. Cooperative game theory and in particular the Shapley methodology, is used to renormalize coherent states, into a particular type of coherent density matrices (dressed coherent states). The Q-function of a Hermitian operator, is then renormalized into a physical analogue of the Shapley values. Both the Q-function and the Shapley values, are used to study the relocation of a Hamiltonian in phase space as the coupling constant varies, and its effect on the ground state of the system. The formalism is also generalized for any total set of states, for which we have no resolution of the identity. The dressing formalism leads to density matrices that resolve the identity, and makes them practically useful.
Open-quantum-systems approach to complementarity in neutral-kaon interferometry
NASA Astrophysics Data System (ADS)
de Souza, Gustavo; de Oliveira, J. G. G.; Varizi, Adalberto D.; Nogueira, Edson C.; Sampaio, Marcos D.
2016-12-01
In bipartite quantum systems, entanglement correlations between the parties exerts direct influence in the phenomenon of wave-particle duality. This effect has been quantitatively analyzed in the context of two qubits by Jakob and Bergou [Opt. Commun. 283, 827 (2010), 10.1016/j.optcom.2009.10.044]. Employing a description of the K -meson propagation in free space where its weak decay states are included as a second party, we study here this effect in the kaon-antikaon oscillations. We show that a new quantitative "triality" relation holds, similar to the one considered by Jakob and Bergou. In our case, it relates the distinguishability between the decay-product states corresponding to the distinct kaon propagation modes KS, KL, the amount of wave-like path interference between these states, and the amount of entanglement given by the reduced von Neumann entropy. The inequality can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature, therefore allowing one to see how it is affected by entanglement correlations. As we will discuss, it allows one to visualize clearly through the K0-K ¯0 oscillations the fundamental role of entanglement in quantum complementarity.
Direct Approach to Quantum Tunneling
NASA Astrophysics Data System (ADS)
Andreassen, Anders; Farhi, David; Frost, William; Schwartz, Matthew D.
2016-12-01
The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical potential and on the saddle-point approximation. While the resulting procedure can be checked against other semiclassical approaches in some one-dimensional cases, it is challenging to trace the role of the relevant physical scales, and any intuitive handle on the precision of the approximations involved is at best obscure. In this Letter, we use a physical definition of the tunneling probability to derive a formula for the decay rate in both quantum mechanics and quantum field theory directly from the Minkowski path integral, without reference to unphysical deformations of the potential. There are numerous benefits to this approach, from nonperturbative applications to precision calculations and aesthetic simplicity.
Quantum system identification.
Burgarth, Daniel; Yuasa, Kazuya
2012-02-24
The aim of quantum system identification is to estimate the ingredients inside a black box, in which some quantum-mechanical unitary process takes place, by just looking at its input-output behavior. Here we establish a basic and general framework for quantum system identification, that allows us to classify how much knowledge about the quantum system is attainable, in principle, from a given experimental setup. We show that controllable closed quantum systems can be estimated up to unitary conjugation. Prior knowledge on some elements of the black box helps the system identification. We present an example in which a Bell measurement is more efficient to identify the system. When the topology of the system is known, the framework enables us to establish a general criterion for the estimability of the coupling constants in its Hamiltonian.
Zhang, Tianyuan; Evangelista, Francesco A
2016-09-13
In this work we propose a novel approach to solve the Schrödinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased toward any determinant. Therefore, the PCI approach can equally well describe static and dynamic electron correlation effects. This point is illustrated in benchmark computations on N2 at both equilibrium and stretched geometries. In both cases, the PCI achieves chemical accuracy with wave functions that contain less than 0.5% determinants of full CI space. We also report computations on the ground state of C2 with up to quaduple-ζ basis sets and wave functions as large as 200 million determinants, which allow a direct comparison of the PCI, FCIQMC, and density matrix renormalization group (DMRG) methods. The size of the PCI wave function grows modestly with the number of unoccupied orbitals, and its accuracy may be tuned to match that of FCIQMC and DMRG.
Time-dependent approach to electron pumping in open quantum systems
NASA Astrophysics Data System (ADS)
Stefanucci, G.; Kurth, S.; Rubio, A.; Gross, E. K. U.
2008-02-01
We use a recently proposed time-dependent approach to investigate the motion of electrons in quantum pump device configurations. The occupied one-particle states are propagated in real time and employed to calculate the local electron density and current. The approach can also be embedded in the framework of time-dependent density functional theory to include electron-electron interactions. An advantage of the present computational scheme is that the same computational effort is required to simulate monochromatic, polychromatic, and nonperiodic drivings. Furthermore, initial-state dependence and history effects are naturally accounted for. We present results for one-dimensional devices exposed to a traveling potential wave. (i) We show that for pumping across a single potential barrier, electrons are transported in pockets and the transport mechanism resembles pumping of water with the Archimedean screw; (ii) we propose a simple model to study pumping through semiconductor nanostructures and we address the phenomenon of the current flowing in the opposite direction to the field propagation; (iii) we present the first numerical evidence of long-lived superimposed oscillations as induced by the presence of bound states and discuss the dependence of their lifetime on the frequency and amplitude of the driving field. By combining Floquet theory with nonequilibrium Green’s functions, we also obtain a general expression for the pumped current in terms of inelastic transmission probabilities. This latter result is used for benchmarking our propagation scheme in the long-time limit. Finally, we discuss the limitations of Floquet-based algorithms and suggest our approach as a possible way to go beyond them.
2008-03-15
0603048 (2006) [3] Q. Zhang et al, Experimental Quantum Teleportation of a Two-Qubit Composite System, quant-ph/0609129 (2006) [4] G. Y. Xiang et...AFOSR project “ Quantum Communication Systems” University of Oxford and UMK Torun Final Report 15 March 2008 Summary This document...temporal characterization by interference with a local oscillator and the theoretical study of their propagation in lossy quantum channels. Also, their
Quantum electromechanical systems
NASA Astrophysics Data System (ADS)
Milburn, Gerard J.; Polkinghorne, Rodney
2001-11-01
We discuss the conditions under which electromechanical systems, fabricated on a sub micron scale, require a quantum description. We illustrate the discussion with the example of a mechanical electroscope for which the resonant frequency of a cantilever changes in response to a local charge. We show how such devices may be used as a quantum noise limited apparatus for detection of a single charge or spin with applications to quantum computing.
Correlation diagrams: an intuitive approach to correlations in quantum Hall systems
NASA Astrophysics Data System (ADS)
Mulay, S. B.; Quinn, J. J.; Shattuck, M. A.
2016-03-01
A trial wave function Ψ(1, 2,..., N) of an N electron system can always be written as the product of an antisymmetric Fermion factor F{zij } = Π i
Danilov, Viatcheslav; Nagaitsev, Sergei; /Fermilab
2011-11-01
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case. In this paper we have described an extension of the Ermakov-like transformation to the Schroedinger and Pauli equations. It is shown that these newly found transformations create a vast variety of time dependent quantum equations that can be solved in analytic functions, or, at least, can be reduced to time-independent ones.
NEW APPROACHES: Quantum bombing reality
NASA Astrophysics Data System (ADS)
Adams, Steve
1998-11-01
The ideas of quantum mechanics are challenging for students. The quantum bomb thought experiment described here shows how the existence of other possible worlds can affect outcomes in the real world as a result of quantum interference.
Quantum correlation of an optically controlled open quantum system
NASA Astrophysics Data System (ADS)
Chan, Ching-Kit; Sham, L. J.
2012-02-01
A precise time-dependent optical control of an open quantum system relies on an accurate account of the quantum interference among the system, the photon control and the dissipative environment. In the spirit of the Keldysh non-equilibrium Green's function approach, we develop a diagrammatic technique to precisely calculate this quantum correlation for a fast multimode coherent photon control against slow relaxation, valid for both Markovian and non-Markovian systems. We demonstrate how this novel formalism can lead to a better accuracy than existing approximations of the master equation. We also describe extensions to cases with controls by photon state other than the coherent Glauber state.
Novel Quantum Monte Carlo Approaches for Quantum Liquids
NASA Astrophysics Data System (ADS)
Rubenstein, Brenda M.
the eventual hope is to apply this algorithm to the exploration of yet unidentified high-pressure, low-temperature phases of hydrogen, I employ this algorithm to determine whether or not quantum hard spheres can form a low-temperature bcc solid if exchange is not taken into account. In the final chapter of this thesis, I use Path Integral Monte Carlo once again to explore whether glassy para-hydrogen exhibits superfluidity. Physicists have long searched for ways to coax hydrogen into becoming a superfluid. I present evidence that, while glassy hydrogen does not crystallize at the temperatures at which hydrogen might become a superfluid, it nevertheless does not exhibit superfluidity. This is because the average binding energy per p-H2 molecule poses a severe barrier to exchange regardless of whether the system is crystalline. All in all, this work extends the reach of Quantum Monte Carlo methods to new systems and brings the power of existing methods to bear on new problems. Portions of this work have been published in Rubenstein, PRE (2010) and Rubenstein, PRA (2012) [167;169]. Other papers not discussed here published during my Ph.D. include Rubenstein, BPJ (2008) and Rubenstein, PRL (2012) [166;168]. The work in Chapters 6 and 7 is currently unpublished. [166] Brenda M. Rubenstein, Ivan Coluzza, and Mark A. Miller. Controlling the folding and substrate-binding of proteins using polymer brushes. Physical Review Letters, 108(20):208104, May 2012. [167] Brenda M. Rubenstein, J.E. Gubernatis, and J.D. Doll. Comparative monte carlo efficiency by monte carlo analysis. Physical Review E, 82(3):036701, September 2010. [168] Brenda M. Rubenstein and Laura J. Kaufman. The role of extracellular matrix in glioma invasion: A cellular potts model approach. Biophysical Journal, 95(12):5661-- 5680, December 2008. [169] Brenda M. Rubenstein, Shiwei Zhang, and David R. Reichman. Finite-temperature auxiliary-field quantum monte carlo for bose-fermi mixtures. Physical Review A, 86
NASA Astrophysics Data System (ADS)
Afzali, R.; Ebrahimian, N.; Eghbalifar, B.
2016-10-01
By approximating the energy gap, entering nano-size effect via gap fluctuation and calculating the Green's functions and the space-spin density matrix, the dependence of quantum correlation (entanglement, discord and tripartite entanglement) on the relative distance of two electron spins forming Cooper pairs, the energy gap and the length of bulk and nano interacting Fermi system (a nodal d-wave superconductor) is determined. In contrast to a s-wave superconductor, quantum correlation of the system is sensitive to the change of the gap magnitude and strongly depends on the length of the grain. Also, quantum discord oscillates. Furthermore, the entanglement length and the correlation length are investigated. Discord becomes zero at a characteristic length of the d-wave superconductor.
Sokkar, Pandian; Boulanger, Eliot; Thiel, Walter; Sanchez-Garcia, Elsa
2015-04-14
We present a hybrid quantum mechanics/molecular mechanics/coarse-grained (QM/MM/CG) multiresolution approach for solvated biomolecular systems. The chemically important active-site region is treated at the QM level. The biomolecular environment is described by an atomistic MM force field, and the solvent is modeled with the CG Martini force field using standard or polarizable (pol-CG) water. Interactions within the QM, MM, and CG regions, and between the QM and MM regions, are treated in the usual manner, whereas the CG-MM and CG-QM interactions are evaluated using the virtual sites approach. The accuracy and efficiency of our implementation is tested for two enzymes, chorismate mutase (CM) and p-hydroxybenzoate hydroxylase (PHBH). In CM, the QM/MM/CG potential energy scans along the reaction coordinate yield reaction energies that are too large, both for the standard and polarizable Martini CG water models, which can be attributed to adverse effects of using large CG water beads. The inclusion of an atomistic MM water layer (10 Å for uncharged CG water and 5 Å for polarizable CG water) around the QM region improves the energy profiles compared to the reference QM/MM calculations. In analogous QM/MM/CG calculations on PHBH, the use of the pol-CG description for the outer water does not affect the stabilization of the highly charged FADHOOH-pOHB transition state compared to the fully atomistic QM/MM calculations. Detailed performance analysis in a glycine-water model system indicates that computation times for QM energy and gradient evaluations at the density functional level are typically reduced by 40-70% for QM/MM/CG relative to fully atomistic QM/MM calculations.
Khatami, Ehsan; Rigol, Marcos; Relaño, Armando; García-García, Antonio M
2012-05-01
We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.
Trejos, Víctor M; Gil-Villegas, Alejandro
2012-05-14
Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.
Quantum criticality in a double-quantum-dot system.
Zaránd, Gergely; Chung, Chung-Hou; Simon, Pascal; Vojta, Matthias
2006-10-20
We discuss the realization of the quantum-critical non-Fermi-liquid state, originally discovered within the two-impurity Kondo model, in double-quantum-dot systems. Contrary to common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries and is unstable only to charge transfer between the two dots. We propose an experimental setup where such charge transfer processes are suppressed, allowing a controlled approach to the quantum-critical state. We also discuss transport and scaling properties in the vicinity of the critical point.
Adiabatic Quantum Search in Open Systems.
Wild, Dominik S; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y; Lukin, Mikhail D
2016-10-07
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Adiabatic Quantum Search in Open Systems
NASA Astrophysics Data System (ADS)
Wild, Dominik S.; Gopalakrishnan, Sarang; Knap, Michael; Yao, Norman Y.; Lukin, Mikhail D.
2016-10-01
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.
Tailoring superradiance to design artificial quantum systems.
Longo, Paolo; Keitel, Christoph H; Evers, Jörg
2016-03-24
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This "reverse engineering" of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.
Tailoring superradiance to design artificial quantum systems
NASA Astrophysics Data System (ADS)
Longo, Paolo; Keitel, Christoph H.; Evers, Jörg
2016-03-01
Cooperative phenomena arising due to the coupling of individual atoms via the radiation field are a cornerstone of modern quantum and optical physics. Recent experiments on x-ray quantum optics added a new twist to this line of research by exploiting superradiance in order to construct artificial quantum systems. However, so far, systematic approaches to deliberately design superradiance properties are lacking, impeding the desired implementation of more advanced quantum optical schemes. Here, we develop an analytical framework for the engineering of single-photon superradiance in extended media applicable across the entire electromagnetic spectrum, and show how it can be used to tailor the properties of an artificial quantum system. This “reverse engineering” of superradiance not only provides an avenue towards non-linear and quantum mechanical phenomena at x-ray energies, but also leads to a unified view on and a better understanding of superradiance across different physical systems.
Quantum Langevin approach for non-Markovian quantum dynamics of the spin-boson model
NASA Astrophysics Data System (ADS)
Zhou, Zheng-Yang; Chen, Mi; Yu, Ting; You, J. Q.
2016-02-01
One longstanding difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due to its crucial applications in quantum noise control and manipulation as well as its central role in developing quantum theories of open systems. Here we solve this important model by developing a non-Markovian quantum Langevin approach. By projecting the quantum Langevin equation onto the coherent states of the bath, we can derive a set of non-Markovian quantum Bloch equations containing no explicit noise variables. This special feature offers a tremendous advantage over the existing stochastic Schrödinger equations in numerical simulations. The physical significance and generality of our approach are briefly discussed.
Yan, YiJing
2014-02-07
This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.
Teleportation in a noisy environment: a quantum trajectories approach.
Carlo, Gabriel G; Benenti, Giuliano; Casati, Giulio
2003-12-19
We study the fidelity of quantum teleportation for the situation in which quantum logic gates are used to provide the long distance entanglement required in the protocol, and where the effect of a noisy environment is modeled by means of a generalized amplitude damping channel. Our results demonstrate the effectiveness of the quantum trajectories approach, which allows the simulation of open systems with a large number of qubits (up to 24). This shows that the method is suitable for modeling quantum information protocols in realistic environments.
Jin, Jinshuang; Welack, Sven; Luo, JunYan; Li, Xin-Qi; Cui, Ping; Xu, Rui-Xue; Yan, YiJing
2007-04-07
A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed.
Network realization of triplet-type quantum stochastic systems
NASA Astrophysics Data System (ADS)
Zhou, Shaosheng; Fu, Shizhou; Chen, Yuping
2017-01-01
This paper focuses on a problem of network synthesis for a class of quantum stochastic systems. The systems under consideration are of triplet-type form and stem from linear quantum optics and linear quantum circuits. A new quantum network realization approach is proposed by generalizing the scattering operator from the scalar form to a unitary matrix in network components. It shows that the triplet-type quantum stochastic system can be approximated by a quantum network which consists of some one-degree-of-freedom generalized open-quantum harmonic oscillators (1DGQHOs) via series, concatenation and feedback connections.
Hidden Statistics Approach to Quantum Simulations
NASA Technical Reports Server (NTRS)
Zak, Michail
2010-01-01
Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the
Resonances in open quantum systems
NASA Astrophysics Data System (ADS)
Eleuch, Hichem; Rotter, Ingrid
2017-02-01
The Hamilton operator of an open quantum system is non-Hermitian. Its eigenvalues are generally complex and provide not only the energies but also the lifetimes of the states of the system. The states may couple via the common environment of scattering wave functions into which the system is embedded. This causes an external mixing (EM) of the states. Mathematically, EM is related to the existence of singular (the so-called exceptional) points. The eigenfunctions of a non-Hermitian operator are biorthogonal, in contrast to the orthogonal eigenfunctions of a Hermitian operator. A quantitative measure for the ratio between biorthogonality and orthogonality is the phase rigidity of the wave functions. At and near an exceptional point (EP), the phase rigidity takes its minimum value. The lifetimes of two nearby eigenstates of a quantum system bifurcate under the influence of an EP. At the parameter value of maximum width bifurcation, the phase rigidity approaches the value one, meaning that the two eigenfunctions become orthogonal. However, the eigenfunctions are externally mixed at this parameter value. The S matrix and therewith the cross section do contain, in the one-channel case, almost no information on the EM of the states. The situation is completely different in the case with two (or more) channels where the resonance structure is strongly influenced by the EM of the states and interesting features of non-Hermitian quantum physics are revealed. We provide numerical results for two and three nearby eigenstates of a non-Hermitian Hamilton operator that are embedded in one common continuum and are influenced by two adjoining EPs. The results are discussed. They are of interest for an experimental test of the non-Hermitian quantum physics as well as for applications.
The quantum Hall effects: Philosophical approach
NASA Astrophysics Data System (ADS)
Lederer, P.
2015-05-01
The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as gauge invariance, strong interactions in Condensed Matter physics, emergence of new paradigms. This paper focuses on some related philosophical questions. Various brands of positivism or agnosticism are confronted with the physics of the Quantum Hall Effects. Hacking's views on Scientific Realism, Chalmers' on Non-Figurative Realism are discussed. It is argued that the difficulties with those versions of realism may be resolved within a dialectical materialist approach. The latter is argued to provide a rational approach to the phenomena, theory and ontology of the Quantum Hall Effects.
Number-resolved master equation approach to quantum measurement and quantum transport
NASA Astrophysics Data System (ADS)
Li, Xin-Qi
2016-08-01
In addition to the well-known Landauer-Büttiker scattering theory and the nonequilibrium Green's function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number ( n)-resolved master equation ( n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.
Quantum approach to Bertrand duopoly
NASA Astrophysics Data System (ADS)
Fraçkiewicz, Piotr; Sładkowski, Jan
2016-09-01
The aim of the paper is to study the Bertrand duopoly example in the quantum domain. We use two ways to write the game in terms of quantum theory. The first one adapts the Li-Du-Massar scheme for the Cournot duopoly. The second one is a simplified model that exploits a two qubit entangled state. In both cases, we focus on finding Nash equilibria in the resulting games. Our analysis allows us to take another look at the classic model of Bertrand.
Universal freezing of quantum correlations within the geometric approach
Cianciaruso, Marco; Bromley, Thomas R.; Roga, Wojciech; Lo Franco, Rosario; Adesso, Gerardo
2015-01-01
Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation of the phenomenon for noisy quantum technologies. PMID:26053239
NASA Astrophysics Data System (ADS)
Iqbal, A.; Toor, A. H.
2002-03-01
We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory, i.e., an evolutionarily stable strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.
Quantum Effects in Biological Systems
NASA Astrophysics Data System (ADS)
Roy, Sisir
2014-07-01
The debates about the trivial and non-trivial effects in biological systems have drawn much attention during the last decade or so. What might these non-trivial sorts of quantum effects be? There is no consensus so far among the physicists and biologists regarding the meaning of "non-trivial quantum effects". However, there is no doubt about the implications of the challenging research into quantum effects relevant to biology such as coherent excitations of biomolecules and photosynthesis, quantum tunneling of protons, van der Waals forces, ultrafast dynamics through conical intersections, and phonon-assisted electron tunneling as the basis for our sense of smell, environment assisted transport of ions and entanglement in ion channels, role of quantum vacuum in consciousness. Several authors have discussed the non-trivial quantum effects and classified them into four broad categories: (a) Quantum life principle; (b) Quantum computing in the brain; (c) Quantum computing in genetics; and (d) Quantum consciousness. First, I will review the above developments. I will then discuss in detail the ion transport in the ion channel and the relevance of quantum theory in brain function. The ion transport in the ion channel plays a key role in information processing by the brain.
Quantum technologies with hybrid systems
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-01-01
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field. PMID:25737558
Quantum technologies with hybrid systems
NASA Astrophysics Data System (ADS)
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-03-01
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.
Quantum technologies with hybrid systems.
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-03-31
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field.
Quantum thermodynamics: a nonequilibrium Green's function approach.
Esposito, Massimiliano; Ochoa, Maicol A; Galperin, Michael
2015-02-27
We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.
NASA Astrophysics Data System (ADS)
Zelovich, Tamar; Hansen, Thorsten; Liu, Zhen-Fei; Neaton, Jeffrey B.; Kronik, Leeor; Hod, Oded
2017-03-01
A parameter-free version of the recently developed driven Liouville-von Neumann equation [T. Zelovich et al., J. Chem. Theory Comput. 10(8), 2927-2941 (2014)] for electronic transport calculations in molecular junctions is presented. The single driving rate, appearing as a fitting parameter in the original methodology, is replaced by a set of state-dependent broadening factors applied to the different single-particle lead levels. These broadening factors are extracted explicitly from the self-energy of the corresponding electronic reservoir and are fully transferable to any junction incorporating the same lead model. The performance of the method is demonstrated via tight-binding and extended Hückel calculations of simple junction models. Our analytic considerations and numerical results indicate that the developed methodology constitutes a rigorous framework for the design of "black-box" algorithms to simulate electron dynamics in open quantum systems out of equilibrium.
Dissipative quantum transport in macromolecules: Effective field theory approach
NASA Astrophysics Data System (ADS)
Schneider, E.; a Beccara, S.; Faccioli, P.
2013-08-01
We introduce an atomistic approach to the dissipative quantum dynamics of charged or neutral excitations propagating through macromolecular systems. Using the Feynman-Vernon path integral formalism, we analytically trace out from the density matrix the atomic coordinates and the heat bath degrees of freedom. This way we obtain an effective field theory which describes the real-time evolution of the quantum excitation and is fully consistent with the fluctuation-dissipation relation. The main advantage of the field-theoretic approach is that it allows us to avoid using the Keldysh contour formulation. This simplification makes it straightforward to derive Feynman diagrams to analytically compute the effects of the interaction of the propagating quantum excitation with the heat bath and with the molecular atomic vibrations. For illustration purposes, we apply this formalism to investigate the loss of quantum coherence of holes propagating through a poly(3-alkylthiophene) polymer.
Marquette, Ian; Quesne, Christiane
2015-06-15
We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.
Decoherence in infinite quantum systems
Blanchard, Philippe; Hellmich, Mario
2012-09-01
We review and discuss a notion of decoherence formulated in the algebraic framework of quantum physics. Besides presenting some sufficient conditions for the appearance of decoherence in the case of Markovian time evolutions we provide an overview over possible decoherence scenarios. The framework for decoherence we establish is sufficiently general to accommodate quantum systems with infinitely many degrees of freedom.
Efficient simulation of open quantum system in duality quantum computing
NASA Astrophysics Data System (ADS)
Wei, Shi-Jie; Long, Gui-Lu
2016-11-01
Practical quantum systems are open systems due to interactions with their environment. Understanding the evolution of open systems dynamics is important for quantum noise processes , designing quantum error correcting codes, and performing simulations of open quantum systems. Here we proposed an efficient quantum algorithm for simulating the evolution of an open quantum system on a duality quantum computer. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality algorithm, the time evolution of open quantum system is realized by using Kraus operators which is naturally realized in duality quantum computing. Compared to the Lloyd's quantum algorithm [Science.273, 1073(1996)] , the dependence on the dimension of the open quantum system in our algorithm is decreased. Moreover, our algorithm uses a truncated Taylor series of the evolution operators, exponentially improving the performance on the precision compared with existing quantum simulation algorithms with unitary evolution operations.
Nonlinear Ginzburg-Landau-type approach to quantum dissipation.
López, José L
2004-02-01
We formally derive two nonlinear Ginzburg-Landau type models starting from the Wigner-Fokker-Planck system, which rules the evolution of a quantum electron gas interacting with a heat bath in thermodynamic equilibrium. These models mainly consist of a quantum, dissipative O(Planck 3) hydrodynamic/O(Planck 4) stochastic correction to the frictional (Caldeira-Leggett-)Schrödinger equation. The main ingredient lies in the use of the hydrodynamic/stochastic fluid model approach associated with the quantum Fokker-Planck equation and the identification of the associated pressure field. Then, Madelung transformations set the problem in the Schrödinger picture of dissipative quantum mechanics. We also describe the stationary dynamics associated with both systems.
Pachón, Leonardo A; Yu, Li; Brumer, Paul
2013-01-01
The underlying mechanisms for one photon phase control are revealed through a master equation approach. Specifically, two mechanisms are identified, one operating on the laser time scale and the other on the time scale of the system-bath interaction. The effects of the secular and non-secular Markovian approximations are carefully examined.
Quantum Resonance Approach to Combinatorial Optimization
NASA Technical Reports Server (NTRS)
Zak, Michail
1997-01-01
It is shown that quantum resonance can be used for combinatorial optimization. The advantage of the approach is in independence of the computing time upon the dimensionality of the problem. As an example, the solution to a constraint satisfaction problem of exponential complexity is demonstrated.
Measuring entanglement entropy in a quantum many-body system
NASA Astrophysics Data System (ADS)
Rispoli, Matthew; Preiss, Philipp; Tai, Eric; Lukin, Alex; Schittko, Robert; Kaufman, Adam; Ma, Ruichao; Islam, Rajibul; Greiner, Markus
2016-05-01
The presence of large-scale entanglement is a defining characteristic of exotic quantum phases of matter. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. However, measuring entanglement remains a challenge. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. We demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. This protocol enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. In general, these experiments exemplify a method enabling the measurement and characterization of quantum phase transitions and in particular would be apt for studying systems such as magnetic ordering within the quantum Ising model.
Preconditioned quantum linear system algorithm.
Clader, B D; Jacobs, B C; Sprouse, C R
2013-06-21
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.
Coherent control in simple quantum systems
NASA Technical Reports Server (NTRS)
Prants, Sergey V.
1995-01-01
Coherent dynamics of two, three, and four-level quantum systems, simultaneously driven by concurrent laser pulses of arbitrary and different forms, is treated by using a nonperturbative, group-theoretical approach. The respective evolution matrices are calculated in an explicit form. General aspects of controllability of few-level atoms by using laser fields are treated analytically.
Mechanism for quantum speedup in open quantum systems
NASA Astrophysics Data System (ADS)
Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu
2016-02-01
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
Screening in quantum charged systems
NASA Astrophysics Data System (ADS)
Martin, Ph. A.; Gruber, Ch.
1984-07-01
For stationary states of quantum charged systems in ν dimensions, ν>=2, it is proven that the reduced-density matrices satisfy a set of sum rules whenever the clustering is faster than |x|-(ν+l). These sum rules, describing the screening properties, are analogous to those previously derived for classical systems. For neutral quantum fluids, it is shown that the clustering cannot be faster than the decay of the force.
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
NASA Astrophysics Data System (ADS)
Li, Jun; Lu, Dawei; Luo, Zhihuang; Laflamme, Raymond; Peng, Xinhua; Du, Jiangfeng
2016-07-01
Precisely characterizing and controlling realistic quantum systems under noises is a challenging frontier in quantum sciences and technologies. In developing reliable controls for open quantum systems, one is often confronted with the problem of the lack of knowledge on the system controllability. The purpose of this paper is to give a numerical approach to this problem, that is, to approximately compute the reachable set of states for coherently controlled quantum Markovian systems. The approximation consists of setting both upper and lower bounds for system's reachable region of states. Furthermore, we apply our reachability analysis to the control of the relaxation dynamics of a two-qubit nuclear magnetic resonance spin system. We implement some experimental tasks of quantum state engineering in this open system at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudopure states. These results demonstrate the usefulness of our theory and show interesting and promising applications of environment-assisted quantum dynamics.
Kishi, Ryohei; Fujii, Hiroaki; Minami, Takuya; Shigeta, Yasuteru; Nakano, Masayoshi
2015-01-22
In this study, we apply the ab initio molecular orbital - configuration interaction based quantum master equation (MOQME) approach to the calculation and analysis of the dynamic first hyperpolarizabilities (β) of asymmetric π-conjugated molecules. In this approach, we construct the excited state models by the ab initio configuration interaction singles method. Then, time evolutions of system reduced density matrix ρ(t) and system polarization p(t) are calculated by the QME approach. Dynamic β in the second harmonic generation is calculated based on the nonperturbative definition of nonlinear optical susceptibility, using the frequency domain system polarization p(ω). Spatial contributions of electrons to β are analyzed based on the dynamic hyperpolarizability density map, which visualizes the second-order response of charge density oscillating with a frequency of 2ω. We apply the present method to the calculation of the dynamic β of a series of donor/acceptor substituted polyene oligomers, and then discuss the applicability of the MOQME method to the calculation and analysis of dynamic NLO properties of molecular systems.
Time-dependent Kohn-Sham approach to quantum electrodynamics
Ruggenthaler, M.; Mackenroth, F.; Bauer, D.
2011-10-15
We prove a generalization of the van Leeuwen theorem toward quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. We circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.
Revealing Open Quantum Systems with Subsystem DFT
NASA Astrophysics Data System (ADS)
Krishtal, Alisa; Pavanello, Michele
The traditional quantum chemical methods, wave function or density based, are designed to solve for a closed system, where the Hamiltonian contains all relevant interactions. The closed system is, however, not realistic, as in real life the system is embedded in an environment with which it interacts to some degree. Including the description of the environment at the full quantum mechanical level leads to the Open Quantum Systems (OQS) theory: the only theory which can describe non-Markovian dynamics between the system and the environment. By allowing the flow of information in both directions phenomena such as quantum entanglement, relevant for the design of quantum computers, become available. While most OQS theories rely on the density matrix to describe the system-bath interaction, time-dependent subsystem DFT allows to approach the problem using the electron density. Through Dyson-like equations connecting the density-density response kernels of the OQS and its environment, the extent to which non-Markovian dynamics is present can be revealed. We illustrate this for the process of excitation energy transfer in coupled chromophores embedded in explicit solvent.
On a full Monte Carlo approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Sellier, J. M.; Dimov, I.
2016-12-01
The Monte Carlo approach to numerical problems has shown to be remarkably efficient in performing very large computational tasks since it is an embarrassingly parallel technique. Additionally, Monte Carlo methods are well known to keep performance and accuracy with the increase of dimensionality of a given problem, a rather counterintuitive peculiarity not shared by any known deterministic method. Motivated by these very peculiar and desirable computational features, in this work we depict a full Monte Carlo approach to the problem of simulating single- and many-body quantum systems by means of signed particles. In particular we introduce a stochastic technique, based on the strategy known as importance sampling, for the computation of the Wigner kernel which, so far, has represented the main bottleneck of this method (it is equivalent to the calculation of a multi-dimensional integral, a problem in which complexity is known to grow exponentially with the dimensions of the problem). The introduction of this stochastic technique for the kernel is twofold: firstly it reduces the complexity of a quantum many-body simulation from non-linear to linear, secondly it introduces an embarassingly parallel approach to this very demanding problem. To conclude, we perform concise but indicative numerical experiments which clearly illustrate how a full Monte Carlo approach to many-body quantum systems is not only possible but also advantageous. This paves the way towards practical time-dependent, first-principle simulations of relatively large quantum systems by means of affordable computational resources.
Quantum Communications Systems
2012-09-21
X.- M . Jin, B.J. Smith, M.B. Plenio , and I.A. Walmsley, Mapping coherence in measurement via full quantum tomog- raphy of a hybrid optical detector...K. C. Lee, B . J. Sussman, M . R. Sprague, P. Michelberger,K. F. Reim,J. Nunn, N. K. Lang- ford,P. J. Bustard, D. Jaksch, and I. A. Walmsley...Macroscopic non-classical states and tera- hertz quantum processing in room-temperature diamond, Nature Photonics 6, 41 (2011) [15] K. C. Lee, M . R. Sprague, B
Toward simulating complex systems with quantum effects
NASA Astrophysics Data System (ADS)
Kenion-Hanrath, Rachel Lynn
Quantum effects like tunneling, coherence, and zero point energy often play a significant role in phenomena on the scales of atoms and molecules. However, the exact quantum treatment of a system scales exponentially with dimensionality, making it impractical for characterizing reaction rates and mechanisms in complex systems. An ongoing effort in the field of theoretical chemistry and physics is extending scalable, classical trajectory-based simulation methods capable of capturing quantum effects to describe dynamic processes in many-body systems; in the work presented here we explore two such techniques. First, we detail an explicit electron, path integral (PI)-based simulation protocol for predicting the rate of electron transfer in condensed-phase transition metal complex systems. Using a PI representation of the transferring electron and a classical representation of the transition metal complex and solvent atoms, we compute the outer sphere free energy barrier and dynamical recrossing factor of the electron transfer rate while accounting for quantum tunneling and zero point energy effects. We are able to achieve this employing only a single set of force field parameters to describe the system rather than parameterizing along the reaction coordinate. Following our success in describing a simple model system, we discuss our next steps in extending our protocol to technologically relevant materials systems. The latter half focuses on the Mixed Quantum-Classical Initial Value Representation (MQC-IVR) of real-time correlation functions, a semiclassical method which has demonstrated its ability to "tune'' between quantum- and classical-limit correlation functions while maintaining dynamic consistency. Specifically, this is achieved through a parameter that determines the quantumness of individual degrees of freedom. Here, we derive a semiclassical correction term for the MQC-IVR to systematically characterize the error introduced by different choices of simulation
Bosson, Maël; Grudinin, Sergei; Redon, Stephane
2013-03-05
We present a novel Block-Adaptive Quantum Mechanics (BAQM) approach to interactive quantum chemistry. Although quantum chemistry models are known to be computationally demanding, we achieve interactive rates by focusing computational resources on the most active parts of the system. BAQM is based on a divide-and-conquer technique and constrains some nucleus positions and some electronic degrees of freedom on the fly to simplify the simulation. As a result, each time step may be performed significantly faster, which in turn may accelerate attraction to the neighboring local minima. By applying our approach to the nonself-consistent Atom Superposition and Electron Delocalization Molecular Orbital theory, we demonstrate interactive rates and efficient virtual prototyping for systems containing more than a thousand of atoms on a standard desktop computer.
Hybrid quantum systems with trapped charged particles
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Simmonds, Raymond W.; Leibfried, Dietrich; Wineland, David J.
2017-02-01
Trapped charged particles have been at the forefront of quantum information processing (QIP) for a few decades now, with deterministic two-qubit logic gates reaching record fidelities of 99.9 % and single-qubit operations of much higher fidelity. In a hybrid system involving trapped charges, quantum degrees of freedom of macroscopic objects such as bulk acoustic resonators, superconducting circuits, or nanomechanical membranes, couple to the trapped charges and ideally inherit the coherent properties of the charges. The hybrid system therefore implements a "quantum transducer," where the quantum reality (i.e., superpositions and entanglement) of small objects is extended to include the larger object. Although a hybrid quantum system with trapped charges could be valuable both for fundamental research and for QIP applications, no such system exists today. Here we study theoretically the possibilities of coupling the quantum-mechanical motion of a trapped charged particle (e.g., an ion or electron) to the quantum degrees of freedom of superconducting devices, nanomechanical resonators, and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e., the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples by using parameters that are experimentally attainable in the foreseeable future. We conclude that hybrid quantum systems involving a single atomic ion are unfavorable compared with the use of a single electron because the coupling rates between the ion and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates that significantly exceed decoherence rates. Moreover, it might have appealing properties such
Dynamics of open bosonic quantum systems in coherent state representation
Dalvit, D. A. R.; Berman, G. P.; Vishik, M.
2006-01-15
We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation values of observables evaluated in a coherent state representation. We examine a model of a quantum nonlinear oscillator with a density-density interaction with a collection of environmental oscillators at finite temperature. We derive the exact solution for dynamics of observables and demonstrate a consistent perturbation approach.
Quantum walk public-key cryptographic system
NASA Astrophysics Data System (ADS)
Vlachou, C.; Rodrigues, J.; Mateus, P.; Paunković, N.; Souto, A.
2015-12-01
Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum public-key cryptographic system based on quantum walks. In particular, in the proposed protocol the public-key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of public key generation and encryption/decryption procedures.
Duality quantum algorithm efficiently simulates open quantum systems
NASA Astrophysics Data System (ADS)
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Duality quantum algorithm efficiently simulates open quantum systems.
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-28
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Numerical approach for unstructured quantum key distribution
Coles, Patrick J.; Metodiev, Eric M.; Lütkenhaus, Norbert
2016-01-01
Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols with symmetries, since symmetry simplifies the analysis. However, experimental imperfections break symmetries, hence the effect of imperfections on key rates is difficult to estimate. Furthermore, it is an interesting question whether (intentionally) asymmetric protocols could outperform symmetric ones. Here we develop a robust numerical approach for calculating the key rate for arbitrary discrete-variable QKD protocols. Ultimately this will allow researchers to study ‘unstructured' protocols, that is, those that lack symmetry. Our approach relies on transforming the key rate calculation to the dual optimization problem, which markedly reduces the number of parameters and hence the calculation time. We illustrate our method by investigating some unstructured protocols for which the key rate was previously unknown. PMID:27198739
Quantum dynamics of nonlinear cavity systems
NASA Astrophysics Data System (ADS)
Nation, Paul David
In this work we investigate the quantum dynamics of three different configurations of nonlinear cavity systems. We begin by carrying out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprising a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing an external flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal and noise response where it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state. Next, we consider the use of a superconducting transmission line formed from an array of dc-SQUIDs for investigating analogue Hawking radiation. We will show that biasing the array with a space-time varying flux modifies the propagation velocity of the transmission line, leading to an effective metric with a horizon. As a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as backreaction and analogue space-time fluctuations on the Hawking process. Finally, we investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. The conditions are derived under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviation occurs once the pump mode (black hole) has released nearly half of its initial energy in the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the quantum state of the black hole and is entangled with the black hole's quantum
Quantum dynamics in open quantum-classical systems.
Kapral, Raymond
2015-02-25
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.
Quantum energy teleportation in a quantum Hall system
Yusa, Go; Izumida, Wataru; Hotta, Masahiro
2011-09-15
We propose an experimental method for a quantum protocol termed quantum energy teleportation (QET), which allows energy transportation to a remote location without physical carriers. Using a quantum Hall system as a realistic model, we discuss the physical significance of QET and estimate the order of energy gain using reasonable experimental parameters.
Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems
NASA Astrophysics Data System (ADS)
Frérot, Irénée; Roscilde, Tommaso
2016-08-01
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed many-body quantum states remains a formidable challenge, with fundamental implications in areas as broad as quantum condensed matter, quantum information, quantum metrology, and quantum biology. Here, we provide a quantitative definition of the variance of quantum coherent fluctuations (the quantum variance) of any observable on generic quantum states. The quantum variance generalizes the concept of thermal de Broglie wavelength (for the position of a free quantum particle) to the space of eigenvalues of any observable, quantifying the degree of coherent delocalization in that space. The quantum variance is generically measurable and computable as the difference between the static fluctuations and the static susceptibility of the observable; despite its simplicity, it is found to provide a tight lower bound to most widely accepted estimators of "quantumness" of observables (both as a feature as well as a resource), such as the Wigner-Yanase skew information and the quantum Fisher information. When considering bipartite fluctuations in an extended quantum system, the quantum variance expresses genuine quantum correlations among the two parts. In the case of many-body systems, it is found to obey an area law at finite temperature, extending therefore area laws of entanglement and quantum fluctuations of pure states to the mixed-state context. Hence the quantum variance paves the way to the measurement of macroscopic quantum coherence and quantum correlations in most complex quantum systems.
Takahashi, Hideaki; Omi, Atsushi; Morita, Akihiro; Matubayasi, Nobuyuki
2012-06-07
We present a simple and exact numerical approach to compute the free energy contribution δμ in solvation due to the electron density polarization and fluctuation of a quantum-mechanical solute in the quantum-mechanical/molecular-mechanical (QM/MM) simulation combined with the theory of the energy representation (QM/MM-ER). Since the electron density fluctuation is responsible for the many-body QM-MM interactions, the standard version of the energy representation method cannot be applied directly. Instead of decomposing the QM-MM polarization energy into the pairwise additive and non-additive contributions, we take sum of the polarization energies in the QM-MM interaction and adopt it as a new energy coordinate for the method of energy representation. Then, it is demonstrated that the free energy δμ can be exactly formulated in terms of the energy distribution functions for the solution and reference systems with respect to this energy coordinate. The benchmark tests were performed to examine the numerical efficiency of the method with respect to the changes in the individual properties of the solvent and the solute. Explicitly, we computed the solvation free energy of a QM water molecule in ambient and supercritical water, and also the free-energy change associated with the isomerization reaction of glycine from neutral to zwitterionic structure in aqueous solution. In all the systems examined, it was demonstrated that the computed free energy δμ agrees with the experimental value, irrespective of the choice of the reference electron density of the QM solute. The present method was also applied to a prototype reaction of adenosine 5'-triphosphate hydrolysis where the effect of the electron density fluctuation is substantial due to the excess charge. It was demonstrated that the experimental free energy of the reaction has been accurately reproduced with the present approach.
Quantum systems under frequency modulation.
Silveri, M P; Tuorila, J A; Thuneberg, E V; Paraoanu, G S
2017-05-01
We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the appearance of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.
Relativistic quantum metrology in open system dynamics.
Tian, Zehua; Wang, Jieci; Fan, Heng; Jing, Jiliang
2015-01-22
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.
Quantum Entanglement and Quantum Discord in Gaussian Open Systems
Isar, Aurelian
2011-10-03
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal bath.
Quantum cloning attacks against PUF-based quantum authentication systems
NASA Astrophysics Data System (ADS)
Yao, Yao; Gao, Ming; Li, Mo; Zhang, Jian
2016-08-01
With the advent of physical unclonable functions (PUFs), PUF-based quantum authentication systems have been proposed for security purposes, and recently, proof-of-principle experiment has been demonstrated. As a further step toward completing the security analysis, we investigate quantum cloning attacks against PUF-based quantum authentication systems and prove that quantum cloning attacks outperform the so-called challenge-estimation attacks. We present the analytical expression of the false-accept probability by use of the corresponding optimal quantum cloning machines and extend the previous results in the literature. In light of these findings, an explicit comparison is made between PUF-based quantum authentication systems and quantum key distribution protocols in the context of cloning attacks. Moreover, from an experimental perspective, a trade-off between the average photon number and the detection efficiency is discussed in detail.
Quantization and Quantum-Like Phenomena: A Number Amplitude Approach
NASA Astrophysics Data System (ADS)
Robinson, T. R.; Haven, E.
2015-12-01
Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.
Thermalization of field driven quantum systems
Fotso, H.; Mikelsons, K.; Freericks, J. K.
2014-01-01
There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a small energy window have essentially the same value; it is violated for integrable systems due to the infinite number of conserved quantities. Here, we show that when a system is driven by a DC electric field there are five generic behaviors: (i) monotonic or (ii) oscillatory approach to an infinite-temperature steady state; (iii) monotonic or (iv) oscillatory approach to a nonthermal steady state; or (v) evolution to an oscillatory state. Examining the Hubbard model (which thermalizes under a quench) and the Falicov-Kimball model (which does not), we find both exhibit scenarios (i–iv), while only Hubbard shows scenario (v). This shows richer behavior than in interaction quenches and integrability in the absence of a field plays no role. PMID:24736404
EDITORIAL: CAMOP: Quantum Non-Stationary Systems CAMOP: Quantum Non-Stationary Systems
NASA Astrophysics Data System (ADS)
Dodonov, Victor V.; Man'ko, Margarita A.
2010-09-01
-stationary systems, they nonetheless show some general trends. However, readers should remember that these comments represent the personal points of view of their authors. About a third of the comments are devoted to the evolution of quantum systems in the presence of dissipation or other sources of decoherence. This area, started by Landau in 1927, still contains many extremely interesting and unsolved problems. Here they are discussed in view of such different applications as the dynamics of quantum entanglement, cavity QED, optomechanics and the dynamical Casimir effect. Another group of comments deals with different (e.g. geometrical, tomographic, PT-symmetric) approaches to the dynamics of quantum systems, which have been developed in the past two decades. In particular, the problem of transition from quantum to classical description is considered and the inequalities generalizing the standard uncertainty relations are discussed in this connection. Three comments are devoted to the applications of nonclassical states, analytic representations and the algebraic techniques for resolving problems in quantum information and quantum statistical physics. The other contributions are related to different aspects of the dynamics of concrete physical systems, such as the wave-packet approach to the description of transport phenomena in mesoscopic systems, tunneling phenomena in low-dimensional semiconductor structures and resonance states of two-electron quantum dots. We thank all the authors and referees for their efforts in preparing this special issue. We hope that the comments in this collection will be useful for interested readers.
Quantum Entanglement in Open Systems
Isar, Aurelian
2008-01-24
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, the master equation for two independent harmonic oscillators interacting with an environment is solved in the asymptotic long-time regime. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems become asymptotically entangled for certain environments, so that in the long-time regime they manifest non-local quantum correlations. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.
Heat exchange mediated by a quantum system
NASA Astrophysics Data System (ADS)
Panasyuk, George Y.; Levin, George A.; Yerkes, Kirk L.
2012-08-01
We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the scanning tunneling microscope (STM) tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.
Heat exchange mediated by a quantum system.
Panasyuk, George Y; Levin, George A; Yerkes, Kirk L
2012-08-01
We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the scanning tunneling microscope (STM) tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.
Biosensing with quantum dots: a microfluidic approach.
Vannoy, Charles H; Tavares, Anthony J; Noor, M Omair; Uddayasankar, Uvaraj; Krull, Ulrich J
2011-01-01
Semiconductor quantum dots (QDs) have served as the basis for signal development in a variety of biosensing technologies and in applications using bioprobes. The use of QDs as physical platforms to develop biosensors and bioprobes has attracted considerable interest. This is largely due to the unique optical properties of QDs that make them excellent choices as donors in fluorescence resonance energy transfer (FRET) and well suited for optical multiplexing. The large majority of QD-based bioprobe and biosensing technologies that have been described operate in bulk solution environments, where selective binding events at the surface of QDs are often associated with relatively long periods to reach a steady-state signal. An alternative approach to the design of biosensor architectures may be provided by a microfluidic system (MFS). A MFS is able to integrate chemical and biological processes into a single platform and allows for manipulation of flow conditions to achieve, by sample transport and mixing, reaction rates that are not entirely diffusion controlled. Integrating assays in a MFS provides numerous additional advantages, which include the use of very small amounts of reagents and samples, possible sample processing before detection, ultra-high sensitivity, high throughput, short analysis time, and in situ monitoring. Herein, a comprehensive review is provided that addresses the key concepts and applications of QD-based microfluidic biosensors with an added emphasis on how this combination of technologies provides for innovations in bioassay designs. Examples from the literature are used to highlight the many advantages of biosensing in a MFS and illustrate the versatility that such a platform offers in the design strategy.
NASA Astrophysics Data System (ADS)
Makino, Hironori; Minami, Nariyuki
2014-07-01
The theory of the quantal level statistics of a classically integrable system, developed by Makino et al. in order to investigate the non-Poissonian behaviors of level-spacing distribution (LSD) and level-number variance (LNV) [H. Makino and S. Tasaki, Phys. Rev. E 67, 066205 (2003); H. Makino and S. Tasaki, Prog. Theor. Phys. Suppl. 150, 376 (2003); H. Makino, N. Minami, and S. Tasaki, Phys. Rev. E 79, 036201 (2009); H. Makino and S. Tasaki, Prog. Theor. Phys. 114, 929 (2005)], is successfully extended to the study of the E(K,L) function, which constitutes a fundamental measure to determine most statistical observables of quantal levels in addition to LSD and LNV. In the theory of Makino et al., the eigenenergy level is regarded as a superposition of infinitely many components whose formation is supported by the Berry-Robnik approach in the far semiclassical limit [M. Robnik, Nonlinear Phenom. Complex Syst. 1, 1 (1998)]. We derive the limiting E(K,L) function in the limit of infinitely many components and elucidate its properties when energy levels show deviations from the Poisson statistics.
Alternative algebraic approaches in quantum chemistry
Mezey, Paul G.
2015-01-22
Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.
NASA Astrophysics Data System (ADS)
Alhaidari, A. D.; Taiwo, T. J.
2017-02-01
Using a recent formulation of quantum mechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.
Quantum Indeterminacy of Cosmic Systems
Hogan, Craig J.
2013-12-30
It is shown that quantum uncertainty of motion in systems controlled mainly by gravity generally grows with orbital timescale $H^{-1}$, and dominates classical motion for trajectories separated by distances less than $\\approx H^{-3/5}$ in Planck units. For example, the cosmological metric today becomes indeterminate at macroscopic separations, $H_0^{-3/5}\\approx 60$ meters. Estimates suggest that entangled non-localized quantum states of geometry and matter may significantly affect fluctuations during inflation, and connect the scale of dark energy to that of strong interactions.
Ergodicity in randomly perturbed quantum systems
NASA Astrophysics Data System (ADS)
Gherardini, Stefano; Lovecchio, Cosimo; Müller, Matthias M.; Lombardi, Pietro; Caruso, Filippo; Saverio Cataliotti, Francesco
2017-03-01
The theoretical cornerstone of statistical mechanics is the ergodic assumption, i.e. the assumption that the time average of an observable equals its ensemble average. Here, we show how such a property is present when an open quantum system is continuously perturbed by an external environment effectively observing the system at random times while the system dynamics approaches the quantum Zeno regime. In this context, by large deviation theory we analytically show how the most probable value of the probability for the system to be in a given state eventually deviates from the non-stochastic case when the Zeno condition is not satisfied. We experimentally test our results with ultra-cold atoms prepared on an atom chip.
Polygamy of entanglement in multipartite quantum systems
NASA Astrophysics Data System (ADS)
Kim, Jeong San
2009-08-01
We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytical upper bound for the concurrence of assistance in bipartite quantum systems and derive a polygamy inequality of multipartite entanglement in arbitrary-dimensional quantum systems.
Control of decoherence in open quantum systems using feedback
NASA Astrophysics Data System (ADS)
Ganesan, Narayan
Decoherence, which is caused due to the interaction of a quantum system with its environment plagues all quantum systems and leads to the loss of quantum properties that are vital for quantum computation and quantum information processing. In this work we propose a novel strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Almost all the earlier work on decoherence control employ density matrix and stochastic master equations to analyze the problem. Our approach to decoherence control involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and Decoherence Free Subspaces (DFS). Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. The two concepts are contrasted and an improved theory of disturbance decoupling for general input affine systems is developed. In the process of calculating a suitable feedback the system has to be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. Finally the results are also shown to be superior to the ones obtained via master equations. In order to apply feedback a reliable information extraction scheme is presented that employs continuous indirect measurements with the help of a quantum probe. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform
Novel Numerical Approaches to Loop Quantum Cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter
2015-04-01
Loop Quantum Gravity (LQG) is an (as yet incomplete) approach to the quantization of gravity. When applied to symmetry reduced cosmological spacetimes (Loop Quantum Cosmology or LQC) one of the predictions of the theory is that the Big Bang is replaced by a Big Bounce, i.e. a previously existing contracting universe underwent a bounce at finite volume before becoming our expanding universe. The evolution equations of LQC take the form of difference equations (with the discretization given by the theory) that in the large volume limit can be approximated by partial differential equations (PDEs). In this talk I will first discuss some of the unique challenges encountered when trying to numerically solve these difference equations. I will then present some of the novel approaches that have been employed to overcome the challenges. I will here focus primarily on the Chimera scheme that takes advantage of the fact that the LQC difference equations can be approximated by PDEs in the large volume limit. I will finally also briefly discuss some of the results that have been obtained using these numerical techniques by performing simulations in regions of parameter space that were previously unreachable. This work is supported by a grant from the John Templeton Foundation and by NSF grant PHYS1068743.
Understanding quantum work in a quantum many-body system
NASA Astrophysics Data System (ADS)
Wang, Qian; Quan, H. T.
2017-03-01
Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015), 10.1103/PhysRevX.5.031038] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016), 10.1103/PhysRevE.93.062108], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems.
Software Systems for High-performance Quantum Computing
Humble, Travis S; Britt, Keith A
2016-01-01
Quantum computing promises new opportunities for solving hard computational problems, but harnessing this novelty requires breakthrough concepts in the design, operation, and application of computing systems. We define some of the challenges facing the development of quantum computing systems as well as software-based approaches that can be used to overcome these challenges. Following a brief overview of the state of the art, we present models for the quantum programming and execution models, the development of architectures for hybrid high-performance computing systems, and the realization of software stacks for quantum networking. This leads to a discussion of the role that conventional computing plays in the quantum paradigm and how some of the current challenges for exascale computing overlap with those facing quantum computing.
Few-body treatment of the quantum Hall system
NASA Astrophysics Data System (ADS)
Greene, Chris; Daily, Kevin; Wooten, Rachel
2015-03-01
The quantum Hall system is perhaps the simplest real physical system to exhibit complicated, highly-correlated quantum behavior. Our initial theoretical exploration of this problem approaches it from a few-body perspective using the adiabatic hyperspherical representation developed originally for atomic systems. Such a 2D system with interacting charged particles that move in an external magnetic field can be simulated for cold atoms using artificial vector gauge potentials. Supported by NSF.
Localization in Open Quantum Systems
NASA Astrophysics Data System (ADS)
Yusipov, I.; Laptyeva, T.; Denisov, S.; Ivanchenko, M.
2017-02-01
In an isolated single-particle quantum system, a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that a proper dissipation can drive a disordered system into a steady state with tunable localization properties. This can be achieved with a set of identical dissipative operators, each one acting nontrivially on a pair of sites. Operators are parametrized by a uniform phase, which controls the selection of Anderson modes contributing to the state. On the microscopic level, quantum trajectories of a system in the asymptotic regime exhibit intermittent dynamics consisting of long-time sticking events near selected modes interrupted by intermode jumps.
Using pseudopotentials within the interacting quantum atoms approach.
Tiana, Davide; Francisco, E; Blanco, M A; Pendás, A Martín
2009-07-09
A general strategy to extend the interacting quantum atoms (IQA) approach to pseudopotential or effective core potential electronic structure calculations is presented. With the protocol proposed here, the scope of IQA thinking opens to chemical bonding problems in heavy-atom systems, as well as to larger molecules than those presently allowed by computational limitations. We show that, provided that interatomic surfaces are computed from core-reconstructed densities, reasonable results are obtained by integrating reduced density matrices built from the pseudowave functions. Comparison with all-electron results in a few test systems shows that exchange-correlation energies are better reproduced than Coulombic contributions, an effect which is traced to inadequate atomic populations and leakage of the core population into the surrounding quantum atoms.
Optimal protocols for slowly driven quantum systems
NASA Astrophysics Data System (ADS)
Zulkowski, Patrick R.; DeWeese, Michael R.
2015-09-01
The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.
NASA Astrophysics Data System (ADS)
Hagar, Amit
Among the alternatives of non-relativistic quantum mechanics (NRQM) there are those that give different predictions than quantum mechanics in yet-untested circumstances, while remaining compatible with current empirical findings. In order to test these predictions, one must isolate one's system from environmental induced decoherence, which, on the standard view of NRQM, is the dynamical mechanism that is responsible for the 'apparent' collapse in open quantum systems. But while recent advances in condensed-matter physics may lead in the near future to experimental setups that will allow one to test the two hypotheses, namely genuine collapse vs. decoherence, hence make progress toward a solution to the quantum measurement problem, those philosophers and physicists who are advocating an information-theoretic approach to the foundations of quantum mechanics are still unwilling to acknowledge the empirical character of the issue at stake. Here I argue that in doing so they are displaying an unwarranted double standard.
Repeated interactions in open quantum systems
Bruneau, Laurent; Joye, Alain; Merkli, Marco
2014-07-15
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.
NASA Astrophysics Data System (ADS)
Cui, Ping
celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system
Novel Approaches to Quantum Computation Using Solid State Qubits
2007-12-31
Han, A scheme for the teleportation of multiqubit quantum information via the control of many agents in a network, submitted to Phys. Lett. A, 343...approach, Phys. Rev. B 70, 094513 (2004). 22. C.-P. Yang, S.-I. Chu, and S. Han, Efficient many party controlled teleportation of multiqubit quantum ...June 1, 2001- September 30, 2007 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER "Novel Approaches to Quantum Computation Using Solid State Qubits" F49620
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
Global quantum discord in multipartite systems
Rulli, C. C.; Sarandy, M. S.
2011-10-15
We propose a global measure for quantum correlations in multipartite systems, which is obtained by suitably recasting the quantum discord in terms of relative entropy and local von Neumann measurements. The measure is symmetric with respect to subsystem exchange and is shown to be nonnegative for an arbitrary state. As an illustration, we consider tripartite correlations in the Werner-GHZ (Greenberger-Horne-Zeilinger) state and multipartite correlations at quantum criticality. In particular, in contrast with the pairwise quantum discord, we show that the global quantum discord is able to characterize the infinite-order quantum phase transition in the Ashkin-Teller spin chain.
Decoherence control in open quantum systems via classical feedback
NASA Astrophysics Data System (ADS)
Ganesan, Narayan; Tarn, Tzyh-Jong
2007-03-01
In this work we propose a strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done. A construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with nontrivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and decoherence free subspaces. Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system must be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. In the subsequent section we discuss a general information extraction scheme to gain knowledge of the state and the amount of decoherence based on indirect continuous measurement. The analysis of continuous measurement on a decohering quantum system has not been extensively studied before. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free quantum computing. The results obtained are qualitatively different and superior to the ones obtained via master equations.
On Mathematical Modeling Of Quantum Systems
Achuthan, P.; Narayanankutty, Karuppath
2009-07-02
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
On Mathematical Modeling Of Quantum Systems
NASA Astrophysics Data System (ADS)
Achuthan, P.; Narayanankutty, Karuppath
2009-07-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Reexamination of strong subadditivity: A quantum-correlation approach
NASA Astrophysics Data System (ADS)
Taghiabadi, Razieh; Akhtarshenas, Seyed Javad; Sarbishaei, Mohsen
2017-03-01
The strong subadditivity inequality of von Neumann entropy relates the entropy of subsystems of a tripartite state ρA B C to that of the composite system. Here, we define T(a )(ρA B C) as the extent to which ρA B C fails to satisfy the strong subadditivity inequality S (ρB) +S (ρC) ≤S (ρA B) +S (ρA C) with equality and investigate its properties. In particular, by introducing auxiliary subsystem E , we consider any purification | ψA B C E> of ρA B C and formulate T(a )(ρA B C) as the extent to which the bipartite quantum correlations of ρA B and ρA C, measured by entanglement of formation and quantum discord, change under the transformation B →B E and C →C E . Invariance of quantum correlations of ρA B and ρA C under such transformation is shown to be a necessary and sufficient condition for vanishing T(a )(ρA B C) . Our approach allows one to characterize, intuitively, the structure of states for which the strong subadditivity is saturated. Moreover, along with providing a conservation law for quantum correlations of states for which the strong subadditivity inequality is satisfied with equality, we find that such states coincide with those that the Koashi-Winter monogamy relation is saturated.
Green's function approach for quantum graphs: An overview
NASA Astrophysics Data System (ADS)
Andrade, Fabiano M.; Schmidt, A. G. M.; Vicentini, E.; Cheng, B. K.; da Luz, M. G. E.
2016-08-01
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function (G) framework. This approach is particularly interesting because G can be written as a sum over classical-like paths, where local quantum effects are taken into account through the scattering matrix elements (basically, transmission and reflection amplitudes) defined on each one of the graph vertices. Hence, the exact G has the functional form of a generalized semiclassical formula, which through different calculation techniques (addressed in detail here) always can be cast into a closed analytic expression. It allows to solve exactly arbitrary large (although finite) graphs in a recursive and fast way. Using the Green's function method, we survey many properties of open and closed quantum graphs as scattering solutions for the former and eigenspectrum and eigenstates for the latter, also considering quasi-bound states. Concrete examples, like cube, binary trees and Sierpiński-like topologies are presented. Along the work, possible distinct applications using the Green's function methods for quantum graphs are outlined.
Calvani, Dario; Cuccoli, Alessandro; Gidopoulos, Nikitas I; Verrucchi, Paola
2013-04-23
The behavior of most physical systems is affected by their natural surroundings. A quantum system with an environment is referred to as open, and its study varies according to the classical or quantum description adopted for the environment. We propose an approach to open quantum systems that allows us to follow the cross-over from quantum to classical environments; to achieve this, we devise an exact parametric representation of the principal system, based on generalized coherent states for the environment. The method is applied to the s = 1/2 Heisenberg star with frustration, where the quantum character of the environment varies with the couplings entering the Hamiltonian H. We find that when the star is in an eigenstate of H, the central spin behaves as if it were in an effective magnetic field, pointing in the direction set by the environmental coherent-state angle variables (θ, ϕ), and broadened according to their quantum probability distribution. Such distribution is independent of ϕ, whereas as a function of θ is seen to get narrower as the quantum character of the environment is reduced, collapsing into a Dirac-δ function in the classical limit. In such limit, because ϕ is left undetermined, the Von Neumann entropy of the central spin remains finite; in fact, it is equal to the entanglement of the original fully quantum model, a result that establishes a relation between this latter quantity and the Berry phase characterizing the dynamics of the central spin in the effective magnetic field.
A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics
ERIC Educational Resources Information Center
Pujol, O.; Perez, J. P.
2007-01-01
The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…
NASA Astrophysics Data System (ADS)
Henner, Victor K.; Klots, Andrey; Belozerova, Tatyana
2016-12-01
Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used to model spin systems. In this paper we show that a classical spins based approach can be used to describe the phenomena essentially quantum in nature such as of the Pake doublet.
Quantum Hysteresis in Coupled Light-Matter Systems
NASA Astrophysics Data System (ADS)
Gómez-Ruiz, Fernando; Acevedo, Oscar; Quiroga, Luis; Rodríguez, Ferney; Johnson, Neil
2016-09-01
We investigate the non-equilibrium quantum dynamics of a canonical light-matter system, namely the Dicke model, when the light-matter interaction is ramped up and down through a cycle across the quantum phase transition. Our calculations reveal a rich set of dynamical behaviors determined by the cycle times, ranging from the slow, near adiabatic regime through to the fast, sudden quench regime. As the cycle time decreases, we uncover a crossover from an oscillatory exchange of quantum information between light and matter that approaches a reversible adiabatic process, to a dispersive regime that generates large values of light-matter entanglement. The phenomena uncovered in this work have implications in quantum control, quantum interferometry, as well as in quantum information theory.
Anonymous voting for multi-dimensional CV quantum system
NASA Astrophysics Data System (ADS)
Rong-Hua, Shi; Yi, Xiao; Jin-Jing, Shi; Ying, Guo; Moon-Ho, Lee
2016-06-01
We investigate the design of anonymous voting protocols, CV-based binary-valued ballot and CV-based multi-valued ballot with continuous variables (CV) in a multi-dimensional quantum cryptosystem to ensure the security of voting procedure and data privacy. The quantum entangled states are employed in the continuous variable quantum system to carry the voting information and assist information transmission, which takes the advantage of the GHZ-like states in terms of improving the utilization of quantum states by decreasing the number of required quantum states. It provides a potential approach to achieve the efficient quantum anonymous voting with high transmission security, especially in large-scale votes. Project supported by the National Natural Science Foundation of China (Grant Nos. 61272495, 61379153, and 61401519), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130162110012), and the MEST-NRF of Korea (Grant No. 2012-002521).
Thermodynamics of Weakly Measured Quantum Systems
NASA Astrophysics Data System (ADS)
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-01
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
Thermodynamics of Weakly Measured Quantum Systems.
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-26
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
Geometric phase for open quantum systems and stochastic unravelings
Bassi, Angelo; Ippoliti, Emiliano
2006-06-15
We analyze the geometric phase for an open quantum system when computed by resorting to a stochastic unraveling of the reduced density matrix (quantum jump approach or stochastic Schroedinger equations). We show that the resulting phase strongly depends on the type of unraveling used for the calculations: as such, this phase is not a geometric object since it depends on nonphysical parameters, which are not related to the path followed by the density matrix during the evolution of the system.
Zeno dynamics in quantum open systems
Zhang, Yu-Ran; Fan, Heng
2015-01-01
Quantum Zeno effect shows that frequent observations can slow down or even stop the unitary time evolution of an unstable quantum system. This effect can also be regarded as a physical consequence of the statistical indistinguishability of neighboring quantum states. The accessibility of quantum Zeno dynamics under unitary time evolution can be quantitatively estimated by quantum Zeno time in terms of Fisher information. In this work, we investigate the accessibility of quantum Zeno dynamics in quantum open systems by calculating noisy Fisher information when a trace preserving and completely positive map is assumed. We firstly study the consequences of non-Markovian noise on quantum Zeno effect and give the exact forms of the dissipative Fisher information and the quantum Zeno time. Then, for the operator-sum representation, an achievable upper bound of the quantum Zeno time is given with the help of the results in noisy quantum metrology. It is of significance that the noise reducing the accuracy in the entanglement-enhanced parameter estimation can conversely be favorable for the accessibility of quantum Zeno dynamics of entangled states. PMID:26099840
Lee, Sang-Bong
1993-09-01
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.
A quantum-like approach to the stock market
NASA Astrophysics Data System (ADS)
Aerts, Diederik; D'Hooghe, Bart; Sozzo, Sandro
2012-03-01
Modern approaches to stock pricing in quantitative finance are typically founded on the Black-Scholes model and the underlying random walk hypothesis. Empirical data indicate that this hypothesis works well in stable situations but, in abrupt transitions such as during an economical crisis, the random walk model fails and alternative descriptions are needed. For this reason, several proposals have been recently forwarded which are based on the formalism of quantum mechanics. In this paper we apply the SCoP formalism, elaborated to provide an operational foundation of quantum mechanics, to the stock market. We argue that a stock market is an intrinsically contextual system where agents' decisions globally influence the market system and stocks prices, determining a nonclassical behavior. More specifically, we maintain that a given stock does not generally have a definite value, e.g., a price, but its value is actualized as a consequence of the contextual interactions in the trading process. This contextual influence is responsible of the non-Kolmogorovian quantumlike behavior of the market at a statistical level. Then, we propose a sphere model within our hidden measurement formalism that describes a buying/selling process of a stock and shows that it is intuitively reasonable to assume that the stock has not a definite price until it is traded. This result is relevant in our opinion since it provides a theoretical support to the use of quantum models in finance.
Quantum speed limits in open system dynamics.
del Campo, A; Egusquiza, I L; Plenio, M B; Huelga, S F
2013-02-01
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.
Quantum teleportation of composite systems via mixed entangled states
Bandyopadhyay, Somshubhro; Sanders, Barry C.
2006-09-15
We analyze quantum teleportation for composite systems, specifically for concatenated teleporation (decomposing a large composite state into smaller states of dimension commensurate with the channel) and partial teleportation (teleporting one component of a larger quantum state). We obtain an exact expression for teleportation fidelity that depends solely on the dimension and singlet fraction for the entanglement channel and entanglement (measures by I concurrence) for the state; in fact quantum teleportation for composite systems provides an operational interpretation for I concurrence. In addition we obtain tight bounds on teleportation fidelity and prove that the average fidelity approaches the lower bound of teleportation fidelity in the high-dimension limit.
Quantum interference between independent reservoirs in open quantum systems
NASA Astrophysics Data System (ADS)
Chan, Ching-Kit; Lin, Guin-Dar; Yelin, Susanne F.; Lukin, Mikhail D.
2014-04-01
When a quantum system interacts with multiple reservoirs, the environmental effects are usually treated in an additive manner. We show that this assumption breaks down for non-Markovian environments that have finite memory times. Specifically, we demonstrate that quantum interferences between independent environments can qualitatively modify the dynamics of the physical system. We illustrate this effect with a two-level system coupled to two structured photonic reservoirs, discuss its origin using a nonequilibrium diagrammatic technique, and show an example when the application of this interference can result in an improved dark state preparation in a Λ system.
The operator algebra approach to quantum groups
Kustermans, Johan; Vaes, Stefaan
2000-01-01
A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116
Closed-Loop and Robust Control of Quantum Systems
Wang, Lin-Cheng
2013-01-01
For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H∞ control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention. PMID:23997680
Few-body treatment of the quantum Hall system
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Daily, Kevin; Greene, Chris H.
2015-05-01
When confined to a finite, two-dimensional area and exposed to a strong magnetic field, fermions exhibit complicated, highly-correlated quantum behavior known as the quantum Hall effect. At certain electron densities and magnetic fields, the system exhibits strong quantization due entirely to Coulomb interactions. Typical theoretical studies in the field consist of many-body numerical configuration interaction calculations performed in an energy-restricted single-particle Hilbert subspace. So far, quantum Hall behavior has been observed experimentally only in condensed matter systems, but there is significant interest in reproducing and studying the effect in highly-controlled cold atom systems. In light of such potential experimental developments, we approach the theoretical study of the quantum Hall system from a few-body perspective using the hyperspherical adiabatic technique developed originally for atomic systems. We gratefully acknowledge support from NSF.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
Nonadiabatic molecular dynamics simulation: An approach based on quantum measurement picture
Feng, Wei; Xu, Luting; Li, Xin-Qi; Fang, Weihai; Yan, YiJing
2014-07-15
Mixed-quantum-classical molecular dynamics simulation implies an effective quantum measurement on the electronic states by the classical motion of atoms. Based on this insight, we propose a quantum trajectory mean-field approach for nonadiabatic molecular dynamics simulations. The new protocol provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also bridges two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. Excellent agreement with the exact results is illustrated with representative model systems, including the challenging ones for traditional methods.
Quasi-Periodically Driven Quantum Systems
NASA Astrophysics Data System (ADS)
Verdeny, Albert; Puig, Joaquim; Mintert, Florian
2016-10-01
Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.
Quantum information metric and Berry curvature from a Lagrangian approach
NASA Astrophysics Data System (ADS)
Alvarez-Jimenez, Javier; Dector, Aldo; Vergara, J. David
2017-03-01
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of quantum systems. Our scheme provides a conceptually complete description and introduces a different point of view of earlier works. Using our formalism, we show how this expression can be applied to well-known quantum mechanical systems.
Quantum Interference between independent environments in open quantum systems
NASA Astrophysics Data System (ADS)
Chan, Ching-Kit; Lin, Guin-Dar; Yelin, Susanne; Lukin, Mikhail
2014-03-01
When a general quantum system interacts with multiple environments, the environmental effects are usually treated in an additive manner in the master equation. This assumption becomes questionable for non-Markovian environments that have finite memory times. Here, we show that quantum interferences between independent environments exist and can qualitatively modify the dynamics of the reduced physical system. We illustrate this effect with examples of atomic systems coupled to structured reservoirs, and discuss its origin in general using a non-equilibrium diagrammatic technique. The consequential decoherence dynamics cannot be captured by an additive master equation.
Surveying Instructors' Attitudes and Approaches to Teaching Quantum Mechanics
NASA Astrophysics Data System (ADS)
Siddiqui, Shabnam; Singh, Chandralekha
2010-10-01
Understanding instructors' attitudes and approaches to teaching quantum mechanics can be helpful in developing research-based learning tools. Here we discuss the findings from a survey in which 13 instructors reflected on issues related to quantum mechanics teaching. Topics included opinions about the goals of a quantum mechanics course, general challenges in teaching the subject, students' preparation for the course, comparison between their own learning of quantum mechanics vs. how they teach it and the extent to which contemporary topics are incorporated into the syllabus.
Driven harmonic oscillator as a quantum simulator for open systems
Piilo, Jyrki; Maniscalco, Sabrina
2006-09-15
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.
Architectures and Applications for Scalable Quantum Information Systems
2007-01-01
collaboration between computer science and physical sciences involving four groups: MIT, providing experimental quantum technology parameters and...quantum information processing system. Our project was a collaborative computer science and physical sciences effort involving four groups working in tight...Automate QRAM / QCL / Q QCC ARQOptimizers QASM QCPOL Layout Tools QIR • Approach: • Open-source • Layered hierarchy • Results: • Physical requirements
Holonomy, quantum mechanics and the signal-tuned Gabor approach to the striate cortex
NASA Astrophysics Data System (ADS)
Torreão, José R. A.
2016-02-01
It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantum systems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantum system whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantum mechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.
A quantum approach to homomorphic encryption
Tan, Si-Hui; Kettlewell, Joshua A.; Ouyang, Yingkai; Chen, Lin; Fitzsimons, Joseph F.
2016-01-01
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data. The quantum data is encoded on bosons of distinct species in distinct spatial modes, and the quantum computations are manipulations of these bosons in a manner independent of their species. A particular instance of our encoding hides up to a constant fraction of the information encrypted. This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length. This highlights the potential of our protocol to hide a non-trivial amount of information, and is suggestive of a large class of encodings that might yield better security. PMID:27658349
A quantum approach to homomorphic encryption
NASA Astrophysics Data System (ADS)
Tan, Si-Hui; Kettlewell, Joshua A.; Ouyang, Yingkai; Chen, Lin; Fitzsimons, Joseph F.
2016-09-01
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data. The quantum data is encoded on bosons of distinct species in distinct spatial modes, and the quantum computations are manipulations of these bosons in a manner independent of their species. A particular instance of our encoding hides up to a constant fraction of the information encrypted. This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length. This highlights the potential of our protocol to hide a non-trivial amount of information, and is suggestive of a large class of encodings that might yield better security.
A quantum approach to homomorphic encryption.
Tan, Si-Hui; Kettlewell, Joshua A; Ouyang, Yingkai; Chen, Lin; Fitzsimons, Joseph F
2016-09-23
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data. The quantum data is encoded on bosons of distinct species in distinct spatial modes, and the quantum computations are manipulations of these bosons in a manner independent of their species. A particular instance of our encoding hides up to a constant fraction of the information encrypted. This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length. This highlights the potential of our protocol to hide a non-trivial amount of information, and is suggestive of a large class of encodings that might yield better security.
Probabilistic Approach to Teaching the Principles of Quantum Mechanics
ERIC Educational Resources Information Center
Santos, Emilio
1976-01-01
Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)
Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach.
Borrelli, Raffaele; Gelin, Maxim F
2016-12-14
Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.
Controlling the shannon entropy of quantum systems.
Xing, Yifan; Wu, Jun
2013-01-01
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
Quantum chaos on hyperbolic manifolds: A new approach to cosmology
NASA Astrophysics Data System (ADS)
Tomaschitz, Roman
1992-04-01
We consider classical and quantum motion on multiply connected hyperbolic spaces, which appear as space-like slices in Robertson-Walker cosmologies. The topological structure of these manifolds creates on the one hand bounded chaotic trajectories, and on the other hand quantal bound states whose wave functions can be reconstructed from the chaotic geodesics. We obtain an exact relation between a probabilistic quantum mechanical wave field and the corresponding classical system, which is likewise probabilistic because of the instabilities of the trajectories with respect to the initial conditions. The central part in this reconstruction is played by the fractal limit set of the covering group of the manifold. This limit set determines the bounded chaotic trajectories on the manifold. Its Hausdorff measure and dimension determine the wave function of the quantum mechanical bound state for geodesic motion. We investigate relativistic scalar wave fields in de Sitter cosmologies, coupled to the curvature scalar of the manifold. We study the influence of the topological structure of space-time on their time evolution. Likewise we calculate the time asymptotics of their energies in the early and late stages of the cosmic expansion. While in the late stages both bounded and unbounded states approach the same rest energy, they show significantly different behavior at the beginning of the expansion. While the stable bound states have simple power law behavior, extended states show oscillations in their energy, with a frequency and an amplitude both diverging to infinity, indicating the instability of the quantum field at the beginning of the cosmic expansion.
Experimental demonstration of subcarrier multiplexed quantum key distribution system.
Mora, José; Ruiz-Alba, Antonio; Amaya, Waldimar; Martínez, Alfonso; García-Muñoz, Víctor; Calvo, David; Capmany, José
2012-06-01
We provide, to our knowledge, the first experimental demonstration of the feasibility of sending several parallel keys by exploiting the technique of subcarrier multiplexing (SCM) widely employed in microwave photonics. This approach brings several advantages such as high spectral efficiency compatible with the actual secure key rates, the sharing of the optical fainted pulse by all the quantum multiplexed channels reducing the system complexity, and the possibility of upgrading with wavelength division multiplexing in a two-tier scheme, to increase the number of parallel keys. Two independent quantum SCM channels featuring a sifted key rate of 10 Kb/s/channel over a link with quantum bit error rate <2% is reported.
Electron-phonon interaction in quantum transport through quantum dots and molecular systems
NASA Astrophysics Data System (ADS)
Ojeda, J. H.; Duque, C. A.; Laroze, D.
2016-12-01
The quantum transport and effects of decoherence properties are studied in quantum dots systems and finite homogeneous chains of aromatic molecules connected to two semi-infinite leads. We study these systems based on the tight-binding approach through Green's function technique within a real space renormalization and polaron transformation schemes. In particular, we calculate the transmission probability following the Landauer-Büttiker formalism, the I - V characteristics and the noise power of current fluctuations taken into account the decoherence. Our results may explain the inelastic effects through nanoscopic systems.
A geometric approach to quantum control in projective hilbert spaces
NASA Astrophysics Data System (ADS)
Pastorello, Davide
2017-02-01
A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper geometric Hamiltonian theory as explained in [2, 3, 7, 9]. From this point of view a quantum system can be described within a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by a projective Hilbert space. This paper is devoted to investigating how the notion of an accessibility algebra from classical control theory can be applied within the geometric Hamiltonian formulation of quantum mechanics to study controllability of a quantum system. A new characterization of quantum controllability in terms of Killing vector fields w.r.t. the Fubini-Study metric on projective space is also discussed.
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.
A minimalist approach to conceptualization of time in quantum theory
NASA Astrophysics Data System (ADS)
Kitada, Hitoshi; Jeknić-Dugić, Jasmina; Arsenijević, Momir; Dugić, Miroljub
2016-12-01
Ever since Schrödinger, Time in quantum theory is postulated Newtonian for every reference frame. With the help of certain known mathematical results, we show that the concept of the so-called Local Time allows avoiding the postulate. In effect, time appears as neither fundamental nor universal on the quantum-mechanical level while being consistently attributable to every, at least approximately, closed quantum system as well as to every of its (conservative or not) subsystems.
Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach
Sirjoosingh, Andrew; Pak, Michael V.; Brorsen, Kurt R.; Hammes-Schiffer, Sharon
2015-06-07
The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF{sup −} systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF{sup −} system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.
Simulation of n-qubit quantum systems. V. Quantum measurements
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2010-02-01
The FEYNMAN program has been developed during the last years to support case studies on the dynamics and entanglement of n-qubit quantum registers. Apart from basic transformations and (gate) operations, it currently supports a good number of separability criteria and entanglement measures, quantum channels as well as the parametrizations of various frequently applied objects in quantum information theory, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions. With the present update of the FEYNMAN program, we provide a simple access to (the simulation of) quantum measurements. This includes not only the widely-applied projective measurements upon the eigenspaces of some given operator but also single-qubit measurements in various pre- and user-defined bases as well as the support for two-qubit Bell measurements. In addition, we help perform generalized and POVM measurements. Knowing the importance of measurements for many quantum information protocols, e.g., one-way computing, we hope that this update makes the FEYNMAN code an attractive and versatile tool for both, research and education. New version program summaryProgram title: FEYNMAN Catalogue identifier: ADWE_v5_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v5_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 27 210 No. of bytes in distributed program, including test data, etc.: 1 960 471 Distribution format: tar.gz Programming language: Maple 12 Computer: Any computer with Maple software installed Operating system: Any system that supports Maple; the program has been tested under Microsoft Windows XP and Linux Classification: 4.15 Catalogue identifier of previous version: ADWE_v4_0 Journal reference of previous version: Comput. Phys. Commun
Classical field approach to quantum weak measurements.
Dressel, Justin; Bliokh, Konstantin Y; Nori, Franco
2014-03-21
By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.
Accidental degeneracies in nonlinear quantum deformed systems
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
2011-09-01
We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.
Quantum Simulation of Tunneling in Small Systems
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
NASA Astrophysics Data System (ADS)
Inoue, Jun-Ichi
2011-03-01
We analytically derive deterministic equations of order parameters such as spontaneous magnetization in infinite-range quantum spin systems obeying quantum Monte Carlo dynamics. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. We discuss several possible applications of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we argue the ground state searching for infinite-range random spin systems via quantum adiabatic evolution. We were financially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science, No. 22500195.
Introducing Systems Approaches
NASA Astrophysics Data System (ADS)
Reynolds, Martin; Holwell, Sue
Systems Approaches to Managing Change brings together five systems approaches to managing complex issues, each having a proven track record of over 25 years. The five approaches are: System Dynamics (SD) developed originally in the late 1950s by Jay Forrester Viable Systems Model (VSM) developed originally in the late 1960s by Stafford Beer Strategic Options Development and Analysis (SODA: with cognitive mapping) developed originally in the 1970s by Colin Eden Soft Systems Methodology (SSM) developed originally in the 1970s by Peter Checkland Critical Systems Heuristics (CSH) developed originally in the late 1970s by Werner Ulrich
Self-assembled quantum dots in a nanowire system for quantum photonics.
Heiss, M; Fontana, Y; Gustafsson, A; Wüst, G; Magen, C; O'Regan, D D; Luo, J W; Ketterer, B; Conesa-Boj, S; Kuhlmann, A V; Houel, J; Russo-Averchi, E; Morante, J R; Cantoni, M; Marzari, N; Arbiol, J; Zunger, A; Warburton, R J; Fontcuberta i Morral, A
2013-05-01
Quantum dots embedded within nanowires represent one of the most promising technologies for applications in quantum photonics. Whereas the top-down fabrication of such structures remains a technological challenge, their bottom-up fabrication through self-assembly is a potentially more powerful strategy. However, present approaches often yield quantum dots with large optical linewidths, making reproducibility of their physical properties difficult. We present a versatile quantum-dot-in-nanowire system that reproducibly self-assembles in core-shell GaAs/AlGaAs nanowires. The quantum dots form at the apex of a GaAs/AlGaAs interface, are highly stable, and can be positioned with nanometre precision relative to the nanowire centre. Unusually, their emission is blue-shifted relative to the lowest energy continuum states of the GaAs core. Large-scale electronic structure calculations show that the origin of the optical transitions lies in quantum confinement due to Al-rich barriers. By emitting in the red and self-assembling on silicon substrates, these quantum dots could therefore become building blocks for solid-state lighting devices and third-generation solar cells.
Non-Lipschitz Approach to Quantum Mechnics
NASA Technical Reports Server (NTRS)
Zak, Michail
1997-01-01
An attempt to reconcile quantum mechanics with Newton's laws represented by the non-Lipschitz formalism has been made. As a Proof-of-concept, a line of equally spaced atoms was studied. It appeared that enforcement of atom incompressibility required relaxation of the lipschitz condition at the points of contact.
Quantum Supersymmetric Models in the Causal Approach
NASA Astrophysics Data System (ADS)
Grigore, Dan-Radu
2007-04-01
We consider the massless supersymmetric vector multiplet in a purely quantum framework. First order gauge invariance determines uniquely the interaction Lagrangian as in the case of Yang-Mills models. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make the analysis of the model working only with the component fields.
Combinatorial Approach to Studying Metal Enhanced Fluorescence from Quantum Dots
NASA Astrophysics Data System (ADS)
Le, Nguyet; Corrigan, Timothy; Norton, Michael; Neff, David
2013-03-01
Fluorescence is extensively used in biochemistry for determining the concentration or purity of molecules in a biological environment. In metal-enhanced fluorescence (MEF), the fluorescence molecules separated from a metal surface by several nanometers can be enhanced. The fluorescent enhancement is dependent on the size and spacing of the nanoparticles, as has been shown previously for a number of fluorophore molecules. Fluorescence from quantum dots is of particular interest because the quantum dots do not lose fluorescence ability when exposed to light and they have higher intensity of fluorescence. The purpose of this study is to determine the effect of size and spacing on fluorescence intensity when coupling gold nano-particles with quantum dots. We employ a combinatorial approach, depositing gold particles ranging in diameter from 30 nm to 130 nm with varied spacings onto the substrate, followed by a protein spacer-layer and quantum dots. The fluorescence signal from the metal enhanced quantum dots were determined by confocal microscopy.
Schroedinger-equation formalism for a dissipative quantum system
Anisimovas, E.; Matulis, A.
2007-02-15
We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role of a dissipative element. The coupling between the two--quantum and classical--parts of the compound system is treated in the spirit of the mean-field approximation and justification of the validity of such an approach is given. The equations of motion of the classical subsystem are solved explicitly and an effective dissipative Schroedinger equation for the quantum subsystem is obtained. The proposed formalism is illustrated by its application to two basic problems: the decay of the quasistationary state and the calculation of the nonlinear resonance line shape.
Galilei invariant technique for quantum system description
Kamuntavičius, Gintautas P.
2014-04-15
Problems with quantum systems models, violating Galilei invariance are examined. The method for arbitrary non-relativistic quantum system Galilei invariant wave function construction, applying a modified basis where center-of-mass excitations have been removed before Hamiltonian matrix diagonalization, is developed. For identical fermion system, the Galilei invariant wave function can be obtained while applying conventional antisymmetrization methods of wave functions, dependent on single particle spatial variables.
Quantum Simulation for Open-System Dynamics
NASA Astrophysics Data System (ADS)
Wang, Dong-Sheng; de Oliveira, Marcos Cesar; Berry, Dominic; Sanders, Barry
2013-03-01
Simulations are essential for predicting and explaining properties of physical and mathematical systems yet so far have been restricted to classical and closed quantum systems. Although forays have been made into open-system quantum simulation, the strict algorithmic aspect has not been explored yet is necessary to account fully for resource consumption to deliver bounded-error answers to computational questions. An open-system quantum simulator would encompass classical and closed-system simulation and also solve outstanding problems concerning, e.g. dynamical phase transitions in non-equilibrium systems, establishing long-range order via dissipation, verifying the simulatability of open-system dynamics on a quantum Turing machine. We construct an efficient autonomous algorithm for designing an efficient quantum circuit to simulate many-body open-system dynamics described by a local Hamiltonian plus decoherence due to separate baths for each particle. The execution time and number of gates for the quantum simulator both scale polynomially with the system size. DSW funded by USARO. MCO funded by AITF and Brazilian agencies CNPq and FAPESP through Instituto Nacional de Ciencia e Tecnologia-Informacao Quantica (INCT-IQ). DWB funded by ARC Future Fellowship (FT100100761). BCS funded by AITF, CIFAR, NSERC and USARO.
Versatile microwave-driven trapped ion spin system for quantum information processing.
Piltz, Christian; Sriarunothai, Theeraphot; Ivanov, Svetoslav S; Wölk, Sabine; Wunderlich, Christof
2016-07-01
Using trapped atomic ions, we demonstrate a tailored and versatile effective spin system suitable for quantum simulations and universal quantum computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system and, thus, can serve as a quantum memory, while simultaneously, other coupled spins perform conditional quantum dynamics. Also, microwave pulses can change the sign of spin-spin couplings, as well as their effective strength, even during the course of a quantum algorithm. Taking advantage of the simultaneous long-range coupling between three spins, a coherent quantum Fourier transform-an essential building block for many quantum algorithms-is efficiently realized. This approach, which is based on microwave-driven trapped ions and is complementary to laser-based methods, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer.
Versatile microwave-driven trapped ion spin system for quantum information processing
Piltz, Christian; Sriarunothai, Theeraphot; Ivanov, Svetoslav S.; Wölk, Sabine; Wunderlich, Christof
2016-01-01
Using trapped atomic ions, we demonstrate a tailored and versatile effective spin system suitable for quantum simulations and universal quantum computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system and, thus, can serve as a quantum memory, while simultaneously, other coupled spins perform conditional quantum dynamics. Also, microwave pulses can change the sign of spin-spin couplings, as well as their effective strength, even during the course of a quantum algorithm. Taking advantage of the simultaneous long-range coupling between three spins, a coherent quantum Fourier transform—an essential building block for many quantum algorithms—is efficiently realized. This approach, which is based on microwave-driven trapped ions and is complementary to laser-based methods, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer. PMID:27419233
Optimized probabilistic quantum processors: A unified geometric approach 1
NASA Astrophysics Data System (ADS)
Bergou, Janos; Bagan, Emilio; Feldman, Edgar
Using probabilistic and deterministic quantum cloning, and quantum state separation as illustrative examples we develop a complete geometric solution for finding their optimal success probabilities. The method is related to the approach that we introduced earlier for the unambiguous discrimination of more than two states. In some cases the method delivers analytical results, in others it leads to intuitive and straightforward numerical solutions. We also present implementations of the schemes based on linear optics employing few-photon interferometry
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
ERIC Educational Resources Information Center
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Coarse-graining approach to quantum cosmology
NASA Astrophysics Data System (ADS)
Calzetta, Esteban; Castagnino, Mario; Scoccimarro, Román
1992-04-01
We consider a Friedmann-Robertson-Walker model with both classical radiation and a massive (conformally coupled) quantum scalar field in the framework of quantum cosmology. We define a density matrix and introduce a notion of ``relevance'' which splits this density matrix into a ``relevant'' and an ``irrelevant'' part. A ``generalized coarse-graining method'' is used to obtain the evolution (in Robertson-Walker a ``time'') of the relevant density matrix, taking into account the back reaction of the irrelevant variables. We discuss the physical basis for the choice of a concept of relevance, and the features of cosmic evolution brought forward by the effective dynamics. In the limit of ``small universes,'' the relevant subdynamics is dissipative.
A lattice approach to spinorial quantum gravity
NASA Technical Reports Server (NTRS)
Renteln, Paul; Smolin, Lee
1989-01-01
A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
An Alternative Approach to Quantum Statistics,
1983-06-21
by block wsimb-’r)9 " Quantum Statistics, Fermi -Dirac, Bose-Einstein __j_ __ _ _ __ _ _ _ L _ 20. AE’STYRCT (Continue on roeraisde It nocosaary and...identify by block numbor) The Fermi -Dirac, Bose-Einstein and, for completeness the ri1axw~ell-Boltzniant’ C-1" distributions are obtained respectively...D.C. 20375 and A. K. Rajagopal Department of Physics and Astronomy, Louisiana State University Baton Rouge, LA 70803-4001 Abstract The Fermi -Dirac
An approach to nonstandard quantum mechanics
NASA Astrophysics Data System (ADS)
Raab, A.
2004-12-01
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to nonrelativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the Mo/ller wave operators and the S-matrix.
Geometric control of quantum mechanical and nonlinear classical systems
NASA Astrophysics Data System (ADS)
Nelson, Richard Joseph
1999-10-01
Geometric control refers to the judicious use of the non- commuting nature of inputs and natural dynamics as the basis for control. The last few decades in control system theory have seen the application of differential geometry in proving several important properties of systems, including controllability and observability. Until recently, however, the results of this mathematical geometry have rarely been used as the basis for designing and implementing an actual controller. This thesis demonstrates the application of a judicious selection of inputs, so that if the system is proven to be controllable using geometric methods, one can design input sequences using the same geometry. A demonstration of this method is shown in simulating the attitude control of a satellite: a highly non-linear, non- holonomic control problem. Although not a practical method for large re-orientations of a typical satellite, the approach can be applied to other nonlinear systems. The method is also applied to the closed-loop performance of a quantum mechanical system to demonstrate the feasibility of coherent quantum feedback-something impossible using a conventional controller. Finally, the method is applied in the open-loop control of a quantum mechanical system: in this case, the creation of Greenberger-Horne-Zeilinger correlations among the nuclei of an ensemble of alanine molecules in a nuclear magnetic resonance spectrometer. In each case, the data demonstrate the usefulness of a geometric approach to control. In addition to demonstrations of geometric control in practice, the quantum mechanical experiments also demonstrate for the first time peculiar quantum correlations, including GHZ correlations, that have no classical analog. The quantum experiments further establish nuclear magnetic resonance as a viable and accessible testbed of quantum predictions and processes. (Copies available exclusively from MIT Libraries, Rm. 14- 0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax
Quantum entanglement in condensed matter systems
NASA Astrophysics Data System (ADS)
Laflorencie, Nicolas
2016-08-01
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial information can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contain key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in detail. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.
Characteristic Energy Scales of Quantum Systems.
ERIC Educational Resources Information Center
Morgan, Michael J.; Jakovidis, Greg
1994-01-01
Provides a particle-in-a-box model to help students understand and estimate the magnitude of the characteristic energy scales of a number of quantum systems. Also discusses the mathematics involved with general computations. (MVL)
Software-defined Quantum Communication Systems
Humble, Travis S; Sadlier, Ronald J
2013-01-01
We show how to extend the paradigm of software-defined communication to include quantum communication systems. We introduce the decomposition of a quantum communication terminal into layers separating the concerns of the hardware, software, and middleware. We provide detailed descriptions of how each component operates and we include results of an implementation of the super-dense coding protocol. We argue that the versatility of software-defined quantum communication test beds can be useful for exploring new regimes in communication and rapidly prototyping new systems.
Generation of cluster states in optomechanical quantum systems
NASA Astrophysics Data System (ADS)
Houhou, Oussama; Aissaoui, Habib; Ferraro, Alessandro
2015-12-01
We consider an optomechanical quantum system composed of a single cavity mode interacting with N mechanical resonators. We propose a scheme for generating continuous-variable graph states of arbitrary size and shape, including the so-called cluster states for universal quantum computation. The main feature of this scheme is that, differently from previous approaches, the graph states are hosted in the mechanical degrees of freedom rather than in the radiative ones. Specifically, via a 2 N -tone drive, we engineer a linear Hamiltonian which is instrumental to dissipatively drive the system to the desired target state. The robustness of this scheme is assessed against finite interaction times and mechanical noise, confirming it as a valuable approach towards quantum state engineering for continuous-variable computation in a solid-state platform.
Correlation inequalities for quantum spin systems with quenched centered disorder
NASA Astrophysics Data System (ADS)
Contucci, Pierluigi; Lebowitz, Joel L.
2010-02-01
It is shown that random quantum spin systems with centered disorder satisfy correlation inequalities previously proved [P. Contucci and J. Lebowitz, Ann. Henri Poincare 8, 1461 (2007)] in the classical case. Consequences include monotone approach of pressure and ground state energy to the thermodynamic limit. Signs and bounds on the surface pressures for different boundary conditions are also derived for finite range potentials.
Loop quantum cosmology: confronting the hybrid quantization approach with observations
NASA Astrophysics Data System (ADS)
Olmedo, Javier; Martin de Blas, Daniel
2017-01-01
In loop quantum cosmology there are several approaches for the confrontation of the theory with observations. Here, we focus on the hybrid quantization approach. We provide an exhaustive analysis including scalar and tensor perturbations on effective (quantum-mechanically corrected) homogeneous and isotropic cosmologies coupled to a massive scalar field. We compute the primordial power spectrum of the perturbations at the end of inflation for a set of initial vacuum states defined at the deep quantum regime of the cosmological model. We then analyze the tensor-to-scalar ratio and the consistency relation between this quantity and the spectral index of the tensor power spectrum. Eventually, we compute the temperature-temperature, electric-electric, temperature-electric and magnetic-magnetic correlation functions predicted by this approach and compare them with present observations.
Software-defined Quantum Communication Systems
Humble, Travis S; Sadlier, Ronald J
2014-01-01
Quantum communication systems harness modern physics through state-of-the-art optical engineering to provide revolutionary capabilities. An important concern for quantum communication engineering is designing and prototyping these systems to prototype proposed capabilities. We apply the paradigm of software-defined communica- tion for engineering quantum communication systems to facilitate rapid prototyping and prototype comparisons. We detail how to decompose quantum communication terminals into functional layers defining hardware, software, and middleware concerns, and we describe how each layer behaves. Using the super-dense coding protocol as a test case, we describe implementations of both the transmitter and receiver, and we present results from numerical simulations of the behavior. We find that while the theoretical benefits of super dense coding are maintained, there is a classical overhead associated with the full implementation.
Isoperiodic classical systems and their quantum counterparts
NASA Astrophysics Data System (ADS)
Asorey, M.; Cariñena, J. F.; Marmo, G.; Perelomov, A.
2007-06-01
One-dimensional isoperiodic classical systems have been first analyzed by Abel. Abel's characterization can be extended for singular potentials and potentials which are not defined on the whole real line. The standard shear equivalence of isoperiodic potentials can also be extended by using reflection and inversion transformations. We provide a full characterization of isoperiodic rational potentials showing that they are connected by translations, reflections or Joukowski transformations. Upon quantization many of these isoperiodic systems fail to exhibit identical quantum energy spectra. This anomaly occurs at order O( ℏ2) because semiclassical corrections of energy levels of order O( ℏ) are identical for all isoperiodic systems. We analyze families of systems where this quantum anomaly occurs and some special systems where the spectral identity is preserved by quantization. Conversely, we point out the existence of isospectral quantum systems which do not correspond to isoperiodic classical systems.
Robust observer for uncertain linear quantum systems
Yamamoto, Naoki
2006-09-15
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analog due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators--the optimal Kalman filter and risk-sensitive observer--fail in the estimation.
Barnes, George L.; Kellman, Michael E.
2013-12-07
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is “designed” by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of “classicalizing” behavior in the approach to thermal equilibrium are briefly considered.
NASA Astrophysics Data System (ADS)
Barnes, George L.; Kellman, Michael E.
2013-12-01
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
Barnes, George L; Kellman, Michael E
2013-12-07
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
A new teaching approach to quantum mechanical tunneling
NASA Astrophysics Data System (ADS)
Gilfoyle, G. P.
1999-09-01
The transfer matrix method has been used to investigate quantum mechanical tunneling in introductory quantum mechanics. The method is applied first to calculate the transmission coefficient for tunneling through a rectangular barrier and is then extended to the problem of potential barriers of arbitrary shape, in particular, to radioactive decay. This approach uses matrix methods that are accessible to a broader range of undergraduates than other numerical techniques, the connection between the rectangular barrier problem and potential barriers of arbitrary shape is transparent, and it can be readily executed by undergraduates. The classroom experience with this approach is discussed.
Computational approach for calculating bound states in quantum field theory
NASA Astrophysics Data System (ADS)
Lv, Q. Z.; Norris, S.; Brennan, R.; Stefanovich, E.; Su, Q.; Grobe, R.
2016-09-01
We propose a nonperturbative approach to calculate bound-state energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively discretized and truncated Hilbert space. We illustrate this approach for a Yukawa-like interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlung-induced widening.
An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
NASA Astrophysics Data System (ADS)
Höhn, Philipp A.; Müller, Markus P.
2016-06-01
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest, within a much simpler setting, that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distinct laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are ‘enough’ observables that can be measured universally on several different quantum systems, we show that the observers’ descriptions are related by an element of the orthochronous Lorentz group {{{O}}}+(3,1), together with a global scaling factor. Not only does this operational approach predict the Lorentz transformations, but it also accurately describes the behavior of relativistic Stern-Gerlach devices in the WKB approximation, and it correctly predicts that quantum systems carry Lorentz group representations of different spin. This result thus hints at a novel information-theoretic perspective on spacetime.
NASA Astrophysics Data System (ADS)
Blutner, Reinhard
2009-03-01
Recently, Gerd Niestegge developed a new approach to quantum mechanics via conditional probabilities developing the well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization. I will apply his powerful and rigorous approach to the treatment of concepts using a geometrical model of meaning. In this model, instances are treated as vectors of a Hilbert space H. In the present approach there are at least two possibilities to form categories. The first possibility sees categories as a mixture of its instances (described by a density matrix). In the simplest case we get the classical probability theory including the Bayesian formula. The second possibility sees categories formed by a distinctive prototype which is the superposition of the (weighted) instances. The construction of prototypes can be seen as transferring a mixed quantum state into a pure quantum state freezing the probabilistic characteristics of the superposed instances into the structure of the formed prototype. Closely related to the idea of forming concepts by prototypes is the existence of interference effects. Such inference effects are typically found in macroscopic quantum systems and I will discuss them in connection with several puzzles of bounded rationality. The present approach nicely generalizes earlier proposals made by authors such as Diederik Aerts, Andrei Khrennikov, Ricardo Franco, and Jerome Busemeyer. Concluding, I will suggest that an active dialogue between cognitive approaches to logic and semantics and the modern approach of quantum information science is mandatory.
Second-order superintegrable quantum systems
Miller, W.; Kalnins, E. G.; Kress, J. M.
2007-03-15
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n - 1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, then the system is second-order superintegrable, the most tractable case and the one we study here. Such systems have remarkable properties: multi-integrability and separability, a quadratic algebra of symmetries whose representation theory yields spectral information about the Schroedinger operator, and deep connections with expansion formulas relating classes of special functions. For n = 2 and for conformally flat spaces when n = 3, we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here, we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension.
Quantum optical properties in plasmonic systems
NASA Astrophysics Data System (ADS)
Ooi, C. H. Raymond
2015-04-01
Plasmonic metallic particle (MP) can affect the optical properties of a quantum system (QS) in a remarkable way. We develop a general quantum nonlinear formalism with exact vectorial description for the scattered photons by the QS. The formalism enables us to study the variations of the dielectric function and photon spectrum of the QS with the particle distance between QS and MP, exciting laser direction, polarization and phase in the presence of surface plasmon resonance (SPR) in the MP. The quantum formalism also serves as a powerful tool for studying the effects of these parameters on the nonclassical properties of the scattered photons. The plasmonic effect of nanoparticles has promising possibilities as it provides a new way for manipulating quantum optical properties of light in nanophotonic systems.
Boolean approach to dichotomic quantum measurement theories
NASA Astrophysics Data System (ADS)
Nagata, K.; Nakamura, T.; Batle, J.; Abdalla, S.; Farouk, A.
2017-02-01
Recently, a new measurement theory based on truth values was proposed by Nagata and Nakamura [Int. J. Theor. Phys. 55, 3616 (2016)], that is, a theory where the results of measurements are either 0 or 1. The standard measurement theory accepts a hidden variable model for a single Pauli observable. Hence, we can introduce a classical probability space for the measurement theory in this particular case. Additionally, we discuss in the present contribution the fact that projective measurement theories (the results of which are either +1 or -1) imply the Bell, Kochen, and Specker (BKS) paradox for a single Pauli observable. To justify our assertion, we present the BKS theorem in almost all the two-dimensional states by using a projective measurement theory. As an example, we present the BKS theorem in two-dimensions with white noise. Our discussion provides new insight into the quantum measurement problem by using this measurement theory based on the truth values.
Quantum Approach to One-body Dissipation
NASA Astrophysics Data System (ADS)
Rizea, M.; Carjan, N.
The nuclear dissipation, i.e. the conversion of collective energy into intrinsic energy is investigated in the frame of quantum mechanics. Using appropiate numerical procedures, we follow the motion of individual nucleons according to the time-dependent Schr̈odinger equation with time-dependent potential. In particular we study the transition from the saddle to the scission point during the low energy fission of 236U. Different rates T of change of the nuclear shape along this path were considered. The overlap integrals between the static solutions of the bi-dimensional Schr̈odinger equation and the time-dependent wave packets yield the transition probabilities and hence the singleparticle excitations during the saddle-to-scission descent. Using the numerical solutions other relevant pre-scission properties have been evaluated as well.
Critical properties of dissipative quantum spin systems in finite dimensions
NASA Astrophysics Data System (ADS)
Takada, Kabuki; Nishimori, Hidetoshi
2016-10-01
We study the critical properties of finite-dimensional dissipative quantum spin systems with uniform ferromagnetic interactions. Starting from the transverse field Ising model coupled to a bath of harmonic oscillators with Ohmic spectral density, we generalize its classical representation to classical spin systems with O(n) symmetry and then take the large-n limit to reduce the system to a spherical model. The exact solution to the resulting spherical model with long-range interactions along the imaginary time axis shows a phase transition with static critical exponents coinciding with those of the conventional short-range spherical model in d+2 dimensions, where d is the spatial dimensionality of the original quantum system. This implies that the dynamical exponent is z = 2. These conclusions are consistent with the results of Monte Carlo simulations and renormalization group calculations for dissipative transverse field Ising and O(n) models in one and two dimensions. The present approach therefore serves as a useful tool for analytically investigating the properties of quantum phase transitions of the dissipative transverse field Ising and other related models. Our method may also offer a platform to study more complex phase transitions in dissipative finite-dimensional quantum spin systems, which have recently received renewed interest in the context of quantum annealing in a noisy environment.
Note on quantum groups and integrable systems
NASA Astrophysics Data System (ADS)
Popolitov, A.
2016-01-01
The free-field formalism for quantum groups [preprint ITEP-M3/94, CRM-2202 hep-th/9409093] provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system [arXiv:1207.1869] is especially simple. This choice also fits into general framework of cluster varieties [math.AG/0311245]—natural changes in coordinates are cluster mutations.
Stabilization of quantum energy flows within the approximate quantum trajectory approach.
Garashchuk, Sophya; Rassolov, Vitaly
2007-10-18
The hydrodynamic, or the de Broglie-Bohm, formulation provides an alternative to the conventional time-dependent Schrödinger equation based on quantum trajectories. The trajectory dynamics scales favorably with the system size, but it is, generally, unstable due to singularities in the exact quantum potential. The approximate quantum potential based on the fitting of the nonclassical component of the momentum operator in terms of a small basis is numerically stable but can lead to inaccurate large net forces in bound systems. We propose to compensate errors in the approximate quantum potential by applying a semiempirical friction-like force. This significantly improves the description of zero-point energy in bound systems. Examples are given for one-dimensional models relevant to nuclear dynamics.
Quantum Chemical Approach to Estimating the Thermodynamics of Metabolic Reactions
Jinich, Adrian; Rappoport, Dmitrij; Dunn, Ian; Sanchez-Lengeling, Benjamin; Olivares-Amaya, Roberto; Noor, Elad; Even, Arren Bar; Aspuru-Guzik, Alán
2014-01-01
Thermodynamics plays an increasingly important role in modeling and engineering metabolism. We present the first nonempirical computational method for estimating standard Gibbs reaction energies of metabolic reactions based on quantum chemistry, which can help fill in the gaps in the existing thermodynamic data. When applied to a test set of reactions from core metabolism, the quantum chemical approach is comparable in accuracy to group contribution methods for isomerization and group transfer reactions and for reactions not including multiply charged anions. The errors in standard Gibbs reaction energy estimates are correlated with the charges of the participating molecules. The quantum chemical approach is amenable to systematic improvements and holds potential for providing thermodynamic data for all of metabolism. PMID:25387603
Quantum chemical approach to estimating the thermodynamics of metabolic reactions.
Jinich, Adrian; Rappoport, Dmitrij; Dunn, Ian; Sanchez-Lengeling, Benjamin; Olivares-Amaya, Roberto; Noor, Elad; Even, Arren Bar; Aspuru-Guzik, Alán
2014-11-12
Thermodynamics plays an increasingly important role in modeling and engineering metabolism. We present the first nonempirical computational method for estimating standard Gibbs reaction energies of metabolic reactions based on quantum chemistry, which can help fill in the gaps in the existing thermodynamic data. When applied to a test set of reactions from core metabolism, the quantum chemical approach is comparable in accuracy to group contribution methods for isomerization and group transfer reactions and for reactions not including multiply charged anions. The errors in standard Gibbs reaction energy estimates are correlated with the charges of the participating molecules. The quantum chemical approach is amenable to systematic improvements and holds potential for providing thermodynamic data for all of metabolism.
The consistent histories approach to loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David A.
2016-06-01
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on “measurements” to convert unrealized quantum potentialities into physical outcomes that can be assigned probabilities. In the early universe and other physical contexts in which there are no observers or measuring apparatus (or indeed, in any closed quantum system), what criteria determine which alternative outcomes may be realized and what their probabilities are? In the consistent histories formulation it is the vanishing of interference between the branch wave functions describing alternative histories — as determined by the system’s decoherence functional — that determines which alternatives may be assigned probabilities. We describe the consistent histories formulation and how it may be applied to canonical loop quantum cosmology, describing in detail the application to homogeneous and isotropic cosmological models with scalar matter. We show how the theory may be used to make definite physical predictions in the absence of “observers”. As an application, we demonstrate how the theory predicts that loop quantum models “bounce” from large volume to large volume, while conventional “Wheeler-DeWitt”-quantized universes are invariably singular. We also briefly indicate the relation to other work.
Quantum hacking: attacking practical quantum key distribution systems
NASA Astrophysics Data System (ADS)
Qi, Bing; Fung, Chi-Hang Fred; Zhao, Yi; Ma, Xiongfeng; Tamaki, Kiyoshi; Chen, Christine; Lo, Hoi-Kwong
2007-09-01
Quantum key distribution (QKD) can, in principle, provide unconditional security based on the fundamental laws of physics. Unfortunately, a practical QKD system may contain overlooked imperfections and violate some of the assumptions in a security proof. Here, we report two types of eavesdropping attacks against a practical QKD system. The first one is "time-shift" attack, which is applicable to QKD systems with gated single photon detectors (SPDs). In this attack, the eavesdropper, Eve, exploits the time mismatch between the open windows of the two SPDs. She can acquire a significant amount of information on the final key by simply shifting the quantum signals forwards or backwards in time domain. Our experimental results in [9] with a commercial QKD system demonstrate that, under this attack, the original QKD system is breakable. This is the first experimental demonstration of a feasible attack against a commercial QKD system. This is a surprising result. The second one is "phase-remapping" attack [10]. Here, Eve exploits the fact that a practical phase modulator has a finite response time. In principle, Eve could change the encoded phase value by time-shifting the signal pulse relative to the reference pulse.
An approximate approach to quantum mechanical study of biomacromolecules
NASA Astrophysics Data System (ADS)
Chen, Xihua
This thesis summarizes the author's major work in Prof. John Z.H. Zhang's Threoretical Chemistry research group. In Chapter 1, we present a general description of MFCC (molecular fractionation with conjugated caps) method that has been developed in this group to treat biomacromolecules in a divide-and-conquer fashion. Then we give in detail a computational study of MFCC application to peptide/protein that contains disulfide bonds. Continued on the basis of previous MFCC tests, this study provides another numerical support for the accuracy of the MFCC approach to full quantum mechanical calculation of protein/peptide-small molecule interaction. In Chapter 2, we further develop the MFCC scheme for quantum mechanical computation of DNA-ligand interaction energy. We study three oligonuclear acid interaction systems: dinucleotide dCG/water, trinucleotide dCGT/water and a Watson-Crick paired DNA segment dCGT/dGCA. The MFCC interaction energies are found to be in excellent agreement with the corresponding results obtained from the full system ab initio calculations. This study is an exemplification of the application of the general MFCC approach to biomacromolecules. In Chapter 3, firstly, a MFCC-downhill simplex method is proposed to study binding structures of ligands (atoms, ions, or small molecules) in large molecular complex systems. This method employs the MFCC approach to compute the interaction energy-structure relation of the system and implements the downhill simplex algorithm for structural optimization. Secondly, this method is numerically tested on a system of [KCp(18-crown-6)], as a simplest monatomic case study, to optimize the binding position of the potassium cation in a fixed coordination Cp and 18-crown-6 coordinating sphere. The result of the MFCC-downhill simplex optimization shows good agreement with both the crystal structure and with the full-system downhill simplex optimized structure. The effects of the initial structure of the simplex and of the
NASA Astrophysics Data System (ADS)
Collins, Robert J.; Donaldon, Ross J.; Dunjko, Vedran; Wallden, Petros; Clarke, Patrick J.; Andersson, Erika; Jeffers, John; Buller, Gerald S.
2014-10-01
Classical digital signatures are commonly used in e-mail, electronic financial transactions and other forms of electronic communications to ensure that messages have not been tampered with in transit, and that messages are transferrable. The security of commonly used classical digital signature schemes relies on the computational difficulty of inverting certain mathematical functions. However, at present, there are no such one-way functions which have been proven to be hard to invert. With enough computational resources certain implementations of classical public key cryptosystems can be, and have been, broken with current technology. It is nevertheless possible to construct information-theoretically secure signature schemes, including quantum digital signature schemes. Quantum signature schemes can be made information theoretically secure based on the laws of quantum mechanics, while classical comparable protocols require additional resources such as secret communication and a trusted authority. Early demonstrations of quantum digital signatures required quantum memory, rendering them impractical at present. Our present implementation is based on a protocol that does not require quantum memory. It also uses the new technique of unambiguous quantum state elimination, Here we report experimental results for a test-bed system, recorded with a variety of different operating parameters, along with a discussion of aspects of the system security.
Optical response in a laser-driven quantum pseudodot system
NASA Astrophysics Data System (ADS)
Kilic, D. Gul; Sakiroglu, S.; Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sokmen, I.
2017-03-01
We investigate theoretically the intense laser-induced optical absorption coefficients and refractive index changes in a two-dimensional quantum pseudodot system under an uniform magnetic field. The effects of non-resonant, monochromatic intense laser field upon the system are treated within the framework of high-frequency Floquet approach in which the system is supposed to be governed by a laser-dressed potential. Linear and nonlinear absorption coefficients and relative changes in the refractive index are obtained by means of the compact-density matrix approach and iterative method. The results of numerical calculations for a typical GaAs quantum dot reveal that the optical response depends strongly on the magnitude of external magnetic field and characteristic parameters of the confinement potential. Moreover, we have demonstrated that the intense laser field modifies the confinement and thereby causes remarkable changes in the linear and nonlinear optical properties of the system.
Quantum.Ligand.Dock: protein–ligand docking with quantum entanglement refinement on a GPU system
Kantardjiev, Alexander A.
2012-01-01
Quantum.Ligand.Dock (protein–ligand docking with graphic processing unit (GPU) quantum entanglement refinement on a GPU system) is an original modern method for in silico prediction of protein–ligand interactions via high-performance docking code. The main flavour of our approach is a combination of fast search with a special account for overlooked physical interactions. On the one hand, we take care of self-consistency and proton equilibria mutual effects of docking partners. On the other hand, Quantum.Ligand.Dock is the the only docking server offering such a subtle supplement to protein docking algorithms as quantum entanglement contributions. The motivation for development and proposition of the method to the community hinges upon two arguments—the fundamental importance of quantum entanglement contribution in molecular interaction and the realistic possibility to implement it by the availability of supercomputing power. The implementation of sophisticated quantum methods is made possible by parallelization at several bottlenecks on a GPU supercomputer. The high-performance implementation will be of use for large-scale virtual screening projects, structural bioinformatics, systems biology and fundamental research in understanding protein–ligand recognition. The design of the interface is focused on feasibility and ease of use. Protein and ligand molecule structures are supposed to be submitted as atomic coordinate files in PDB format. A customization section is offered for addition of user-specified charges, extra ionogenic groups with intrinsic pKa values or fixed ions. Final predicted complexes are ranked according to obtained scores and provided in PDB format as well as interactive visualization in a molecular viewer. Quantum.Ligand.Dock server can be accessed at http://87.116.85.141/LigandDock.html. PMID:22669908
Quantum.Ligand.Dock: protein-ligand docking with quantum entanglement refinement on a GPU system.
Kantardjiev, Alexander A
2012-07-01
Quantum.Ligand.Dock (protein-ligand docking with graphic processing unit (GPU) quantum entanglement refinement on a GPU system) is an original modern method for in silico prediction of protein-ligand interactions via high-performance docking code. The main flavour of our approach is a combination of fast search with a special account for overlooked physical interactions. On the one hand, we take care of self-consistency and proton equilibria mutual effects of docking partners. On the other hand, Quantum.Ligand.Dock is the the only docking server offering such a subtle supplement to protein docking algorithms as quantum entanglement contributions. The motivation for development and proposition of the method to the community hinges upon two arguments-the fundamental importance of quantum entanglement contribution in molecular interaction and the realistic possibility to implement it by the availability of supercomputing power. The implementation of sophisticated quantum methods is made possible by parallelization at several bottlenecks on a GPU supercomputer. The high-performance implementation will be of use for large-scale virtual screening projects, structural bioinformatics, systems biology and fundamental research in understanding protein-ligand recognition. The design of the interface is focused on feasibility and ease of use. Protein and ligand molecule structures are supposed to be submitted as atomic coordinate files in PDB format. A customization section is offered for addition of user-specified charges, extra ionogenic groups with intrinsic pK(a) values or fixed ions. Final predicted complexes are ranked according to obtained scores and provided in PDB format as well as interactive visualization in a molecular viewer. Quantum.Ligand.Dock server can be accessed at http://87.116.85.141/LigandDock.html.
Controlling Atomic, Solid-State and Hybrid Systems for Quantum Information Processing
NASA Astrophysics Data System (ADS)
Gullans, Michael John
Quantum information science involves the use of precise control over quantum systems to explore new technologies. However, as quantum systems are scaled up they require an ever deeper understanding of many-body physics to achieve the required degree of control. Current experiments are entering a regime which requires active control of a mesoscopic number of coupled quantum systems or quantum bits (qubits). This thesis describes several approaches to this goal and shows how mesoscopic quantum systems can be controlled and utilized for quantum information tasks. The first system we consider is the nuclear spin environment of GaAs double quantum dots containing two electrons. We show that the through appropriate control of dynamic nuclear polarization one can prepare the nuclear spin environment in three distinct collective quantum states which are useful for quantum information processing with electron spin qubits. We then investigate a hybrid system in which an optical lattice is formed in the near field scattering off an array of metallic nanoparticles by utilizing the plasmonic resonance of the nanoparticles. We show that such a system would realize new regimes of dense, ultra-cold quantum matter and can be used to create a quantum network of atoms and plasmons. Finally we investigate quantum nonlinear optical systems. We show that the intrinsic nonlinearity for plasmons in graphene can be large enough to make a quantum gate for single photons. We also consider two nonlinear optical systems based on ultracold gases of atoms. In one case, we demonstrate an all-optical single photon switch using cavity quantum electrodynamics (QED) and slow light. In the second case, we study few photon physics in strongly interacting Rydberg polariton systems, where we demonstrate the existence of two and three photon bound states and study their properties.
The path integral picture of quantum systems
NASA Astrophysics Data System (ADS)
Ceperley, David
2011-03-01
The imaginary time path integral ``formalism'' was introduced in 1953 by Feynman to understand the superfluid transition in liquid helium. The equilibrium properties of quantum many body systems is isomorphic to the classical statistical mechanics of cross-linking polymer-like objects. With the Markov Chain Monte Carlo method, invented by Metropolis et al., also in 1953, a potential way of calculating properties of correlated quantum systems was in place. But calculations for many-body quantum systems did not become routine until computers and algorithms had become sufficiently powerful three decades later. Once such simulations could happen, it was realized that simulations provided a deeper insight into boson superfluids, in particular the relation of bose condensation to the polymer end-to-end distance, and the superfluid density to the polymer ``winding number.'' Some recent developments and applications to supersolids, and helium droplets will be given. Finally, limitations of the methodology e.g. to fermion systems are discussed.
Multimode optomechanical system in the quantum regime.
Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S; Schliesser, Albert
2017-01-03
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10(7)) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Multimode optomechanical system in the quantum regime
NASA Astrophysics Data System (ADS)
Hvidtfelt Padkær Nielsen, William; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert
2017-01-01
We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry–Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to ‑2.4 dB (‑3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry–Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Double-Slit Interference Pattern for a Macroscopic Quantum System
NASA Astrophysics Data System (ADS)
Naeij, Hamid Reza; Shafiee, Afshin
2016-12-01
In this study, we solve analytically the Schrödinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in two limiting cases, considering the limits of uncertainty in the position probability distribution. Moreover, we analyze the interference patterns based on a recent proposal called stochastic electrodynamics with spin. Our results show that when the quantum character of the macro-system is decreased, the diffraction pattern becomes more similar to a classical one. We also show that, depending on the size of the slits, the predictions of quantum approach could be apparently different with those of the aforementioned stochastic description.
NASA Astrophysics Data System (ADS)
Onorato, P.
2011-03-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P Feynman and developed by E F Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of propagation amplitude is discussed for unbounded systems. These semiclassical results are obtained when the SOP is limited to the trajectories classically allowed. EBK semiclassical quantization and the topological Maslov index are used to deduce the correct quantum mechanical results for systems which live in a two-dimensional world as quantum dots and quantum rings. In the latter systems, the semiclassical propagation amplitude is used to discuss the Aharonov-Bohm effect. The development involves only elementary calculus and also provides a theoretical introduction to the quantum nature of low-dimensional nanostructures.
Theory of ground state factorization in quantum cooperative systems.
Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio
2008-05-16
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows us to determine rigorously the existence, location, and exact form of separable ground states in a large variety of, generally nonexactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2015-02-01
We propose a quantitative criterion to determine whether the coupled quantum systems can achieve complete synchronization or phase synchronization in the process of analyzing quantum synchronization. Adopting the criterion, we discuss the quantum synchronization effects between optomechanical systems and find that the error between the systems and the fluctuation of error is sensitive to coupling intensity by calculating the largest Lyapunov exponent of the model and quantum fluctuation, respectively. By taking the appropriate coupling intensity, we can control quantum synchronization even under different logical relationships between switches. Finally, we simulate the dynamical evolution of the system to verify the quantum synchronization criterion and to show the ability of synchronization control.
Nonequilibrium Quantum Systems: Fluctuations and Interactions
NASA Astrophysics Data System (ADS)
Subasi, Yigit
We explore some aspects of nonequilibrium statistical mechanics of classical and quantum systems. Two chapters are devoted to fluctuation theorems which were originally derived for classical systems. The main challenge in formulating them in quantum mechanics is the fact that fundamental quantities of interest, like work, are defined via the classical concept of a phase space trajectory. We utilize the decoherent histories conceptual framework, in which classical trajectories emerge in quantum mechanics as a result of coarse graining, and provide a first-principles analysis of the nonequilibrium work relation of Jarzynski and Crooks's fluctuation theorem for a quantum system interacting with a general environment based on the quantum Brownian motion (QBM) model. We indicate a parameter range at low temperatures where the theorems might fail in their original form. Fluctuation theorems of Jarzynski and Crooks for systems obeying classical Hamiltonian dynamics are derived under the assumption that the initial conditions are sampled from a canonical ensemble, even though the equilibrium state of an isolated system is typically associated with the microcanonical ensemble. We address this issue through an exact analysis of the classical Brownian motion model. We argue that a stronger form of ensemble equivalence than usually discussed in equilibrium statistical mechanics is required for these theorems to hold in the infinite environment limit irrespective of the ensemble used, and proceed to prove it for this model. An exact expression for the probability distribution of work is obtained for finite environments. Intuitively one expects a system to relax to an equilibrium state when brought into contact with a thermal environment. Yet it is important to have rigorous results that provide conditions for equilibration and characterize the equilibrium state. We consider the dynamics of open quantum systems using the Langevin and master equations and rigorously show that
Keldysh field theory for driven open quantum systems.
Sieberer, L M; Buchhold, M; Diehl, S
2016-09-01
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Keldysh field theory for driven open quantum systems
NASA Astrophysics Data System (ADS)
Sieberer, L. M.; Buchhold, M.; Diehl, S.
2016-09-01
Recent experimental developments in diverse areas—ranging from cold atomic gases to light-driven semiconductors to microcavity arrays—move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Open Quantum Systems with Applications to Precision Measurements
NASA Astrophysics Data System (ADS)
Tieri, David
A spectrally pure coherent light source is an important component in precision measurement applications, such as an atomic clock. The more spectrally pure the coherent light source, or the narrower the linewidth of its power spectrum, the better for atomic clock experiments. A coherent light light source, such as a laser, is intrinsically an open quantum system, meaning that it gains and loses energy from an external environment. The aim of this thesis is to study various open quantum systems in an attempt to discover a scheme in which an extremely spectrally pure coherent light source might be realized. Therefore, this thesis begins by introducing the two main approaches to treating open quantum systems, the quantum master equation approach, and the quantum Langevin equation approach. In addition to deriving these from first principles, many of the solution methods to these approaches are given and then demonstrated using computer simulations. These include the quantum jump algorithm, the quantum state diffusion algorithm, the cumulant expansion method, and the method of c-number Langevin equations. Using these methods, the theory of the crossover between lasing and steady state superradiance is presented. It is shown that lasing and steady state superradiance might be demonstrated in the same physical system, but in different parameter regimes. The parameter space between these two extreme limits is explored, and the benefits and drawbacks of operating a system at a given set of parameters, i.e. to achieve the most spectrally pure light source, are discussed. We also consider the phase stability of a laser that is locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. Although the atomic motion introduces Doppler broadening, the standing wave nature of the cavity causes saturated absorption, which can be used to achieve an extremely high degree of phase stabilization. The inhomogeneity introduced by finite atomic velocities can
Simulation of n-qubit quantum systems. I. Quantum registers and quantum gates
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2005-12-01
During recent years, quantum computations and the study of n-qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing quantum computations, however, these investigations also revealed a great deal of difficulties which still need to be solved in practice. In quantum computing, unitary and non-unitary quantum operations act on a given set of qubits to form (entangled) states, in which the information is encoded by the overall system often referred to as quantum registers. To facilitate the simulation of such n-qubit quantum systems, we present the FEYNMAN program to provide all necessary tools in order to define and to deal with quantum registers and quantum operations. Although the present version of the program is restricted to unitary transformations, it equally supports—whenever possible—the representation of the quantum registers both, in terms of their state vectors and density matrices. In addition to the composition of two or more quantum registers, moreover, the program also supports their decomposition into various parts by applying the partial trace operation and the concept of the reduced density matrix. Using an interactive design within the framework of MAPLE, therefore, we expect the FEYNMAN program to be helpful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future. Program summaryTitle of program:FEYNMAN Catalogue number:ADWE Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed:All computers with a license of the computer algebra system MAPLE [Maple is a registered trademark of Waterlo Maple Inc.] Operating systems or monitors under which the program has been tested:Linux, MS Windows XP Programming language used:MAPLE 9.5 (but should be compatible
Quantum Hall effect in semiconductor systems with quantum dots and antidots
Beltukov, Ya. M.; Greshnov, A. A.
2015-04-15
The integer quantum Hall effect in systems of semiconductor quantum dots and antidots is studied theoretically as a factor of temperature. It is established that the conditions for carrier localization in quantum-dot systems favor the observation of the quantum Hall effect at higher temperatures than in quantum-well systems. The obtained numerical results show that the fundamental plateau corresponding to the transition between the ground and first excited Landau levels can be retained up to a temperature of T ∼ 50 K, which is an order of magnitude higher than in the case of quantum wells. Implementation of the quantum Hall effect at such temperatures requires quantum-dot systems with controllable characteristics, including the optimal size and concentration and moderate geometrical and composition fluctuations. In addition, ordered arrangement is desirable, hence quantum antidots are preferable.
Time dilation in quantum systems and decoherence
NASA Astrophysics Data System (ADS)
Pikovski, Igor; Zych, Magdalena; Costa, Fabio; Brukner, Časlav
2017-02-01
Both quantum mechanics and general relativity are based on principles that defy our daily intuitions, such as time dilation, quantum interference and entanglement. Because the regimes where the two theories are typically tested are widely separated, their foundational principles are rarely jointly studied. Recent works have found that novel phenomena appear for quantum particles with an internal structure in the presence of time dilation, which can take place at low energies and in weak gravitational fields. Here we briefly review the effects of time dilation on quantum interference and generalize the results to a variety of systems. In addition, we provide an extended study of the basic principles of quantum theory and relativity that are of relevance for the effects and also address several questions that have been raised, such as the description in different reference frames, the role of the equivalence principle and the effective irreversibility of the decoherence. The manuscript clarifies some of the counterintuitive aspects arising when quantum phenomena and general relativistic effects are jointly considered.
Quantum sweeps, synchronization, and Kibble-Zurek physics in dissipative quantum spin systems
NASA Astrophysics Data System (ADS)
Henriet, Loïc; Le Hur, Karyn
2016-02-01
We address dissipation effects on the nonequilibrium quantum dynamics of an ensemble of spins-1/2 coupled via an Ising interaction. Dissipation is modeled by a (Ohmic) bath of harmonic oscillators at zero temperature and correspond either to the sound modes of a one-dimensional Bose-Einstein (quasi-)condensate or to the zero-point fluctuations of a long transmission line. We consider the dimer comprising two spins and the quantum Ising chain with long-range interactions and develop an (mathematically and numerically) exact stochastic approach to address nonequilibrium protocols in the presence of an environment. For the two-spin case, we first investigate the dissipative quantum phase transition induced by the environment through quantum quenches and study the effect of the environment on the synchronization properties. Then we address Landau-Zener-Stueckelberg-Majorana protocols for two spins and for the spin array. In this latter case, we adopt a stochastic mean-field point of view and present a Kibble-Zurek-type argument to account for interaction effects in the lattice. Such dissipative quantum spin arrays can be realized in ultracold atoms, trapped ions, and mesoscopic systems and are related to Kondo lattice models.
Quantum Control in an Atomic Spin System
NASA Astrophysics Data System (ADS)
Phillips, C. S.; Woods, W.; Potts, J. R.; Ponsor, S.; Gardner, J. R.
1998-11-01
The experimental work described here investigates the physics of coherent quantum control in an atomic spin system. This type of system is very attractive for precision studies of coherent control for a number of reasons, including the ease with which it may be manipulated experimentally and the relative simplicity of its theoretical description. To this end, we are studying quantum control of the spin wavefunction of ground state (F=3) ^85Rb atoms confined in a vapor-cell MOT. Application of uniform magnetic and optical fields to this system results in an anharmonic ladder of seven levels whose state can be manipulated arbitrarily using radio-frequency rotating magnetic fields. Using the optimal control formalism of Shi and Rabitz, we have developed a numerical model of this system which predicts the appropriate control pulse shape given the initial and desired final state of the system. As predicted, we find that the control pulse which causes a given system evolution is not unique, allowing the construction of control pulses with multiple goals, such as evolution through specified intermediate states. This freedom should allow for the construction of control pulses that both produce the desired final state and are robust to decoherence effects. This type of precise control may find application in the development of quantum computation devices as well as in other types of nano-technology. An experimental implementation of quantum control in this system, already underway in our lab, will be presented.
Molecular dynamics of large systems with quantum corrections for the nuclei
Gu, Bing; Garashchuk, Sophya
2015-12-31
This paper describes an approximate approach to quantum dynamics based on the quantum trajectory formulation of the Schrödinger equation. The quantum-mechanical effects are incorporated through the quantum potential of the mean-field type, acting on a trajectory ensemble in addition to the classical potential. Efficiency for large systems is achieved by using the quantum corrections for selected degrees of freedom and introduction of empirical friction into the ground-state energy calculations. The classical potential, if needed, can be computed on-the-fly using the Density Functional Tight Binding method of electronic structure merged with the quantum trajectory dynamics code. The approach is practical for a few hundred atoms. Applications include a study of adsorption of quantum hydrogen colliding with the graphene model, C{sub 37}H{sub 15} and a calculation of the ground state of solid {sup 4}He simulated by a cell 180-atoms.
Constraint algebra for interacting quantum systems
NASA Astrophysics Data System (ADS)
Fubini, S.; Roncadelli, M.
1988-04-01
We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix. On leave from Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and INFN, I-27100 Pavia, Italy.
Quons in a quantum dissipative system
NASA Astrophysics Data System (ADS)
Lee, Taejin
2016-03-01
String theory proves to be an imperative tool to explore the critical behavior of the quantum dissipative system. We discuss the quantum particles moving in two dimensions, in the presence of a uniform magnetic field, subject to a periodic potential and a dissipative force, which are described by the dissipative Wannier-Azbel-Hofstadter (DWAH) model. Using string theory formulation of the model, we find that the elementary excitations of the system at the generic points of the off-critical regions, in the zero temperature limit are quons, which satisfy q-deformed statistics.
ERIC Educational Resources Information Center
WIENS, JACOB H.
TO PERMIT COMPARATIVE ANALYSIS FOR PURPOSES OF EDUCATIONAL PLANNING AT SAN MATEO, FIVE INSTITUTIONS WITH SYSTEMS PROGRAMS ARE EVALUATED ON THE BASIS OF TRIP NOTES. OAKLAND COMMUNITY COLLEGE HAS BEEN COMPLETELY ORGANIZED AROUND THE VOLUNTARY WORK-STUDY LABORATORY APPROACH TO LEARNING. ORAL ROBERTS UNIVERSITY, OKLAHOMA CHRISTIAN COLLEGE, HENRY FORD…
Exact propagation of open quantum systems in a system-reservoir context
NASA Astrophysics Data System (ADS)
Stockburger, Jürgen T.
2016-08-01
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on timescales comparable to or shorter than the reservoir correlation time, a notoriously difficult but relevant case in the context of quantum information processing and quantum thermodynamics. A previous stochastic approach is re-formulated for the case of finite reservoir correlation and response times, resulting in a numerical simulation strategy exceeding previous ones by orders of magnitude in efficiency. Although the approach is based on a memory formalism, the dynamical equations propagated in the simulations are time-local. This leaves a wide range of choices in selecting the system to be studied and the numerical method used for propagation. For a series of tests, the dynamics of the spin-boson system is computed in various settings including strong external driving and Landau-Zener transitions.
New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy
Colvin, M; Krishnan, V V
2003-02-07
The power of a quantum computer (QC) relies on the fundamental concept of the superposition in quantum mechanics and thus allowing an inherent large-scale parallelization of computation. In a QC, binary information embodied in a quantum system, such as spin degrees of freedom of a spin-1/2 particle forms the qubits (quantum mechanical bits), over which appropriate logical gates perform the computation. In classical computers, the basic unit of information is the bit, which can take a value of either 0 or 1. Bits are connected together by logic gates to form logic circuits to implement complex logical operations. The expansion of modern computers has been driven by the developments of faster, smaller and cheaper logic gates. As the size of the logic gates become smaller toward the level of atomic dimensions, the performance of such a system is no longer considered classical but is rather governed by quantum mechanics. Quantum computers offer the potentially superior prospect of solving computational problems that are intractable to classical computers such as efficient database searches and cryptography. A variety of algorithms have been developed recently, most notably Shor's algorithm for factorizing long numbers into prime factors in polynomial time and Grover's quantum search algorithm. The algorithms that were of only theoretical interest as recently, until several methods were proposed to build an experimental QC. These methods include, trapped ions, cavity-QED, coupled quantum dots, Josephson junctions, spin resonance transistors, linear optics and nuclear magnetic resonance. Nuclear magnetic resonance (NMR) is uniquely capable of constructing small QCs and several algorithms have been implemented successfully. NMR-QC differs from other implementations in one important way that it is not a single QC, but a statistical ensemble of them. Thus, quantum computing based on NMR is considered as ensemble quantum computing. In NMR quantum computing, the spins with
Systems Biology Approach to Developing “Systems Therapeutics”
2014-01-01
The standard drug development model uses reductionist approaches to discover small molecules targeting one pathway. Although systems biology analyzes multiple pathways, the approach is often used to develop a small molecule interacting at only one pathway in the system. Similar to that in physics where a departure from the old reductionist “Copenhagen View” of quantum physics to a new and predictive systems based, collective model has emerged yielding new breakthroughs such as the LASER, a new model is emerging in biology where systems biology is used to develop a new technology acting at multiple pathways called “systems therapeutics.” PMID:24900858
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
Yeh, L. |
1993-06-23
After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented.
An effective Hamiltonian approach to quantum random walk
NASA Astrophysics Data System (ADS)
Sarkar, Debajyoti; Paul, Niladri; Bhattacharya, Kaushik; Ghosh, Tarun Kanti
2017-03-01
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2016-12-01
In the framework of superconducting hybrid systems, we construct a star quantum network in which a superconducting transmission line resonator as a quantum bus and multiple units constituted by transmission line resonator and superconducting qubits as the carriers of quantum information. We further propose and analyze a theoretical scheme to realize quantum information processing in the quantum network. The coupling between the bus and any two superconducting qubits can be selectively implemented based on the dark state resonances of the highly dissipative transmission line resonators, and it can be found that quantum information processing between any two units can be completed in one step. As examples, the transmission of unknown quantum states and the preparation of quantum entanglement in this quantum network are investigated. At last, we exhibit our simulation results and complete the relevant discussions in order to show the advantages of this kind of quantum network.
Lyapunov Control of Quantum Systems with Impulsive Control Fields
Yang, Wei; Sun, Jitao
2013-01-01
We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method. PMID:23766712
Quantum emulation of quasiperiodic systems
NASA Astrophysics Data System (ADS)
Senaratne, Ruwan; Geiger, Zachary; Fujiwara, Kurt; Singh, Kevin; Rajagopal, Shankari; Weld, David
2016-05-01
Tunable quasiperiodic optical traps can enable quantum emulation of electronic phenomena in quasicrystals. A 1D bichromatic lattice or a Gaussian beam intersecting a 2D square lattice in a direct analogy of the ``cut-and-project'' construction can be used to create tunable 1D quasiperiodic potentials for cold neutral atoms. We report on progress towards the observation of singular continuous diffraction patterns, fractal energy spectra, and Bloch oscillations in these synthetic quasicrystals. We will also discuss the existence of edge states which can be topologically pumped across the lattice by varying a phasonic parameter. We acknowledge support from the ONR, the ARO and the PECASE and DURIP programs, the AFOSR, the Alfred P. Sloan foundation and the President's Research Catalyst Award from the University of California Office of the President.
Classical system boundaries cannot be determined within quantum Darwinism
NASA Astrophysics Data System (ADS)
Fields, Chris
Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantum-mechanical explanation of the "emergence" of classicality.
Lithography system using quantum entangled photons
NASA Technical Reports Server (NTRS)
Williams, Colin (Inventor); Dowling, Jonathan (Inventor); della Rossa, Giovanni (Inventor)
2002-01-01
A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.
Eigenstate tracking in open quantum systems
NASA Astrophysics Data System (ADS)
Jing, Jun; Sarandy, Marcelo S.; Lidar, Daniel A.; Luo, Da-Wei; Wu, Lian-Ao
2016-10-01
Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where environment-mediated transitions introduce additional decoherence channels. Adiabatic passage is a well-established solution but requires a sufficiently slow evolution time that is dictated by the adiabatic theorem. Here we develop a systematic projection theory formulation for the transitionless evolution of general open quantum systems described by time-local master equations. We derive a time-convolutionless dynamical equation for the target instantaneous eigenstate of a given time-dependent Hamiltonian. A transitionless dynamics then arises in terms of a competition between the average Hamiltonian gap and the decoherence rate, which implies optimal adiabaticity timescales. We show how eigenstate tracking can be accomplished via control pulses, without explicitly incorporating counter-diabatic driving, thus offering an alternative route to accelerate adiabaticity. We examine rectangular pulses, chaotic signals, and white noise, and find that, remarkably, the effectiveness of eigenstate tracking hardly depends on the details of the control functions. In all cases the control protocol keeps the system in the desired instantaneous eigenstate throughout the entire evolution, along an accelerated adiabatic path.
Optimal control of complex atomic quantum systems
van Frank, S.; Bonneau, M.; Schmiedmayer, J.; Hild, S.; Gross, C.; Cheneau, M.; Bloch, I.; Pichler, T.; Negretti, A.; Calarco, T.; Montangero, S.
2016-01-01
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations. PMID:27725688
Optimal control of complex atomic quantum systems
NASA Astrophysics Data System (ADS)
van Frank, S.; Bonneau, M.; Schmiedmayer, J.; Hild, S.; Gross, C.; Cheneau, M.; Bloch, I.; Pichler, T.; Negretti, A.; Calarco, T.; Montangero, S.
2016-10-01
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
Hidden supersymmetry in quantum bosonic systems
Correa, Francisco Plyushchay, Mikhail S.
2007-10-15
We show that some simple well-studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Poeschl-Teller potential problems, in which the unbroken and broken N = 2 supersymmetry of linear and nonlinear (polynomial) forms is revealed.
On the consistent effect histories approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Rudolph, Oliver
1996-11-01
A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of ``history'' is generalized to the notion of ``effect history.'' The space of effect histories carries the structure of a D-poset. Recent results of J. D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnès' logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.
Duality in the quantum Hall system
NASA Astrophysics Data System (ADS)
Lütken, C. A.; Ross, G. G.
1992-05-01
We suggest that a unified description of the integer and fractional phases of the quantum Hall system may be possible if the scaling diagram of transport coefficients is invariant under linear fractional (modular) transformations. In this model the hierarchy of states, as well as the observed universality of critical exponents, are consequences of a discrete SL(2,openZ) symmetry acting on the parameter space of an effective quantum-field theory. Available scaling data on the position of delocalization fixed points in the integer case and the position of mobility fixed points in the fractional case agree with the model within experimental accuracy.
Nonperturbative approach to circuit quantum electrodynamics.
Jonasson, Olafur; Tang, Chi-Shung; Goan, Hsi-Sheng; Manolescu, Andrei; Gudmundsson, Vidar
2012-10-01
We outline a rigorous method which can be used to solve the many-body Schrödinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the geometry of the electronic system as well as the polarization of the quantized electromagnetic field are explicitly taken into account. We accomplish this by performing repeated truncations of many-body spaces in order to keep the size of the many particle basis on a manageable level. The electron-electron and electron-photon interactions are treated in a nonperturbative manner using "exact numerical diagonalization." Our results demonstrate that including the diamagnetic term in the photon-electron interaction Hamiltonian drastically improves numerical convergence. Additionally, convergence with respect to the number of photon states in the joint photon-electron Fock space basis is fast. However, the convergence with respect to the number of electronic states is slow and is the main bottleneck in calculations.
Speed limits in Liouville space for open quantum systems
NASA Astrophysics Data System (ADS)
Uzdin, Raam; Kosloff, Ronnie
2016-08-01
One of the defining properties of an open quantum system is the variation of its purity in time. We derive speed limits on the rate of purity change for systems coupled to a Markovian environment. Our speed limits are based on Liouville space where density matrices are represented as vectors. This approach leads to speed limits that are always tighter compared to their parallel speed limits in Hilbert space. These bounds depend solely on the generators of the nonunitary dynamics and are independent of the particular state of the systems. Thus, they are perfectly suited to investigate dephasing, thermalization, and decorrelation processes of arbitrary states. We show that our speed limits can be attained and are therefore tight. As an application of our results we study dephasing of interacting spins, and the speed of classical and quantum correlation erasure in multi-particle system.
Plimak, L.I.; Fleischhauer, M.; Olsen, M.K.; Collett, M.J.
2003-01-01
We present an introduction to phase-space techniques (PST) based on a quantum-field-theoretical (QFT) approach. In addition to bridging the gap between PST and QFT, our approach results in a number of generalizations of the PST. First, for problems where the usual PST do not result in a genuine Fokker-Planck equation (even after phase-space doubling) and hence fail to produce a stochastic differential equation (SDE), we show how the system in question may be approximated via stochastic difference equations (S{delta}E). Second, we show that introducing sources into the SDE's (or S{delta}E's) generalizes them to a full quantum nonlinear stochastic response problem (thus generalizing Kubo's linear reaction theory to a quantum nonlinear stochastic response theory). Third, we establish general relations linking quantum response properties of the system in question to averages of operator products ordered in a way different from time normal. This extends PST to a much wider assemblage of operator products than are usually considered in phase-space approaches. In all cases, our approach yields a very simple and straightforward way of deriving stochastic equations in phase space.
An impurity-induced gap system as a quantum data bus for quantum state transfer
Chen, Bing; Li, Yong; Song, Z.; Sun, C.-P.
2014-09-15
We introduce a tight-binding chain with a single impurity to act as a quantum data bus for perfect quantum state transfer. Our proposal is based on the weak coupling limit of the two outermost quantum dots to the data bus, which is a gapped system induced by the impurity. By connecting two quantum dots to two sites of the data bus, the system can accomplish a high-fidelity and long-distance quantum state transfer. Numerical simulations for finite system show that the numerical and analytical results of the effective coupling strength agree well with each other. Moreover, we study the robustness of this quantum communication protocol in the presence of disorder in the couplings between the nearest-neighbor quantum dots. We find that the gap of the system plays an important role in robust quantum state transfer.
Quantum cryptographic system with reduced data loss
Lo, Hoi-Kwong; Chau, Hoi Fung
1998-01-01
A secure method for distributing a random cryptographic key with reduced data loss. Traditional quantum key distribution systems employ similar probabilities for the different communication modes and thus reject at least half of the transmitted data. The invention substantially reduces the amount of discarded data (those that are encoded and decoded in different communication modes e.g. using different operators) in quantum key distribution without compromising security by using significantly different probabilities for the different communication modes. Data is separated into various sets according to the actual operators used in the encoding and decoding process and the error rate for each set is determined individually. The invention increases the key distribution rate of the BB84 key distribution scheme proposed by Bennett and Brassard in 1984. Using the invention, the key distribution rate increases with the number of quantum signals transmitted and can be doubled asymptotically.
Quantum cryptographic system with reduced data loss
Lo, H.K.; Chau, H.F.
1998-03-24
A secure method for distributing a random cryptographic key with reduced data loss is disclosed. Traditional quantum key distribution systems employ similar probabilities for the different communication modes and thus reject at least half of the transmitted data. The invention substantially reduces the amount of discarded data (those that are encoded and decoded in different communication modes e.g. using different operators) in quantum key distribution without compromising security by using significantly different probabilities for the different communication modes. Data is separated into various sets according to the actual operators used in the encoding and decoding process and the error rate for each set is determined individually. The invention increases the key distribution rate of the BB84 key distribution scheme proposed by Bennett and Brassard in 1984. Using the invention, the key distribution rate increases with the number of quantum signals transmitted and can be doubled asymptotically. 23 figs.
A Quantum Bayes Net Approach to Causal Reasoning
NASA Astrophysics Data System (ADS)
Trueblood, Jennifer S.; Mistry, Percy K.; Pothos, Emmanuel M.
When individuals have little knowledge about a causal system and must make causal inferences based on vague and imperfect information, their judgments often deviate from the normative prescription of classical probability. Previously, many researchers have dealt with violations of normative rules by elaborating causal Bayesian networks through the inclusion of hidden variables. While these models often provide good accounts of data, the addition of hidden variables is often post hoc, included when a Bayes net fails to capture data. Further, Bayes nets with multiple hidden variables are often difficult to test. Rather than elaborating a Bayes net with hidden variables, we generalize the probabilistic rules of these models. The basic idea is that any classic Bayes net can be generalized to a quantum Bayes net by replacing the probabilities in the classic model with probability amplitudes in the quantum model. We discuss several predictions of quantum Bayes nets for human causal reasoning.
Identification of open quantum systems from observable time traces
Zhang, Jun; Sarovar, Mohan
2015-05-27
Estimating the parameters that dictate the dynamics of a quantum system is an important task for quantum information processing and quantum metrology, as well as fundamental physics. In our paper we develop a method for parameter estimation for Markovian open quantum systems using a temporal record of measurements on the system. Furthermore, the method is based on system realization theory and is a generalization of our previous work on identification of Hamiltonian parameters.
Periodic thermodynamics of open quantum systems.
Brandner, Kay; Seifert, Udo
2016-06-01
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
Edge reconstructions in fractional quantum Hall systems.
NASA Astrophysics Data System (ADS)
Joglekar, Yogesh; Nguyen, Hoang; Murthy, Ganpathy
2003-03-01
Two dimensional electron systems exhibiting fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are possible [1]. We present a microscopic calculation of these egde-states at filling factors ν=1/3 and ν=2/5 using the Hamiltonian theory of the fractional quantum Hall effect [2]. We find that the quantum Hall egde undergoes a reconstruction as the confining potential, produced by the background charge density, softens [3,4]. Our results have implications to the tunneling experiments into the edge of a fractional quantum Hall system [5]. 1: X. G.Wen, Phys. Rev. Lett. 64, 2206 (1990). 2: R. Shankar and G. Murthy, Phys. Rev. Lett. 79, 4437 (1997). 3: C. de C. Chamon and X. G. Wen, Phys. Rev. B 49, 8227 (1994). 4: X. Wan, K. Yang, and E. H. Razayi, Phys. Rev. Lett. 88, 056802 (2002). 5: A.M.Chang et al., Phys. Rev. Lett. 86, 143 (2000).
Periodic thermodynamics of open quantum systems
NASA Astrophysics Data System (ADS)
Brandner, Kay; Seifert, Udo
2016-06-01
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
Integrability of Quadratic Non-autonomous Quantum Linear Systems
NASA Astrophysics Data System (ADS)
Lopez, Raquel
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is
Some Theoretical Studies of Disordered Quantum Systems.
NASA Astrophysics Data System (ADS)
Dobrosavljevic, Vladimir
1988-12-01
In the first part of the thesis, two examples of disordered electronic systems are considered. I first investigate the role of conformational disorder relevant to the electronic structure of conjugated polymers such as polydiacetylene. Both in a solid and in solution the polymer undergoes a conformational transition accompanied by color changes as the temperature is increased. A simple statistical mechanical model for the transition is presented and solved, with the result defining the effective distribution of disorder for the electronic system. Renormalization group methods are then used to calculate the density of states and localization length for the model. Next, I study the fate of a hydrogenic atom in a hard sphere fluid. In this case, the disorder comes from the distribution of open spaces in the fluid accommodating the electron on its way around the nucleus. Simplified models for the electronic propagation in limits of small and large orbitals are presented. Simple variational methods can then be used to calculate the shift and broadening of spectral lines as a function of solvent density. In the second part, I examine the effects of quantum fluctuations on phase transitions in disordered systems. An example where such effects are manifestly important is the proton glass--a random mixture of a ferroelectric and an antiferroelectric component. The system can be described using a quantum mechanical Ising spin glass model, and the mean-field theory is solved using a novel combination of discretized path integral methods and replica techniques. The results show that the glassy phase is more susceptible to destruction by tunneling than are the ordered phases. Finally, I also consider the role of randomness in the size of quantum fluctuations, on the example of an Ising model with randomly mixed classical and quantum spins. For this model, the existence of a critical concentration of quantum spins is demonstrated, below which tunneling cannot destroy the ordered
Simulation of Ginger EPR Spectra Obtained by X-Irradiation:Quantum Approach
NASA Astrophysics Data System (ADS)
Laachir, S.; Moussetad, M.; Adhiri, R.; Fahli, A.; Aboulfatah, M.; Mikou, M.
2005-08-01
The ginger sample has been exposed to X-rays at cumulative doses. The foodstuffs irradiation is used in particular to improve their hygienic qualities and increase their shelf lives. This process has been approved by various international organizations: FAO -- AIEA -- WHO. In the present work, we propose to reproduce by simulation, based on a quantum approach, of the ESR (Electron Spin Resonance) spectra. The semi-classical approach is valid for a simple system, but not for a complex system such as an atom with hyperfine structure. In this case a quantum approach, based on spin Hamiltonian, is essential to interpret the ESR spectra. The main result is that the simulated spectra are in good agreement with the experimental ones obtained before and after irradiation.
Uncertainty relation for non-Hamiltonian quantum systems
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.
Quantum chaos and thermalization in gapped systems
Rigol, Marcos; Santos, Lea F.
2010-07-15
We investigate the onset of thermalization and quantum chaos in finite one-dimensional gapped systems of hard-core bosons. Integrability in these systems is broken by next-nearest-neighbor repulsive interactions, which also generate a superfluid to insulator transition. By employing full exact diagonalization, we study chaos indicators and few-body observables. We show that with increasing system size, chaotic behavior is seen over a broader range of parameters and, in particular, deeper into the insulating phase. Concomitantly, we observe that, as the system size increases, the eigenstate thermalization hypothesis extends its range of validity inside the insulating phase and is accompanied by the thermalization of the system.
Approach to non-equilibrium behaviour in quantum field theory
Kripfganz, J.; Perlt, H.
1989-05-01
We study the real-time evolution of quantum field theoretic systems in non-equilibrium situations. Results are presented for the example of scalar /lambda//phi//sup 4/ theory. The degrees of freedom are discretized by studying the system on a torus. Short-wavelength modes are integrated out to one-loop order. The long-wavelength modes considered to be the relevant degrees of freedom are treated by semiclassical phase-space methods. /copyright/ 1989 Academic Press, Inc.
NASA Astrophysics Data System (ADS)
Liu, Cheng-Wei
Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the
Observable measure of quantum coherence in finite dimensional systems.
Girolami, Davide
2014-10-24
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes.
One-qubit quantum gates in a circular graphene quantum dot: genetic algorithm approach.
Amparán, Gibrán; Rojas, Fernando; Pérez-Garrido, Antonio
2013-05-16
The aim of this work was to design and control, using genetic algorithm (GA) for parameter optimization, one-charge-qubit quantum logic gates σx, σy, and σz, using two bound states as a qubit space, of circular graphene quantum dots in a homogeneous magnetic field. The method employed for the proposed gate implementation is through the quantum dynamic control of the qubit subspace with an oscillating electric field and an onsite (inside the quantum dot) gate voltage pulse with amplitude and time width modulation which introduce relative phases and transitions between states. Our results show that we can obtain values of fitness or gate fidelity close to 1, avoiding the leakage probability to higher states. The system evolution, for the gate operation, is presented with the dynamics of the probability density, as well as a visualization of the current of the pseudospin, characteristic of a graphene structure. Therefore, we conclude that is possible to use the states of the graphene quantum dot (selecting the dot size and magnetic field) to design and control the qubit subspace, with these two time-dependent interactions, to obtain the optimal parameters for a good gate fidelity using GA.
One-qubit quantum gates in a circular graphene quantum dot: genetic algorithm approach
2013-01-01
The aim of this work was to design and control, using genetic algorithm (GA) for parameter optimization, one-charge-qubit quantum logic gates σx, σy, and σz, using two bound states as a qubit space, of circular graphene quantum dots in a homogeneous magnetic field. The method employed for the proposed gate implementation is through the quantum dynamic control of the qubit subspace with an oscillating electric field and an onsite (inside the quantum dot) gate voltage pulse with amplitude and time width modulation which introduce relative phases and transitions between states. Our results show that we can obtain values of fitness or gate fidelity close to 1, avoiding the leakage probability to higher states. The system evolution, for the gate operation, is presented with the dynamics of the probability density, as well as a visualization of the current of the pseudospin, characteristic of a graphene structure. Therefore, we conclude that is possible to use the states of the graphene quantum dot (selecting the dot size and magnetic field) to design and control the qubit subspace, with these two time-dependent interactions, to obtain the optimal parameters for a good gate fidelity using GA. PMID:23680153
Multiple-state quantum Otto engine, 1D box system
NASA Astrophysics Data System (ADS)
Latifah, E.; Purwanto, A.
2014-03-01
Quantum heat engines produce work using quantum matter as their working substance. We studied adiabatic and isochoric processes and defined the general force according to quantum system. The processes and general force are used to evaluate a quantum Otto engine based on multiple-state of one dimensional box system and calculate the efficiency. As a result, the efficiency depends on the ratio of initial and final width of system under adiabatic processes.
Multiple-state quantum Otto engine, 1D box system
Latifah, E.; Purwanto, A.
2014-03-24
Quantum heat engines produce work using quantum matter as their working substance. We studied adiabatic and isochoric processes and defined the general force according to quantum system. The processes and general force are used to evaluate a quantum Otto engine based on multiple-state of one dimensional box system and calculate the efficiency. As a result, the efficiency depends on the ratio of initial and final width of system under adiabatic processes.
Optimization Approaches for Designing Quantum Reversible Arithmetic Logic Unit
NASA Astrophysics Data System (ADS)
Haghparast, Majid; Bolhassani, Ali
2016-03-01
Reversible logic is emerging as a promising alternative for applications in low-power design and quantum computation in recent years due to its ability to reduce power dissipation, which is an important research area in low power VLSI and ULSI designs. Many important contributions have been made in the literatures towards the reversible implementations of arithmetic and logical structures; however, there have not been many efforts directed towards efficient approaches for designing reversible Arithmetic Logic Unit (ALU). In this study, three efficient approaches are presented and their implementations in the design of reversible ALUs are demonstrated. Three new designs of reversible one-digit arithmetic logic unit for quantum arithmetic has been presented in this article. This paper provides explicit construction of reversible ALU effecting basic arithmetic operations with respect to the minimization of cost metrics. The architectures of the designs have been proposed in which each block is realized using elementary quantum logic gates. Then, reversible implementations of the proposed designs are analyzed and evaluated. The results demonstrate that the proposed designs are cost-effective compared with the existing counterparts. All the scales are in the NANO-metric area.
Mesoscopic systems: classical irreversibility and quantum coherence.
Barbara, Bernard
2012-09-28
Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn(12)-ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of two-level systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)-like
Electron Dynamics in Finite Quantum Systems
NASA Astrophysics Data System (ADS)
McDonald, Christopher R.
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) and multiconfiguration time-dependent Hartree (MCTDH) methods are employed to investigate nonperturbative multielectron dynamics in finite quantum systems. MCTDHF is a powerful tool that allows for the investigation of multielectron dynamics in strongly perturbed quantum systems. We have developed an MCTDHF code that is capable of treating problems involving three dimensional (3D) atoms and molecules exposed to strong laser fields. This code will allow for the theoretical treatment of multielectron phenomena in attosecond science that were previously inaccessible. These problems include complex ionization processes in pump-probe experiments on noble gas atoms, the nonlinear effects that have been observed in Ne atoms in the presence of an x-ray free-electron laser (XFEL) and the molecular rearrangement of cations after ionization. An implementation of MCTDH that is optimized for two electrons, each moving in two dimensions (2D), is also presented. This implementation of MCTDH allows for the efficient treatment of 2D spin-free systems involving two electrons; however, it does not scale well to 3D or to systems containing more that two electrons. Both MCTDHF and MCTDH were used to treat 2D problems in nanophysics and attosecond science. MCTDHF is used to investigate plasmon dynamics and the quantum breathing mode for several electrons in finite lateral quantum dots. MCTDHF is also used to study the effects of manipulating the potential of a double lateral quantum dot containing two electrons; applications to quantum computing are discussed. MCTDH is used to examine a diatomic model molecular system exposed to a strong laser field; nonsequential double ionization and high harmonic generation are studied and new processes identified and explained. An implementation of MCTDHF is developed for nonuniform tensor product grids; this will allow for the full 3D implementation of MCTDHF and will provide a means to
Vibrational modes in the quantum Hall system
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Yan, Bin; Daily, Kevin; Greene, Chris H.
The hyperspherical adiabatic technique is more familiar to atomic and nuclear few-body systems, but can also be applied with high accuracy to the many-body quantum Hall problem. This technique reformulates the Schrödinger equation for N electrons into hyperspherical coordinates, which, after extracting the trivial center of mass, describes the system in terms of a single global size coordinate known as the hyperradius R, and 2 N - 3 remaining internal angular coordinates. The solutions are approximately separable in the hyperradial coordinate, and solutions in the system are found by treating the hyperradius as an adiabatic coordinate. The approximate separability of the wave functions in this coordinate suggests the presence of hyperradial vibrational modes which are not described in conventional theories. The vibrationally excited states share the internal geometry of their quantum Hall ground states, and their excitation frequencies may vary with the number of participating particles or the strength of the confinement. We plan to discuss the features of these vibrational modes and their possible detection in quantum Hall systems. NSF.
Quantum entanglement for systems of identical bosons: I. General features
NASA Astrophysics Data System (ADS)
Dalton, B. J.; Goold, J.; Garraway, B. M.; Reid, M. D.
2017-02-01
These two accompanying papers are concerned with two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems in which the probabilities for joint measurements on the composite sub-systems are no longer determined from measurement probabilities on the separate sub-systems. There are many aspects of entanglement that can be studied. This two-part review focuses on the meaning of entanglement, the quantum paradoxes associated with entangled states, and the important tests that allow an experimentalist to determine whether a quantum state—in particular, one for massive bosons is entangled. An overall outcome of the review is to distinguish criteria (and hence experiments) for entanglement that fully utilize the symmetrization principle and the super-selection rules that can be applied to bosonic massive particles. In the first paper (I), the background is given for the meaning of entanglement in the context of systems of identical particles. For such systems, the requirement is that the relevant quantum density operators must satisfy the symmetrization principle and that global and local super-selection rules prohibit states in which there are coherences between differing particle numbers. The justification for these requirements is fully discussed. In the second quantization approach that is used, both the system and the sub-systems are modes (or sets of modes) rather than particles, particles being associated with different occupancies of the modes. The definition of entangled states is based on first defining the non-entangled states—after specifying which modes constitute the sub-systems. This work mainly focuses on the two mode entanglement for massive bosons, but is put in the context of tests of local hidden variable theories, where one may not be able to make the above restrictions. The review provides the detailed
Artificial quantum thermal bath: Engineering temperature for a many-body quantum system
NASA Astrophysics Data System (ADS)
Shabani, Alireza; Neven, Hartmut
2016-11-01
Temperature determines the relative probability of observing a physical system in an energy state when that system is energetically in equilibrium with its environment. In this paper we present a theory for engineering the temperature of a quantum system different from its ambient temperature. We define criteria for an engineered quantum bath that, when coupled to a quantum system with Hamiltonian H , drives the system to the equilibrium state e/-H/TTr (e-H /T) with a tunable parameter T . This is basically an analog counterpart of the digital quantum metropolis algorithm. For a system of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body quantum systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid quantum-thermal annealer.
Isochronous classical systems and quantum systems with equally spaced spectra
NASA Astrophysics Data System (ADS)
Cariñena, J. F.; Perelomov, A. M.; Rañada, M. F.
2007-11-01
We study isoperiodic classical systems, what allows us to find the classical isochronous systems, i.e. having a period independent of the energy. The corresponding quantum analog, systems with an equally spaced spectrum are analysed by looking for possible creation-like differential operators. The harmonic oscillator and the isotonic oscillator are the two main essentially unique examples of such situation.
Non-Hermitian approach of edge states and quantum transport in a magnetic field
NASA Astrophysics Data System (ADS)
Ostahie, B.; NiÅ£a, M.; Aldea, A.
2016-11-01
We develop a manifest non-Hermitian approach of spectral and transport properties of two-dimensional mesoscopic systems in a strong magnetic field. The finite system to which several terminals are attached constitutes an open system that can be described by an effective Hamiltonian. The lifetime of the quantum states expressed by the energy imaginary part depends specifically on the lead-system coupling and makes the difference among three regimes: resonant, integer quantum Hall effect, and superradiant. The discussion is carried on in terms of edge state lifetime in different gaps, channel formation, role of hybridization, and transmission coefficients quantization. A toy model helps in understanding non-Hermitian aspects in open systems.
Systemic approaches to biodegradation.
Trigo, Almudena; Valencia, Alfonso; Cases, Ildefonso
2009-01-01
Biodegradation, the ability of microorganisms to remove complex chemicals from the environment, is a multifaceted process in which many biotic and abiotic factors are implicated. The recent accumulation of knowledge about the biochemistry and genetics of the biodegradation process, and its categorization and formalization in structured databases, has recently opened the door to systems biology approaches, where the interactions of the involved parts are the main subject of study, and the system is analysed as a whole. The global analysis of the biodegradation metabolic network is beginning to produce knowledge about its structure, behaviour and evolution, such as its free-scale structure or its intrinsic robustness. Moreover, these approaches are also developing into useful tools such as predictors for compounds' degradability or the assisted design of artificial pathways. However, it is the environmental application of high-throughput technologies from the genomics, metagenomics, proteomics and metabolomics that harbours the most promising opportunities to understand the biodegradation process, and at the same time poses tremendous challenges from the data management and data mining point of view.
Time-correlated blip dynamics of open quantum systems
NASA Astrophysics Data System (ADS)
Wiedmann, Michael; Stockburger, Jürgen T.; Ankerhold, Joachim
2016-11-01
The non-Markovian dynamics of open quantum systems is still a challenging task, particularly in the nonperturbative regime at low temperatures. While the stochastic Liouville-von Neumann equation (SLN) provides a formally exact tool to tackle this problem for both discrete and continuous degrees of freedom, its performance deteriorates for long times due to an inherently nonunitary propagator. Here we present a scheme that combines the SLN with projector operator techniques based on finite dephasing times, gaining substantial improvements in terms of memory storage and statistics. The approach allows for systematic convergence and is applicable in regions of parameter space where perturbative methods fail, up to the long-time domain. Findings are applied to the coherent and incoherent quantum dynamics of two- and three-level systems. In the long-time domain sequential and superexchange transfer rates are extracted and compared to perturbative predictions.
Energy Exchange in Driven Open Quantum Systems at Strong Coupling
NASA Astrophysics Data System (ADS)
Carrega, Matteo; Solinas, Paolo; Sassetti, Maura; Weiss, Ulrich
2016-06-01
The time-dependent energy transfer in a driven quantum system strongly coupled to a heat bath is studied within an influence functional approach. Exact formal expressions for the statistics of energy dissipation into the different channels are derived. The general method is applied to the driven dissipative two-state system. It is shown that the energy flows obey a balance relation, and that, for strong coupling, the interaction may constitute the major dissipative channel. Results in analytic form are presented for the particular value K =1/2 of strong Ohmic dissipation. The energy flows show interesting behaviors including driving-induced coherences and quantum stochastic resonances. It is found that the general characteristics persists for K near 1/2 .
Dynamical systems and quantum bicrossproduct algebras
NASA Astrophysics Data System (ADS)
Arratia, Oscar; del Olmo, Mariano A.
2002-06-01
We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, such as Poincaré, Galilei and Euclidean in N dimensions. The action associated with the bicrossproduct structure allows us to obtain a nonlinear action over a new group linked to the translations. This new nonlinear action associates a dynamical system with each generator which is the object of our study.
Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach
NASA Astrophysics Data System (ADS)
Jimenez, Kevin; Reslen, Jose
2016-08-01
The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.
Open quantum systems and random matrix theory
Mulhall, Declan
2014-10-15
A simple model for open quantum systems is analyzed with RMT. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the level spacing, width distribution and Δ{sub 3}(L) statistic are examined as a function of the strength of this coupling. The usual super-radiant state is observed, and it is seen that as it is formed, the level spacing and Δ{sub 3}(L) statistic exhibit the signatures of missed levels.
Open quantum systems and random matrix theory
NASA Astrophysics Data System (ADS)
Mulhall, Declan
2014-10-01
A simple model for open quantum systems is analyzed with RMT. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the level spacing, width distribution and Δ3(L) statistic are examined as a function of the strength of this coupling. The usual super-radiant state is observed, and it is seen that as it is formed, the level spacing and Δ3(L) statistic exhibit the signatures of missed levels.
Quantum entanglement in multiparticle systems of two-level atoms
Deb, Ram Narayan
2011-09-15
We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express the inherent quantum fluctuations of a composite system of two-level atoms as a sum of the quantum fluctuations of the individual constituent atoms and their correlation terms. This helps to separate out and study solely the quantum correlations among the atoms and obtain the criterion for the presence of entanglement in such multiatomic systems.
Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics
NASA Astrophysics Data System (ADS)
Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro
This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.
A semiclassical hybrid approach to many particle quantum dynamics
NASA Astrophysics Data System (ADS)
Grossmann, Frank
2006-07-01
We analytically derive a correlated approach for a mixed semiclassical many particle dynamics, treating a fraction of the degrees of freedom by the multitrajectory semiclassical initial value method of Herman and Kluk [Chem. Phys. 91, 27 (1984)] while approximately treating the dynamics of the remaining degrees of freedom with fixed initial phase space variables, analogously to the thawed Gaussian wave packet dynamics of Heller [J. Chem. Phys. 62, 1544 (1975)]. A first application of this hybrid approach to the well studied Secrest-Johnson [J. Chem. Phys. 45, 4556 (1966)] model of atom-diatomic collisions is promising. Results close to the quantum ones for correlation functions as well as scattering probabilities could be gained with considerably reduced numerical effort as compared to the full semiclassical Herman-Kluk approach. Furthermore, the harmonic nature of the different degrees of freedom can be determined a posteriori by comparing results with and without the additional approximation.
A semiclassical hybrid approach to many particle quantum dynamics.
Grossmann, Frank
2006-07-07
We analytically derive a correlated approach for a mixed semiclassical many particle dynamics, treating a fraction of the degrees of freedom by the multitrajectory semiclassical initial value method of Herman and Kluk [Chem. Phys. 91, 27 (1984)] while approximately treating the dynamics of the remaining degrees of freedom with fixed initial phase space variables, analogously to the thawed Gaussian wave packet dynamics of Heller [J. Chem. Phys. 62, 1544 (1975)]. A first application of this hybrid approach to the well studied Secrest-Johnson [J. Chem. Phys. 45, 4556 (1966)] model of atom-diatomic collisions is promising. Results close to the quantum ones for correlation functions as well as scattering probabilities could be gained with considerably reduced numerical effort as compared to the full semiclassical Herman-Kluk approach. Furthermore, the harmonic nature of the different degrees of freedom can be determined a posteriori by comparing results with and without the additional approximation.
NASA Astrophysics Data System (ADS)
Angelatos, Gerasimos
Photonic crystal slabs coupled with quantum dipole emitters allow one to control quantum light-matter interactions and are a promising platform for quantum information science technologies; however their development has been hindered by inherent fabrication issues. Inspired by recent nanowire growth techniques and opportunities in fundamental quantum nanophotonics, in this thesis we theoretically investigate light-matter interactions in nanowire photonic crystal structures with embedded quantum dots, a novel engineered quantum system, for applications in quantum optics. We develop designs for currently fabricable structures, including finite-size effects and radiative loss, and investigate their fundamental properties using photonic band structure calculations, finite-difference time-domain computations, and a rigorous photonic Green function technique. We study and engineer realistic nanowire photonic crystal waveguides for single photon applications whose performance can exceed that of state-of-the-art slab photonic crystals, and design a directed single photon source. We then develop a powerful quantum optical formalism using master equation techniques and the photonic Green function to understand the quantum dynamics of these exotic structures in open and lossy photonic environments. This is used to explore the coupling of a pair of quantum dots in a nanowire photonic crystal waveguide, demonstrating long-lived entangled states and a system with a completely controllable Hamiltonian capable of simulating a wide variety of quantum systems and entering a unique regime of cavity quantum electrodynamics characterized by strong exchange-splitting. Lastly, we propose and study a "metamaterial" polariton waveguide comprised of a nanowire photonic crystal waveguide with an embedded quantum dot in each unit cell, and explain the properties of both infinite and finite-sized structures using a Green function approach. We show that an external quantum dot can be strongly
Intuitionistic Quantum Logic of an n-level System
NASA Astrophysics Data System (ADS)
Caspers, Martijn; Heunen, Chris; Landsman, Nicolaas P.; Spitters, Bas
2009-07-01
A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in
Quantum jump model for a system with a finite-size environment.
Suomela, S; Kutvonen, A; Ala-Nissila, T
2016-06-01
Measuring the thermodynamic properties of open quantum systems poses a major challenge. A calorimetric detection has been proposed as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finite-size environment. We use the method to study the common fluctuation relations and prove that they are satisfied.
Enhanced fault-tolerant quantum computing in d-level systems.
Campbell, Earl T
2014-12-05
Error-correcting codes protect quantum information and form the basis of fault-tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transversal non-Clifford gate. Codes with the desired property are presented for d-level qudit systems with prime d. The codes use n=d-1 qudits and can detect up to ∼d/3 errors. We quantify the performance of these codes for one approach to quantum computation known as magic-state distillation. Unlike prior work, we find performance is always enhanced by increasing d.
NASA Astrophysics Data System (ADS)
Aspelmeyer, Markus; Schwab, Keith
2008-09-01
diverse backgrounds and approaches of the researchers. As diverse as the approaches are the manifold of goals and perspectives for operating mechanical systems close to or within the quantum regime. Already now, nanomechanical sensors achieve single-molecule mass detection and magnetic resonance force detection from single-electron spins although they are operated far from quantum. Quantum-limited mechanical devices promise a new technology with hitherto unachieved performance for high-resolution sensing. This is also of high relevance for macroscopic mechanical resonators used in gravitational wave detectors. Furthermore, the increasing capability to couple mechanical modes to individual quantum systems raises the interesting question of whether mechanics can serve as a quantum bus in hybrid implementations of quantum information processing. Finally, the possibility of generating quantum superposition states that involve displacements of a massive macroscopic object (such as the center of mass of a mechanical beam) provides a completely new parameter regime for testing quantum theory over the amazing range from nanomechanical objects of several picograms up to gram-scale mirrors used in gravitational wave interferometers. We are looking forward to these fascinating developments! This Focus Issue is intended to highlight the present status of the field and to provide both introduction and motivation for students and researchers who want to get familiar with this exciting area or even want to join it. It also complements the conference activities of our community during the last year, where a series of dedicated invited sessions at several international conferences (APS March Meeting 2008, CLEO/QELS 2008, OSA Frontiers in Optics 2008, PQE 2008/2009 etc) culminated in the first Gordon Conference on 'Mechanical Systems at the Quantum Limit'. Given the fast development of the field it was not surprising to see that during the collection of the following contributions new
3D Lorentzian loop quantum gravity and the spinor approach
NASA Astrophysics Data System (ADS)
Girelli, Florian; Sellaroli, Giuseppe
2015-12-01
We consider the generalization of the "spinor approach" to the Lorentzian case, in the context of three-dimensional loop quantum gravity with cosmological constant Λ =0 . The key technical tool that allows this generalization is the recoupling theory between unitary infinite-dimensional representations and nonunitary finite-dimensional ones, obtained in the process of generalizing the Wigner-Eckart theorem to SU(1,1). We use SU(1,1) tensor operators to build observables and a solvable quantum Hamiltonian constraint, analogous to the one introduced by V. Bonzom and his collaborators in the Euclidean case (with both Λ =0 and Λ ≠0 ). We show that the Lorentzian Ponzano-Regge amplitude is the solution of the quantum Hamiltonian constraint by recovering the Biedenharn-Elliott relation [generalized to the case where unitary and nonunitary SU(1,1) representations are coupled to each other]. Our formalism is sufficiently general that both the Lorentzian and the Euclidean case can be recovered (with Λ =0 ).
Chimera: a hybrid approach to numerical loop quantum cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter; Gupt, Brajesh; Singh, Parampreet
2014-01-01
The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
Preface of the special issue quantum foundations: information approach
2016-01-01
This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory. PMID:27091161
The Spin-Foam Approach to Quantum Gravity.
Perez, Alejandro
2013-01-01
This article reviews the present status of the spin-foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently-introduced new models for four-dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.
Boundary driven open quantum many-body systems
Prosen, Tomaž
2014-01-08
In this lecture course I outline a simple paradigm of non-eqjuilibrium quantum statistical physics, namely we shall study quantum lattice systems with local, Hamiltonian (conservative) interactions which are coupled to the environment via incoherent processes only at the system's boundaries. This is arguably the simplest nontrivial context where one can study far from equilibrium steady states and their transport properties. We shall formulate the problem in terms of a many-body Markovian master equation (the so-called Lindblad equation, and some of its extensions, e.g. the Redfield eqaution). The lecture course consists of two main parts: Firstly, and most extensively we shall present canonical Liouville-space many-body formalism, the so-called 'third quantization' and show how it can be implemented to solve bi-linear open many-particle problems, the key peradigmatic examples being the XY spin 1/2 chains or quasi-free bosonic (or harmonic) chains. Secondly, we shall outline several recent approaches on how to approach exactly solvable open quantum interacting many-body problems, such as anisotropic Heisenberg ((XXZ) spin chain or fermionic Hubbard chain.
Colloquium: Non-Markovian dynamics in open quantum systems
NASA Astrophysics Data System (ADS)
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of
ERIC Educational Resources Information Center
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
Experimental simulation of quantum tunneling in small systems.
Feng, Guan-Ru; Lu, Yao; Hao, Liang; Zhang, Fei-Hao; Long, Gui-Lu
2013-01-01
It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simulation algorithm and requires very few spin-1/2 nuclei without the need of ancillary qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.
Quantum Random Access Codes Using Single d -Level Systems
NASA Astrophysics Data System (ADS)
Tavakoli, Armin; Hameedi, Alley; Marques, Breno; Bourennane, Mohamed
2015-05-01
Random access codes (RACs) are used by a party to, with limited communication, access an arbitrary subset of information held by another party. Quantum resources are known to enable RACs that break classical limitations. Here, we study quantum and classical RACs with high-level communication. We derive average performances of classical RACs and present families of high-level quantum RACs. Our results show that high-level quantum systems can significantly increase the advantage of quantum RACs over their classical counterparts. We demonstrate our findings in an experimental realization of a quantum RAC with four-level communication.
Preparing ground States of quantum many-body systems on a quantum computer.
Poulin, David; Wocjan, Pawel
2009-04-03
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to determine the one with lowest energy, requiring a running time proportional to N. A quantum computer, if it could be built, could solve this problem in time sqrt[N]. Here, we present a powerful extension of this result to the case of interacting quantum particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems.
Ramsey interference in a multilevel quantum system
NASA Astrophysics Data System (ADS)
Lee, J. P.; Bennett, A. J.; Skiba-Szymanska, J.; Ellis, D. J. P.; Farrer, I.; Ritchie, D. A.; Shields, A. J.
2016-02-01
We report Ramsey interference in the excitonic population of a negatively charged quantum dot measured in resonant fluorescence. Our experiments show that the decay time of the Ramsey interference is limited by the spectral width of the transition. Applying a vertical magnetic field induces Zeeman split transitions that can be addressed by changing the laser detuning to reveal two-, three-, and four-level system behavior. We show that under finite field the phase-sensitive control of two optical pulses from a single laser can be used to prepare both population and spin states simultaneously. We also demonstrate the coherent optical manipulation of a trapped spin in a quantum dot in a Faraday geometry magnetic field.
Coherent manipulation of single quantum systems in the solid state
NASA Astrophysics Data System (ADS)
Childress, Lilian Isabel
2007-12-01
The controlled, coherent manipulation of quantum-mechanical systems is an important challenge in modern science and engineering, with significant applications in quantum information science. Solid-state quantum systems such as electronic spins, nuclear spins, and superconducting islands are among the most promising candidates for realization of quantum bits (qubits). However, in contrast to isolated atomic systems, these solid-state qubits couple to a complex environment which often results in rapid loss of coherence, and, in general, is difficult to understand. Additionally, the strong interactions which make solid-state quantum systems attractive can typically only occur between neighboring systems, leading to difficulties in coupling arbitrary pairs of quantum bits. This thesis presents experimental progress in understanding and controlling the complex environment of a solid-state quantum bit, and theoretical techniques for extending the distance over which certain quantum bits can interact coherently. Coherent manipulation of an individual electron spin associated with a nitrogen-vacancy center in diamond is used to gain insight into its mesoscopic environment. Furthermore, techniques for exploiting coherent interactions between the electron spin and a subset of the environment are developed and demonstrated, leading to controlled interactions with single isolated nuclear spins. The quantum register thus formed by a coupled electron and nuclear spin provides the basis for a theoretical proposal for fault-tolerant long-distance quantum communication with minimal physical resource requirements. Finally, we consider a mechanism for long-distance coupling between quantum dots based on chip-scale cavity quantum electrodynamics.
Quantum integrable systems related to lie algebras
NASA Astrophysics Data System (ADS)
Olshanetsky, M. A.; Perelomov, A. M.
1983-03-01
Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors [83] devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g2v( q) of the following 5 types: vI( q) = q-2, vII( q) = sinh-2q, vIII( q) = sin-2q, v IV(q) = P(q) , vV( q) = q-2 + ω2q2. Here P(q) is the Weierstrass function, so that the first three cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbour potential exp( qjqj+ 1 ) is moreover considered. This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest.
Teaching the environment to control quantum systems
Pechen, Alexander; Rabitz, Herschel
2006-06-15
A nonequilibrium, generally time-dependent, environment whose form is deduced by optimal learning control is shown to provide a means for incoherent manipulation of quantum systems. Incoherent control by the environment (ICE) can serve to steer a system from an initial state to a target state, either mixed or in some cases pure, by exploiting dissipative dynamics. Implementing ICE with either incoherent radiation or a gas as the control is explicitly considered, and the environmental control is characterized by its distribution function. Simulated learning control experiments are performed with simple illustrations to find the shape of the optimal nonequilibrium distribution function that best affects the posed dynamical objectives.
Evolution of Quantum Entanglement in Open Systems
Isar, A.
2010-08-04
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a thermal environment. Using Peres-Simon necessary sufficient criterion for separability of two-mode Gaussian states, we show that for some values of diffusion coefficient, dissipation constant and temperature of the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a periodic collapse revival of entanglement take place.
The quantum trajectory approach to quantum feedback control of an oscillator revisited.
Doherty, Andrew C; Szorkovszky, A; Harris, G I; Bowen, W P
2012-11-28
We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driving and may have wider interest.
Non-equilibrium slave bosons approach to quantum pumping in interacting quantum dots
NASA Astrophysics Data System (ADS)
Citro, Roberta; Romeo, Francesco
2016-03-01
We review a time-dependent slave bosons approach within the non-equilibrium Green's function technique to analyze the charge and spin pumping in a strongly interacting quantum dot. We study the pumped current as a function of the pumping phase and of the dot energy level and show that a parasitic current arises, beyond the pure pumping one, as an effect of the dynamical constraints. We finally illustrate an all-electrical mean for spin-pumping and discuss its relevance for spintronics applications.
Gauge invariance of quantum gravity in the causal approach
NASA Astrophysics Data System (ADS)
Schorn, Ivo
1997-03-01
We investigate gauge invariance of perturbative quantum gravity without matter fields in the causal Epstein - Glaser approach. This approach uses free fields only so that all objects of the theory are mathematically well defined. The first-order graviton self-couplings are obtained from the Einstein - Hilbert Lagrangian written in terms of Goldberg variables and expanded to lowest order on the flat Minkowski background metric (linearized Einstein theory). Similar to Yang - Mills theory, gauge invariance to first order requires an additional coupling to fermionic ghost fields. For second-order tree graphs, gauge invariance generates four-graviton normalization terms, which agree exactly with the next order of the expansion of the Einstein - Hilbert Lagrangian. Gauge invariance of the ghost sector is then examined in detail. It is stressed that, despite some formal similarities, the concept of operator gauge invariance used in the causal method is different from the conventional BRS-invariance commonly used in the literature.
Inverse engineering control in open quantum systems
NASA Astrophysics Data System (ADS)
Jing, Jun; Wu, Lian-Ao; Sarandy, Marcelo S.; Muga, J. Gonzalo
2013-11-01
We propose a scheme for inverse engineering control in open quantum systems. Starting from an undetermined time evolution operator, a time-dependent Hamiltonian is derived in order to guide the system to attain an arbitrary target state at a predefined time. We calculate the fidelity of our inverse engineering control protocol in the presence of the noise with respect to the stochastic fluctuation of the linear parameters of the Hamiltonian during the time evolution. For a special family of Hamiltonians for two-level systems, we show that the control evolution of the system under noise can be categorized into two standard decohering processes: dephasing and depolarization, for both Markovian and non-Markovian conditions. In particular, we illustrate our formalism by analyzing the robustness of the engineered target state against errors. Moreover, we discuss the generalization of the inverse protocol for higher-dimensional systems.
Thermalization and Pseudolocality in Extended Quantum Systems
NASA Astrophysics Data System (ADS)
Doyon, Benjamin
2017-04-01
Recently, it was understood that modified concepts of locality played an important role in the study of extended quantum systems out of equilibrium, in particular in so-called generalized Gibbs ensembles. In this paper, we rigorously study pseudolocal charges and their involvement in time evolutions and in the thermalization process of arbitrary states with strong enough clustering properties. We show that the densities of pseudolocal charges form a Hilbert space, with inner product determined by thermodynamic susceptibilities. Using this, we define the family of pseudolocal states, which are determined by pseudolocal charges. This family includes thermal Gibbs states at high enough temperatures, as well as (a precise definition of) generalized Gibbs ensembles. We prove that the family of pseudolocal states is preserved by finite time evolution, and that, under certain conditions, the stationary state emerging at infinite time is a generalized Gibbs ensemble with respect to the evolution dynamics. If the evolution dynamics does not admit any conserved pseudolocal charges other than the evolution Hamiltonian, we show that any stationary pseudolocal state with respect to these dynamics is a thermal Gibbs state, and that Gibbs thermalization occurs. The framework is that of translation-invariant states on hypercubic quantum lattices of any dimensionality (including quantum chains) and finite-range Hamiltonians, and does not involve integrability.
Optimization Via Open System Quantum Annealing
2016-01-07
mapping between the Ising spin glass partition function and circuit model decision problems, discovered in a previous ARO Quantum Algorithms funded...of tunneling in providing quantum annealing speedup over classical algorithms • Characterized the effects of classical hardness on the performance...15 Annual APS March meeting, Tutorial on Quantum Annealing 12/14 Quantum Sensing, Metrology, and Algorithms Workshop, Northrop Grumman, Los
Wang, Qian; Hammes-Schiffer, Sharon
2006-11-14
A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.
A quantum theoretical approach to information processing in neural networks
NASA Astrophysics Data System (ADS)
Barahona da Fonseca, José; Barahona da Fonseca, Isabel; Suarez Araujo, Carmen Paz; Simões da Fonseca, José
2000-05-01
A reinterpretation of experimental data on learning was used to formulate a law on data acquisition similar to the Hamiltonian of a mechanical system. A matrix of costs in decision making specifies values attributable to a barrier that opposed to hypothesis formation about decision making. The interpretation of the encoding costs as frequencies of oscillatory phenomena leads to a quantum paradigm based in the models of photoelectric effect as well as of a particle against a potential barrier. Cognitive processes are envisaged as complex phenomena represented by structures linked by valence bounds. This metaphor is used to find some prerequisites to certain types of conscious experience as well as to find an explanation for some pathological distortions of cognitive operations as they are represented in the context of the isolobal model. Those quantum phenomena are understood as representing an analogue programming for specific special purpose computations. The formation of complex chemical structures within the context of isolobal theory is understood as an analog quantum paradigm for complex cognitive computations.
Semidirect Products of C*-Quantum Groups: Multiplicative Unitaries Approach
NASA Astrophysics Data System (ADS)
Meyer, Ralf; Roy, Sutanu; Woronowicz, Stanisław Lech
2017-04-01
C*-quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford's Theorem about Hopf algebras with projection suggests that any C*-quantum group with projection decomposes uniquely into an ordinary C*-quantum group and a "braided" C*-quantum group. We establish this on the level of manageable multiplicative unitaries.
NASA Astrophysics Data System (ADS)
Singha, Aniket; Fauzi, M. H.; Hirayama, Y.; Muralidharan, Bhaskaran
2017-03-01
The interplay of spin-polarized electronic edge states with the dynamics of the host nuclei in quantum Hall systems presents rich and nontrivial transport physics. Here, we develop a Landauer-Büttiker approach to understand various experimental features observed in the integer quantum Hall setups featuring quantum point contacts. The approach developed here entails a phenomenological description of spin-resolved interedge scattering induced via hyperfine assisted electron-nuclear spin flip-flop processes. A self-consistent simulation framework between the nuclear spin dynamics and edge state electronic transport is presented in order to gain crucial insights into the dynamic nuclear polarization effects on electronic transport and in turn the electron-spin polarization effects on the nuclear spin dynamics. In particular, we show that the hysteresis noted experimentally in the conductance-voltage trace as well as in the resistively detected NMR line-shape results from a lack of quasiequilibrium between electronic transport and nuclear polarization evolution. In addition, we present circuit models to emulate such hyperfine mediated transport effects to further facilitate a clear understanding of the electronic transport processes occurring around the quantum point contact. Finally, we extend our model to account for the effects of quadrupolar splitting of nuclear levels and also depict the electronic transport signatures that arise from single and multiphoton processes.
Dynamics of non-Markovian open quantum systems
NASA Astrophysics Data System (ADS)
de Vega, Inés; Alonso, Daniel
2017-01-01
Open quantum systems (OQSs) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. An overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation. Some of these techniques, such as master equations, Heisenberg equations, and stochastic methods, are based on solving the reduced OQS dynamics, while others, such as path integral Monte Carlo or chain mapping approaches, are based on solving the dynamics of the full system. The physical interpretation and derivation of the various approaches are emphasized, how they are connected is explored, and how different methods may be suitable for solving different problems is examined.
Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing
2014-06-28
Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.
Quantum transport: A unified approach via a multivariate hypergeometric generating function
NASA Astrophysics Data System (ADS)
Macedo-Junior, A. F.; Macêdo, A. M. S.
2014-07-01
We introduce a characteristic function method to describe charge-counting statistics (CCS) in phase coherent systems that directly connects the three most successful approaches to quantum transport: random-matrix theory (RMT), the nonlinear σ-model and the trajectory-based semiclassical method. The central idea is the construction of a generating function based on a multivariate hypergeometric function, which can be naturally represented in terms of quantities that are well-defined in each approach. We illustrate the power of our scheme by obtaining exact analytical results for the first four cumulants of CCS in a chaotic quantum dot coupled ideally to electron reservoirs via perfectly conducting leads with arbitrary number of open scattering channels.
Quantum simulation. Coherent imaging spectroscopy of a quantum many-body spin system.
Senko, C; Smith, J; Richerme, P; Lee, A; Campbell, W C; Monroe, C
2014-07-25
Quantum simulators, in which well-controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics inaccessible to modeling with classical computers. However, checking the results of such simulations also becomes classically intractable as system sizes increase. Here, we introduce and implement a coherent imaging spectroscopic technique, akin to magnetic resonance imaging, to validate a quantum simulation. We use this method to determine the energy levels and interaction strengths of a fully connected quantum many-body system. Additionally, we directly measure the critical energy gap near a quantum phase transition. We expect this general technique to become a verification tool for quantum simulators once experiments advance beyond proof-of-principle demonstrations and exceed the resources of conventional computers.
Measuring entanglement entropy in a quantum many-body system.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-03
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Quantum dot-ring nanostructure — A comparison of different approaches
NASA Astrophysics Data System (ADS)
Janus-Zygmunt, Iwona; Kȩdzierska, Barbara; Gorczyca-Goraj, Anna; Zipper, Elżbieta; Maśka, Maciej M.
2016-03-01
It has been shown recently that a nanostructure composed of a quantum dot (QD) surrounded by a quantum ring (QR) possesses a set of very unique characteristics that make it a good candidate for future nanoelectronic devices. Its main advantage is the ability to easily tune transport properties on demand by so-called “wavefunction engineering”. In practice, the distribution of the electron wavefunction in the nanostructure can be controlled by, e.g., electrical gating. In order to predict some particular properties of the system, one has to know the exact wavefunctions for different shapes of the confining potential that defines the structure. In this paper, we compare three different methods that can be used to determine the energy spectrum, electron wavefunctions and transport properties of the system under investigation. In the first approach, we utilize the cylindrical symmetry of the confining potential and solve only the radial part of the Schrödinger equation; in the second approach, we discretize the Schrödinger equation in two dimensions and find the eigenstates with the help of the Lanczös method; in the third approach, we use package Kwant to solve a tight-binding approximation of the original system. To study the transport properties in all these approaches, we calculate microscopically the strength of the coupling between the nanosystem and leads. In the first two approaches, we use the Bardeen method, in the third one calculations are performed with the help of package Kwant.
Noncommutative Skyrmions in Quantum Hall Systems
NASA Astrophysics Data System (ADS)
Ezawa, Z. F.; Tsitsishvili, G.
Charged excitations in quantum Hall (QH) systems are noncommutative skyrmions. QH systems represent an ideal system equipped with noncommutative geometry. When an electron is confined within the lowest Landau level, its position is described solely by the guiding center, whose X and Y coordinates do not commute with one another. Topological excitations in such a noncommutative plane are noncommutative skyrmions flipping several spins coherently. We construct a microscopic skyrmion state by applying a certain unitary transformation to an electron or hole state. A remarkable property is that a noncommutative skyrmion carries necessarily the electron number proportional to the topological charge. More remarkable is the bilayer QH system with the layer degree of freedom acting as the pseudospin, where the quasiparticle is a topological soliton to be identified with the pseudospin skyrmion. Such a skyrmion is deformed into a bimeron (a pair of merons) by the parallel magnetic field penetrated between the two layers. Each meron carries the electric charge ±e/2.
Partitioning technique for discrete quantum systems
Jin, L.; Song, Z.
2011-06-15
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.
Entanglement in fermion systems and quantum metrology
NASA Astrophysics Data System (ADS)
Benatti, F.; Floreanini, R.; Marzolino, U.
2014-03-01
Entanglement in fermion many-body systems is studied using a generalized definition of separability based on partitions of the set of observables, rather than on particle tensor products. In this way, the characterizing properties of nonseparable fermion states can be explicitly analyzed, allowing a precise description of the geometric structure of the corresponding state space. These results have direct applications in fermion quantum metrology: Sub-shot-noise accuracy in parameter estimation can be obtained without the need of a preliminary state entangling operation.
Detecting relay attacks on RFID communication systems using quantum bits
NASA Astrophysics Data System (ADS)
Jannati, Hoda; Ardeshir-Larijani, Ebrahim
2016-11-01
RFID systems became widespread in variety of applications because of their simplicity in manufacturing and usability. In the province of critical infrastructure protection, RFID systems are usually employed to identify and track people, objects and vehicles that enter restricted areas. The most important vulnerability which is prevalent among all protocols employed in RFID systems is against relay attacks. Until now, to protect RFID systems against this kind of attack, the only approach is the utilization of distance-bounding protocols which are not applicable over low-cost devices such as RFID passive tags. This work presents a novel technique using emerging quantum technologies to detect relay attacks on RFID systems. Recently, it is demonstrated that quantum key distribution (QKD) can be implemented in a client-server scheme where client only requires an on-chip polarization rotator that may be integrated into a handheld device. Now we present our technique for a tag-reader scenario which needs similar resources as the mentioned QKD scheme. We argue that our technique requires less resources and provides lower probability of false alarm for the system, compared with distance-bounding protocols, and may pave the way to enhance the security of current RFID systems.
Coherence length of photons from a single quantum system
Jelezko, F.; Volkmer, A.; Popa, I.; Wrachtrup, J.; Rebane, K.K.
2003-04-01
We present a methodology that allows recording the coherence length of photons emitted by a single quantum system in a solid. The feasibility of this approach is experimentally demonstrated by measuring the self-interference of photons from the zero-phonon line emission of a single nitrogen-vacancy defect in diamond at 1.6 K. The first-order correlation function has been recorded and analyzed in terms of a single exponential decay time. A coherence time of {approx}5 ps has been obtained, which is in good agreement with the corresponding spectral line width and demonstrates the feasibility of the Fourier-transform spectroscopy with single photons.
Energy transport in closed quantum systems.
Levin, G A; Jones, W A; Walczak, K; Yerkes, K L
2012-03-01
We examine energy transport in an ensemble of closed quantum systems driven by stochastic perturbations. One can show that the probability and energy fluxes can be described in terms of quantum advection modes (QAMs) associated with the off-diagonal elements of the density matrix. These QAMs play the role of Landauer channels in a system with discrete energy spectrum and the eigenfunctions that cannot be described as plane waves. In order to determine the type of correlations that exist between the direction and magnitudes of each QAM and the average direction of energy and probability fluxes we have numerically solved the time-dependent Schrödinger equation describing a single particle trapped in a parabolic potential well which is perturbed by stochastic ripples. The ripples serve as a localized energy source and are offset to one side of the potential well. As the result a nonzero net energy flux flows from one part of the potential well to another across the symmetry center of the potential. We find that some modes exhibit positive correlation with the direction of the energy flow. Other modes, that carry a smaller energy per unit of the probability flux, anticorrelate with the energy flow and thus provide a backflow of the probability. The overall picture of energy transport that emerges from our results is very different from the conventional one based on a system with continuous energy spectrum.
Energy transport in closed quantum systems
NASA Astrophysics Data System (ADS)
Levin, G. A.; Jones, W. A.; Walczak, K.; Yerkes, K. L.
2012-03-01
We examine energy transport in an ensemble of closed quantum systems driven by stochastic perturbations. One can show that the probability and energy fluxes can be described in terms of quantum advection modes (QAMs) associated with the off-diagonal elements of the density matrix. These QAMs play the role of Landauer channels in a system with discrete energy spectrum and the eigenfunctions that cannot be described as plane waves. In order to determine the type of correlations that exist between the direction and magnitudes of each QAM and the average direction of energy and probability fluxes we have numerically solved the time-dependent Schrödinger equation describing a single particle trapped in a parabolic potential well which is perturbed by stochastic ripples. The ripples serve as a localized energy source and are offset to one side of the potential well. As the result a nonzero net energy flux flows from one part of the potential well to another across the symmetry center of the potential. We find that some modes exhibit positive correlation with the direction of the energy flow. Other modes, that carry a smaller energy per unit of the probability flux, anticorrelate with the energy flow and thus provide a backflow of the probability. The overall picture of energy transport that emerges from our results is very different from the conventional one based on a system with continuous energy spectrum.
Bahrami, M; Donadi, S; Ferialdi, L; Bassi, A; Curceanu, C; Di Domenico, A; Hiesmayr, B C
2013-01-01
Collapse models provide a theoretical framework for understanding how classical world emerges from quantum mechanics. Their dynamics preserves (practically) quantum linearity for microscopic systems, while it becomes strongly nonlinear when moving towards macroscopic scale. The conventional approach to test collapse models is to create spatial superpositions of mesoscopic systems and then examine the loss of interference, while environmental noises are engineered carefully. Here we investigate a different approach: We study systems that naturally oscillate-creating quantum superpositions-and thus represent a natural case-study for testing quantum linearity: neutrinos, neutral mesons, and chiral molecules. We will show how spontaneous collapses affect their oscillatory behavior, and will compare them with environmental decoherence effects. We will show that, contrary to what previously predicted, collapse models cannot be tested with neutrinos. The effect is stronger for neutral mesons, but still beyond experimental reach. Instead, chiral molecules can offer promising candidates for testing collapse models.
Characterizing and quantifying frustration in quantum many-body systems.
Giampaolo, S M; Gualdi, G; Monras, A; Illuminati, F
2011-12-23
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.
Statistical mechanics of quantum-classical systems with holonomic constraints.
Sergi, Alessandro
2006-01-14
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.
Position-dependent mass quantum Hamiltonians: general approach and duality
NASA Astrophysics Data System (ADS)
Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F.
2016-03-01
We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article.
On the consistent histories approach to quantum mechanics
Dowker, F. |; Kent, A.
1996-03-01
We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omnes, Gell-Man, and Hartle, and we describe the classifications of consistent sets. We illustrate some general features of consistent sets by a few lemmas and examples. We also consider various interpretations of the formalism, and we examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omnes characterization of true statements---statements that can be deduced unconditionally in his interpretation---is incorrect. We examine critically Gell-Mann and Hartle`s interpretation of the formalism, and in particular, their discussions of communication, prediction, and retrodiction, and we conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as-yet-unknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.
Intrinsic decoherence in isolated quantum systems
NASA Astrophysics Data System (ADS)
Wu, Yang-Le; Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
2017-01-01
We study the intrinsic, disorder-induced decoherence of an isolated quantum system under its own dynamics. Specifically, we investigate the characteristic time scale (i.e., the decoherence time) associated with an interacting many-body system losing the memory of its initial state. To characterize the erasure of the initial state memory, we define a time scale, the intrinsic decoherence time, by thresholding the gradual decay of the disorder-averaged return probability. We demonstrate the system-size independence of the intrinsic decoherence time in different models, and we study its dependence on the disorder strength. We find that the intrinsic decoherence time increases monotonically as the disorder strength increases in accordance with the relaxation of locally measurable quantities. We investigate several interacting spin (e.g., Ising and Heisenberg) and fermion (e.g., Anderson and Aubry-André) models to obtain the intrinsic decoherence time as a function of disorder and interaction strength.
Variational functions in driven open quantum systems
NASA Astrophysics Data System (ADS)
Jakob, Matthias; Stenholm, Stig
2003-03-01
We consider the Lindblad-type master equation of an open system. We address the question how to construct a functional of the quantum state which displays a monotonic behavior in time. This thus defines uniquely the direction of time in the system. As the generator of time evolution is not a Hermitian operator, the theory requires the considerations of right and left eigenstates. In this paper we assume them to form two complete bases, which allows us to construct the desired quantity. This can be interpreted as a generalized entropy functional. We show how the construction is carried out in the general case, and we illustrate the theory by solving the case of an externally driven and damped two-level system. The treatment is related to earlier work in the field, and its possible relation to time inversion is discussed.
Software-defined quantum communication systems
NASA Astrophysics Data System (ADS)
Humble, Travis S.; Sadlier, Ronald J.
2014-08-01
Quantum communication (QC) systems harness modern physics through state-of-the-art optical engineering to provide revolutionary capabilities. An important concern for QC engineering is designing and prototyping these systems to evaluate the proposed capabilities. We apply the paradigm of software-defined communication for engineering QC systems to facilitate rapid prototyping and prototype comparisons. We detail how to decompose QC terminals into functional layers defining hardware, software, and middleware concerns, and we describe how each layer behaves. Using the superdense coding protocol as an example, we describe implementations of both the transmitter and receiver, and we present results from numerical simulations of the behavior. We conclude that the software-defined QC provides a robust framework in which to explore the large design space offered by this new regime of communication.
An Adynamical, Graphical Approach to Quantum Gravity and Unification
NASA Astrophysics Data System (ADS)
Stuckey, W. M.; Silberstein, Michael; McDevitt, Timothy
We use graphical field gradients in an adynamical, background independent fashion to propose a new approach to quantum gravity (QG) and unification. Our proposed reconciliation of general relativity (GR) and quantum field theory (QFT) is based on a modification of their graphical instantiations, i.e. Regge calculus and lattice gauge theory (LGT), respectively, which we assume are fundamental to their continuum counterparts. Accordingly, the fundamental structure is a graphical amalgam of space, time, and sources (in parlance of QFT) called a "space-time source element". These are fundamental elements of space, time, and sources, not source elements in space and time. The transition amplitude for a space-time source element is computed using a path integral with discrete graphical action. The action for a space-time source element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy-momentum. This construct of K and J represents an adynamical global constraint (AGC) between sources, the space-time metric, and the energy-momentum content of the element, rather than a dynamical law for time-evolved entities. In this view, one manifestation of quantum gravity becomes evident when, for example, a single space-time source element spans adjoining simplices of the Regge calculus graph. Thus, energy conservation for the space-time source element includes contributions to the deficit angles between simplices. This idea is used to correct proper distance in the Einstein-de Sitter (EdS) cosmology model yielding a fit of the Union2 Compilation supernova data that matches ΛCDM without having to invoke accelerating expansion or dark energy. A similar modification to LGT results in an adynamical account of quantum
FPGA based digital phase-coding quantum key distribution system
NASA Astrophysics Data System (ADS)
Lu, XiaoMing; Zhang, LiJun; Wang, YongGang; Chen, Wei; Huang, DaJun; Li, Deng; Wang, Shuang; He, DeYong; Yin, ZhenQiang; Zhou, Yu; Hui, Cong; Han, ZhengFu
2015-12-01
Quantum key distribution (QKD) is a technology with the potential capability to achieve information-theoretic security. Phasecoding is an important approach to develop practical QKD systems in fiber channel. In order to improve the phase-coding modulation rate, we proposed a new digital-modulation method in this paper and constructed a compact and robust prototype of QKD system using currently available components in our lab to demonstrate the effectiveness of the method. The system was deployed in laboratory environment over a 50 km fiber and continuously operated during 87 h without manual interaction. The quantum bit error rate (QBER) of the system was stable with an average value of 3.22% and the secure key generation rate is 8.91 kbps. Although the modulation rate of the photon in the demo system was only 200 MHz, which was limited by the Faraday-Michelson interferometer (FMI) structure, the proposed method and the field programmable gate array (FPGA) based electronics scheme have a great potential for high speed QKD systems with Giga-bits/second modulation rate.
NASA Astrophysics Data System (ADS)
Milburn, T. J.; Kim, M. S.; Vanner, M. R.
2016-05-01
Nonclassical-state generation is an important component throughout experimental quantum science for quantum information applications and probing the fundamentals of physics. Here, we investigate permutations of quantum nondemolition quadrature measurements and single quanta addition or subtraction to prepare quantum superposition states in bosonic systems. The performance of each permutation is quantified and compared using several different nonclassicality criteria including Wigner negativity, nonclassical depth, and optimal fidelity with a coherent-state superposition. We also compare the performance of our protocol using squeezing instead of a quadrature measurement and find that the purification provided by the quadrature measurement can significantly increase the nonclassicality generated. Our approach is ideally suited for implementation in light-matter systems such as quantum optomechanics and atomic spin ensembles, and offers considerable robustness to initial thermal occupation.
Quantum and statistical mechanics in open systems: theory and examples
NASA Astrophysics Data System (ADS)
Zueco, David
2009-08-01
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum master equations, phase space and numerical methods and Linear and non Linear Response Theory. Applications are the transport in periodic potentials and the dynamics of spins.
Repetitive Interrogation of 2-Level Quantum Systems
NASA Technical Reports Server (NTRS)
Prestage, John D.; Chung, Sang K.
2010-01-01
Trapped ion clocks derive information from a reference atomic transition by repetitive interrogations of the same quantum system, either a single ion or ionized gas of many millions of ions. Atomic beam frequency standards, by contrast, measure reference atomic transitions in a continuously replenished "flow through" configuration where initial ensemble atomic coherence is zero. We will describe some issues and problems that can arise when atomic state selection and preparation of the quantum atomic system is not completed, that is, optical pumping has not fully relaxed the coherence and also not fully transferred atoms to the initial state. We present a simple two-level density matrix analysis showing how frequency shifts during the state-selection process can cause frequency shifts of the measured clock transition. Such considerations are very important when a low intensity lamp light source is used for state selection, where there is relatively weak relaxation and re-pumping of ions to an initial state and much weaker 'environmental' relaxation of the atomic coherence set-up in the atomic sample.
Quantum simulation of disordered systems with cold atoms
NASA Astrophysics Data System (ADS)
Garreau, Jean-Claude
2017-01-01
This paper reviews the physics of quantum disorder in relation with a series of experiments using laser-cooled atoms exposed to "kicks" of a standing wave, realizing a paradigmatic model of quantum chaos, the kicked rotor. This dynamical system can be mapped onto a tight-binding Hamiltonian with pseudo-disorder, formally equivalent to the Anderson model of quantum disorder, with quantum chaos playing the role of disorder. This provides a very good quantum simulator for the Anderson physics. xml:lang="fr"
Locally Compact Quantum Groups. A von Neumann Algebra Approach
NASA Astrophysics Data System (ADS)
Van Daele, Alfons
2014-08-01
In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68-92] locally compact quantum groups are also studied in the von Neumann algebraic context. This approach is independent of the original C^*-algebraic approach in the sense that the earlier results are not used. However, this paper is not really independent because for many proofs, the reader is referred to the original paper where the C^*-version is developed. In this paper, we give a completely self-contained approach. Moreover, at various points, we do things differently. We have a different treatment of the antipode. It is similar to the original treatment in [Ann. Sci. & #201;cole Norm. Sup. (4) 33 (2000), 837-934]. But together with the fact that we work in the von Neumann algebra framework, it allows us to use an idea from [Rev. Roumaine Math. Pures Appl. 21 (1976), 1411-1449] to obtain the uniqueness of the Haar weights in an early stage. We take advantage of this fact when deriving the other main results in the theory. We also give a slightly different approach to duality. Finally, we collect, in a systematic way, several important formulas. In an appendix, we indicate very briefly how the C^*-approach and the von Neumann algebra approach eventually yield the same objects. The passage from the von Neumann algebra setting to the C^*-algebra setting is more or less standard. For the other direction, we use a new method. It is based on the observation that the Haar weights on the C^*-algebra extend to weights on the double dual with central support and that all these supports are the same. Of course, we get the von Neumann algebra by cutting down the double dual with this unique
On the no-signaling approach to quantum nonlocality
Méndez, J. M. Urías, Jesús
2015-03-15
The no-signaling approach to nonlocality deals with separable and inseparable multiparty correlations in the same set of probability states without conflicting causality. The set of half-spaces describing the polytope of no-signaling probability states that are admitted by the most general class of Bell scenarios is formulated in full detail. An algorithm for determining the skeleton that solves the no-signaling description is developed upon a new strategy that is partially pivoting and partially incremental. The algorithm is formulated rigorously and its implementation is shown to be effective to deal with the highly degenerate no-signaling descriptions. Several applications of the algorithm as a tool for the study of quantum nonlocality are mentioned. Applied to a large set of bipartite Bell scenarios, we found that the corresponding no-signaling polytopes have a striking high degeneracy that grows up exponentially with the size of the Bell scenario.
Work exchange between quantum systems: the spin-oscillator model.
Schröder, Heiko; Mahler, Günter
2010-02-01
With the development of quantum thermodynamics it has been shown that relaxation to thermal equilibrium and with it the concept of heat flux may emerge directly from quantum mechanics. This happens for a large class of quantum systems if embedded into another quantum environment. In this paper, we discuss the complementary question of the emergence of work flux from quantum mechanics. We introduce and discuss two different methods to assess the work source quality of a system, one based on the generalized factorization approximation, the other based on generalized definitions of work and heat. By means of those methods, we show that small quantum systems can, indeed, act as work reservoirs. We illustrate this behavior for a simple system consisting of a spin coupled to an oscillator and investigate the effects of two different interactions on the work source quality. One case will be shown to allow for a work source functionality of arbitrarily high quality.
Optimal dynamic discrimination of similar quantum systems
NASA Astrophysics Data System (ADS)
Li, Baiqing
2005-07-01
The techniques for identifying and separating similar molecules have always been very important to chemistry and other branches of science and engineering. Similar quantum systems share comparable Hamiltonians, so their eigenenergy levels, transition dipole moments, and therefore their ordinary observable properties are alike. Traditional analytical methods have mostly been restricted by working with the subtle differences in the physical and chemical properties of the similar species. Optimal Dynamic Discrimination (ODD) aims at magnifying the dissimilarity of the agents by actively controlling their quantum evolution, drawing on the extremely rich information embedded in their dynamics. ODD is developed based on the tremendous flexibility of Optimal Control Theory (OCT) and on the practical implementation of closed-loop learning control, which has become a more and more indispensable tool for controlling quantum processes. The ODD experimental paradigm is designed to combat a number of factors that are detrimental to the discrimination of similar molecules: laser pulse noise, signal detection errors, finite time resolution in the signals, and environmental decoherence effects. It utilizes either static signals or time series signal, the latter capable of providing more information. Simulations are performed in this dissertation progressing from the wave function to the density matrix formulation, in order to study the decoherence effects. Analysis of the results reveals the roles of the adverse factors, unravels the underlying mechanisms of ODD, and provides insights on laboratory implementation. ODD emphasizes the incorporation of algorithmic development and laboratory design, and seeks to bridge the gap between theoretical/computational chemistry and experimental chemistry, with the help from applied mathematics and computer science.
Coulomb crystallization in classical and quantum systems
NASA Astrophysics Data System (ADS)
Bonitz, Michael
2007-11-01
Coulomb crystallization occurs in one-component plasmas when the average interaction energy exceeds the kinetic energy by about two orders of magnitude. A simple road to reach such strong coupling consists in using external confinement potentials the strength of which controls the density. This has been succsessfully realized with ions in traps and storage rings and also in dusty plasma. Recently a three-dimensional spherical confinement could be created [1] which allows to produce spherical dust crystals containing concentric shells. I will give an overview on our recent results for these ``Yukawa balls'' and compare them to experiments. The shell structure of these systems can be very well explained by using an isotropic statically screened pair interaction. Further, the thermodynamic properties of these systems, such as the radial density distribution are discussed based on an analytical theory [3]. I then will discuss Coulomb crystallization in trapped quantum systems, such as mesoscopic electron and electron hole plasmas in coupled layers [4,5]. These systems show a very rich correlation behavior, including liquid and solid like states and bound states (excitons, biexcitons) and their crystals. On the other hand, also collective quantum and spin effects are observed, including Bose-Einstein condensation and superfluidity of bound electron-hole pairs [4]. Finally, I consider Coulomb crystallization in two-component neutral plasmas in three dimensions. I discuss the necessary conditions for crystals of heavy charges to exist in the presence of a light component which typically is in the Fermi gas or liquid state. It can be shown that their exists a critical ratio of the masses of the species of the order of 80 [5] which is confirmed by Quantum Monte Carlo simulations [6]. Familiar examples are crystals of nuclei in the core of White dwarf stars, but the results also suggest the existence of other crystals, including proton or α-particle crystals in dense matter
Theory of activated transport in bilayer quantum Hall systems.
Roostaei, B; Mullen, K J; Fertig, H A; Simon, S H
2008-07-25
We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.
On microstates counting in many body polymer quantum systems
Chacon-Acosta, Guillermo; Morales-Tecotl, Hugo A.; Dagdug, Leonardo
2011-10-14
Polymer quantum systems are mechanical models quantized in a similar way as loop quantum gravity but in which loops/graphs resembling polymers are replaced by discrete sets of points. Such systems have allowed to study in a simpler context some novel aspects of loop quantum gravity. Although thermal aspects play a crucial role in cosmology and black hole physics little attention has been given to the thermostatistics of many body polymer quantum systems. In this work we explore how the features of a one-dimensional effective polymer gas, affect its microstate counting and hence the corresponding thermodynamical quantities.
Control and Dynamic Approach to Robust Quantum Computing
2006-01-01
information, quantum error correction 17. SECURITY CLASSIFICATION OF REPORT UNCLASSIFIED NSN 7540-01-280-5500 Hideo Mabuchi California Institute of...stabilization of conditional quantum state preparation, and began work on a second, quantum error correction via continuous syndrome measurement. Below we...obtain. Quantum error correction : Our successes in the state-preparation problem led us to ask whether real-time feedback analysis could also be used for
Holonomic Quantum Control with Continuous Variable Systems
NASA Astrophysics Data System (ADS)
Albert, Victor V.; Shu, Chi; Krastanov, Stefan; Shen, Chao; Liu, Ren-Bao; Yang, Zhen-Biao; Schoelkopf, Robert J.; Mirrahimi, Mazyar; Devoret, Michel H.; Jiang, Liang
2016-04-01
Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems that support tunable nonlinearities, such as trapped ions and circuit QED.
Capacities of linear quantum optical systems
NASA Astrophysics Data System (ADS)
Lupo, Cosmo; Giovannetti, Vittorio; Pirandola, Stefano; Mancini, Stefano; Lloyd, Seth
2012-06-01
A wide variety of communication channels employ the quantized electromagnetic field to convey information. Their communication capacity crucially depends on losses associated to spatial characteristics of the channel such as diffraction and antenna design. Here we focus on the communication via a finite pupil, showing that diffraction is formally described as a memory channel. By exploiting this equivalence we then compute the communication capacity of an optical refocusing system, modeled as a converging lens. Even though loss of information originates from the finite pupil of the lens, we show that the presence of the refocusing system can substantially enhance the communication capacity. We mainly concentrate on communication of classical information, the extension to quantum information being straightforward.
A classical approach to the graph isomorphism problem using quantum walks
NASA Astrophysics Data System (ADS)
Douglas, Brendan L.; Wang, Jingbo B.
2008-02-01
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such algorithms have been scarce. In this work, we enumerate some important differences between quantum and classical walks, leading to their markedly different properties. We show that for many practical purposes, the implementation of quantum walks can be efficiently achieved using a classical computer. We then develop both classical and quantum graph isomorphism algorithms based on discrete-time quantum walks. We show that they are effective in identifying isomorphism classes of large databases of graphs, in particular groups of strongly regular graphs. We consider this approach to represent a promising candidate for an efficient solution to the graph isomorphism problem, and believe that similar methods employing quantum walks, or derivatives of these walks, may prove beneficial in constructing other algorithms for a variety of purposes.
Tasaki, Hal
2016-04-29
Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the thermodynamic system, which is initially in thermal equilibrium, and the "apparatus" which operates on the former, and assume that the whole system evolves autonomously. This provides a satisfactory derivation of the second law for macroscopic systems.
Realization of quantum state privacy amplification in a nuclear magnetic resonance quantum system
NASA Astrophysics Data System (ADS)
Hao, Liang; Wang, Chuan; Long, Gui Lu
2010-06-01
Quantum state privacy amplification (QSPA) is the quantum analogue of classical privacy amplification. If the state information of a series of single-particle states has some leakage, QSPA reduces this leakage by condensing the state information of two particles into the state of one particle. Recursive applications of the operations will eliminate the quantum state information leakage to a required minimum level. In this paper, we report the experimental implementation of a quantum state privacy amplification protocol in a nuclear magnetic resonance system. The density matrices of the states are constructed in the experiment, and the experimental results agree well with theory.
A new approach to shortest paths on networks based on the quantum bosonic mechanism
NASA Astrophysics Data System (ADS)
Jiang, Xin; Wang, Hailong; Tang, Shaoting; Ma, Lili; Zhang, Zhanli; Zheng, Zhiming
2011-01-01
This paper presents quantum bosonic shortest path searching (QBSPS), a natural, practical and highly heuristic physical algorithm for reasoning about the recognition of network structure via quantum dynamics. QBSPS is based on an Anderson-like itinerant bosonic system in which a boson's Green function is used as a navigation pointer for one to accurately approach the terminals. QBSPS is demonstrated by rigorous mathematical and physical proofs and plenty of simulations, showing how it can be used as a greedy routing to seek the shortest path between different locations. In methodology, it is an interesting and new algorithm rooted in the quantum mechanism other than combinatorics. In practice, for the all-pairs shortest-path problem in a random scale-free network with N vertices, QBSPS runs in O(μ(N) ln ln N) time. In application, we suggest that the corresponding experimental realizations are feasible by considering path searching in quantum optical communication networks; in this situation, the method performs a pure local search on networks without requiring the global structure that is necessary for current graph algorithms.
Quantum Computing in Fock Space Systems
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
1997-04-01
Fock space system (FSS) has unfixed number (N) of particles and/or degrees of freedom. In quantum computing (QC) main requirement is sustainability of coherent Q-superpositions. This normally favoured by low noise environment. High excitation/high temperature (T) limit is hence discarded as unfeasible for QC. Conversely, if N is itself a quantized variable, the dimensionality of Hilbert basis for qubits may increase faster (say, N-exponentially) than thermal noise (likely, in powers of N and T). Hence coherency may win over T-randomization. For this type of QC speed (S) of factorization of long integers (with D digits) may increase with D (for 'ordinary' QC speed polynomially decreases with D). This (apparent) paradox rests on non-monotonic bijectivity (cf. Georg Cantor's diagonal counting of rational numbers). This brings entire aleph-null structurality ("Babylonian Library" of infinite informational content of integer field) to superposition determining state of quantum analogue of Turing machine head. Structure of integer infinititude (e.g. distribution of primes) results in direct "Platonic pressure" resembling semi-virtual Casimir efect (presure of cut-off vibrational modes). This "effect", the embodiment of Pythagorean "Number is everything", renders Godelian barrier arbitrary thin and hence FSS-based QC can in principle be unlimitedly efficient (e.g. D/S may tend to zero when D tends to infinity).
Quantum Interference Induced Photon Blockade in a Coupled Single Quantum Dot-Cavity System
Tang, Jing; Geng, Weidong; Xu, Xiulai
2015-01-01
We propose an experimental scheme to implement a strong photon blockade with a single quantum dot coupled to a nanocavity. The photon blockade effect can be tremendously enhanced by driving the cavity and the quantum dot simultaneously with two classical laser fields. This enhancement of photon blockade is ascribed to the quantum interference effect to avoid two-photon excitation of the cavity field. Comparing with Jaynes-Cummings model, the second-order correlation function at zero time delay g(2)(0) in our scheme can be reduced by two orders of magnitude and the system sustains a large intracavity photon number. A red (blue) cavity-light detuning asymmetry for photon quantum statistics with bunching or antibunching characteristics is also observed. The photon blockade effect has a controllable flexibility by tuning the relative phase between the two pumping laser fields and the Rabi coupling strength between the quantum dot and the pumping field. Moreover, the photon blockade scheme based on quantum interference mechanism does not require a strong coupling strength between the cavity and the quantum dot, even with the pure dephasing of the system. This simple proposal provides an effective way for potential applications in solid state quantum computation and quantum information processing. PMID:25783560
Emulation of complex open quantum systems using superconducting qubits
NASA Astrophysics Data System (ADS)
Mostame, Sarah; Huh, Joonsuk; Kreisbeck, Christoph; Kerman, Andrew J.; Fujita, Takatoshi; Eisfeld, Alexander; Aspuru-Guzik, Alán
2017-02-01
With quantum computers being out of reach for now, quantum simulators are alternative devices for efficient and accurate simulation of problems that are challenging to tackle using conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing "hybrid" simulators by combining both techniques. Here we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bacteria with over 250 phonon modes coupled to each electronic state. Furthermore, we propose physical setups that can be used to reproduce the quantum dynamics of a standard and multiple-mode Holstein model. The proposed scheme is based on currently available technology of superconducting circuits consist of flux qubits and quantum oscillators.
Sumner, Isaiah; Iyengar, Srinivasan S
2007-10-18
We have introduced a computational methodology to study vibrational spectroscopy in clusters inclusive of critical nuclear quantum effects. This approach is based on the recently developed quantum wavepacket ab initio molecular dynamics method that combines quantum wavepacket dynamics with ab initio molecular dynamics. The computational efficiency of the dynamical procedure is drastically improved (by several orders of magnitude) through the utilization of wavelet-based techniques combined with the previously introduced time-dependent deterministic sampling procedure measure to achieve stable, picosecond length, quantum-classical dynamics of electrons and nuclei in clusters. The dynamical information is employed to construct a novel cumulative flux/velocity correlation function, where the wavepacket flux from the quantized particle is combined with classical nuclear velocities to obtain the vibrational density of states. The approach is demonstrated by computing the vibrational density of states of [Cl-H-Cl]-, inclusive of critical quantum nuclear effects, and our results are in good agreement with experiment. A general hierarchical procedure is also provided, based on electronic structure harmonic frequencies, classical ab initio molecular dynamics, computation of nuclear quantum-mechanical eigenstates, and employing quantum wavepacket ab initio dynamics to understand vibrational spectroscopy in hydrogen-bonded clusters that display large degrees of anharmonicities.
NASA Astrophysics Data System (ADS)
Renner, R.; Cirac, J. I.
2009-03-01
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.
Renner, R; Cirac, J I
2009-03-20
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.
Dynamical algebra of observables in dissipative quantum systems
NASA Astrophysics Data System (ADS)
Alipour, Sahar; Chruściński, Dariusz; Facchi, Paolo; Marmo, Giuseppe; Pascazio, Saverio; Rezakhani, Ali T.
2017-02-01
Dynamics and features of quantum systems can be drastically different from classical systems. Dissipation is understood as a general mechanism through which quantum systems may lose part or all of their quantum aspects. Here we discuss a method to analyze behaviors of dissipative quantum systems in an algebraic sense. This method employs a time-dependent product between system’s observables which is induced by the underlying dissipative dynamics. We argue that the long-time limit of the algebra of observables defined with this product yields a contractive algebra which reflects the loss of some quantum features of the dissipative system, and it bears relevant information about irreversibility. We illustrate this result through several examples of dissipation in various Markovian and non-Markovian systems.
An excited-state approach within full configuration interaction quantum Monte Carlo
Blunt, N. S.; Smart, Simon D.; Booth, George H.; Alavi, Ali
2015-10-07
We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available.
Quantum Phase Transitions in Conventional Matrix Product Systems
NASA Astrophysics Data System (ADS)
Zhu, Jing-Min; Huang, Fei; Chang, Yan
2017-02-01
For matrix product states(MPSs) of one-dimensional spin-1/2 chains, we investigate a new kind of conventional quantum phase transition(QPT). We find that the system has two different ferromagnetic phases; on the line of the two ferromagnetic phases coexisting equally, the system in the thermodynamic limit is in an isolated mediate-coupling state described by a paramagnetic state and is in the same state as the renormalization group fixed point state, the expectation values of the physical quantities are discontinuous, and any two spin blocks of the system have the same geometry quantum discord(GQD) within the range of open interval (0,0.25) and the same classical correlation(CC) within the range of open interval (0,0.75) compared to any phase having no any kind of correlation. We not only realize the control of QPTs but also realize the control of quantum correlation of quantum many-body systems on the critical line by adjusting the environment parameters, which may have potential application in quantum information fields and is helpful to comprehensively and deeply understand the quantum correlation, and the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems.
Strain-Driven Approach to Quantum Criticality in AFe_{2}As_{2} with A=K, Rb, and Cs.
Eilers, Felix; Grube, Kai; Zocco, Diego A; Wolf, Thomas; Merz, Michael; Schweiss, Peter; Heid, Rolf; Eder, Robert; Yu, Rong; Zhu, Jian-Xin; Si, Qimiao; Shibauchi, Takasada; Löhneysen, Hilbert V
2016-06-10
The iron-based superconductors AFe_{2}As_{2} with A=K, Rb, Cs exhibit large Sommerfeld coefficients approaching those of heavy-fermion systems. We have investigated the magnetostriction and thermal expansion of this series to shed light on this unusual behavior. Quantum oscillations of the magnetostriction allow identifying the band-specific quasiparticle masses which by far exceed the band-structure derived masses. The divergence of the Grüneisen ratio derived from thermal expansion indicates that with increasing volume along the series a quantum critical point is approached. The critical fluctuations responsible for the enhancement of the quasiparticle masses appear to weaken the superconducting state.
Strain-Driven Approach to Quantum Criticality in A Fe2 As2 with A =K , Rb, and Cs
NASA Astrophysics Data System (ADS)
Eilers, Felix; Grube, Kai; Zocco, Diego A.; Wolf, Thomas; Merz, Michael; Schweiss, Peter; Heid, Rolf; Eder, Robert; Yu, Rong; Zhu, Jian-Xin; Si, Qimiao; Shibauchi, Takasada; Löhneysen, Hilbert v.
2016-06-01
The iron-based superconductors A Fe2 As2 with A =K , Rb, Cs exhibit large Sommerfeld coefficients approaching those of heavy-fermion systems. We have investigated the magnetostriction and thermal expansion of this series to shed light on this unusual behavior. Quantum oscillations of the magnetostriction allow identifying the band-specific quasiparticle masses which by far exceed the band-structure derived masses. The divergence of the Grüneisen ratio derived from thermal expansion indicates that with increasing volume along the series a quantum critical point is approached. The critical fluctuations responsible for the enhancement of the quasiparticle masses appear to weaken the superconducting state.
Energy transfer in hybrid systems quantum dot-plasmonic nanostructures
NASA Astrophysics Data System (ADS)
Chaplik, A. V.
2016-06-01
Radiationless relaxation in hybrid systems quantum dot (QD)-plasmonic nanostructure is considered. For the system QD-2D plasma the relaxation rate extremely steeply depends on the radius of quantum dot while in the pair QD-cylindrical wire contacting each other this dependence is logarithmic weak.
Quantum Liquid Crystal Phases in Strongly Correlated Fermionic Systems
ERIC Educational Resources Information Center
Sun, Kai
2009-01-01
This thesis is devoted to the investigation of the quantum liquid crystal phases in strongly correlated electronic systems. Such phases are characterized by their partially broken spatial symmetries and are observed in various strongly correlated systems as being summarized in Chapter 1. Although quantum liquid crystal phases often involve…
Ultracold atoms for simulation of many body quantum systems
NASA Astrophysics Data System (ADS)
Hutchinson, David A. W.
2017-01-01
Feynman famously proposed simulating quantum physics using other, better controlled, quantum systems. This vision is now a reality within the realm of ultracold atomic physics. We discuss how these systems can be used to simulate many body physics, concentrating the Berezinskii-Kosterlitz-Thouless transition in 2D physics and the role of disorder.
NASA Astrophysics Data System (ADS)
Carr, Lincoln; Maeda, Kenji; Wall, Michael L.
2015-03-01
Ultracold molecules trapped in optical lattices present a new regime of physical chemistry and a new state of matter: complex dipolar matter. Such systems open up the prospect of tunable quantum complexity. We present models for the quantum many-body statics and dynamics of present experiments on polar bi-alkali dimer molecules. We are developing Hamiltonians and simulations for upcoming experiments on dimers beyond the alkali metals, including biologically and chemically important naturally occurring free radicals like the hydroxyl free radical (OH), as well as symmetric top polyatomic molecules like methyl fluoride (CH3F). These systems offer surprising opportunities in modeling and design of new materials. For example, symmetric top polyatomics can be used to study quantum molecular magnets and quantum liquid crystals. We use matrix-product-state (MPS) algorithms, supplemented by exact diagonalization, variational, perturbative, and other approaches. MPS algorithms not only produce experimentally measurable quantum phase diagrams but also explore the dynamical interplay between internal and external degrees of freedom inherent in complex dipolar matter. We maintain open source code (openTEBD and openMPS) available freely and used widely. Funded by NSF and AFOSR.
Numerical approach to time-dependent quantum transport and dynamical Kondo transition.
Zheng, Xiao; Jin, Jinshuang; Welack, Sven; Luo, Meng; Yan, YiJing
2009-04-28
An accurate and efficient numerical approach is developed for the transient electronic dynamics of open quantum systems at low temperatures. The calculations are based on a formally exact hierarchical equations of motion quantum dissipation theory [J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)]. We propose a hybrid scheme that combines the Matsubara expansion technique and a frequency dispersion treatment to account for reservoir correlation functions. The new scheme not just admits various forms of reservoir spectral functions but also greatly reduces the computational cost of the resulting hierarchical equations, especially in the low temperature regime. Dynamical Kondo effects are obtained and the cotunneling induced Kondo transitions are resolved in the transient current in response to time-dependent external voltages.
Quantum-classical correspondence in steady states of nonadiabatic systems
Fujii, Mikiya; Yamashita, Koichi
2015-12-31
We first present nonadiabatic path integral which is exact formulation of quantum dynamics in nonadiabatic systems. Then, by applying the stationary phase approximations to the nonadiabatic path integral, a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems is presented as a nonadiabatic trace formula. The present quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow degree of freedom, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels.
Systems Approach to Environmental Pollution.
ERIC Educational Resources Information Center
Chacko, George K., Ed.
The objective of a two-day Symposium on Systems Approach to Environmental Pollution of the Operations Research Society of America at the 137th Annual Meeting of the American Association for the Advancement of Science, December 27-28, 1970 in Chicago, Illinois, was not to raise the litany of a systems approach as the answer to all environmental…
Eigenstate Gibbs ensemble in integrable quantum systems
NASA Astrophysics Data System (ADS)
Nandy, Sourav; Sen, Arnab; Das, Arnab; Dhar, Abhishek
2016-12-01
The eigenstate thermalization hypothesis conjectures that for a thermodynamically large system in one of its energy eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of relevant conserved quantities. In a chaotic quantum system, only the energy is expected to play that role and hence eigenstates appear locally thermal. Integrable systems, on the other hand, possess an extensive number of such conserved quantities and therefore the reduced density matrix requires specification of all the corresponding parameters (generalized Gibbs ensemble). However, here we show by unbiased statistical sampling of the individual eigenstates with a given finite energy density that the local description of an overwhelming majority of these states of even such an integrable system is actually Gibbs-like, i.e., requires only the energy density of the eigenstate. Rare eigenstates that cannot be represented by the Gibbs ensemble can also be sampled efficiently by our method and their local properties are then shown to be described by appropriately truncated generalized Gibbs ensembles. We further show that the presence of these rare eigenstates differentiates the model from the chaotic case and leads to the system being described by a generalized Gibbs ensemble at long time under a unitary dynamics following a sudden quench, even when the initial state is a typical (Gibbs-like) eigenstate of the prequench Hamiltonian.
Ecological optimization of an irreversible quantum Carnot heat engine with spin-1/2 systems
NASA Astrophysics Data System (ADS)
Liu, Xiaowei; Chen, Lingen; Wu, Feng; Sun, Fengrui
2010-02-01
A model of a quantum heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting spin-1/2 systems is established in this paper. The quantum heat engine cycle is composed of two isothermal processes and two irreversible adiabatic processes and is referred to as a spin quantum Carnot heat engine. Based on the quantum master equation and the semi-group approach, equations of some important performance parameters, such as power output, efficiency, entropy generation rate and ecological function (a criterion representing the optimal compromise between exergy output rate and exergy loss rate), for the irreversible spin quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. The effects of internal irreversibility and heat leakage on ecological performance are discussed in detail.
NASA Astrophysics Data System (ADS)
Gao, Zhe
As the dimensions of commonly used semiconductor devices have shrunk into nanometer regime, it is recognized that the influence of quantum effects on their electrostatic and transport properties cannot be ignored. In the past few decades, various computational models and approaches have been developed to analyze these properties in nanostructures and devices. Among these computational models, the Schrodinger-Poisson model has been widely adopted for quantum mechanical electrostatic and transport analysis of nanostructures and devices such as quantum wires, metal--oxide--semiconductor field effect transistors (MOSFETs) and nanoelectromechanical systems (NEMS). The numerical results allow for evaluations of the electrical properties such as charge concentration and potential profile in these structures. The emergence of MOSFETs with multiple gates, such as Trigates, FinFETs and Pi-gates, offers a superior electrostatic control of devices by the gates, which can be therefore used to reduce the short channel effects within those devices. Full 2-D electrostatic and transport analysis enables a better understanding of the scalability of devices, geometric effects on the potential and charge distribution, and transport characteristics of the transistors. The Schrodinger-Poisson model is attractive due to its simplicity and straightforward implementation by using standard numerical methods. However, as it is required to solve a generalized eigenvalue problem generated from the discretization of the Schrodinger equation, the computational cost of the analysis increases quickly when the system's degrees of freedom (DOFs) increase. For this reason, techniques that enable an efficient solution of discretized Schrodinger equation in multidimensional domains are desirable. In this work, we seek to accelerate the numerical solution of the Schrodinger equation by using a component mode synthesis (CMS) approach. In the CMS approach, a nanostructure is divided into a set of
Phonon Overlaps in Molecular Quantum Dot Systems
NASA Astrophysics Data System (ADS)
Chang, Connie; Sethna, James
2004-03-01
We model the amplitudes and frequencies of the vibrational sidebands for the new molecular quantum dot systems. We calculate the Franck-Condon phonon overlaps in the 3N-dimensional configuration sapce. We solve the general case where the vibrational frequencies and eigenmodes change during the transition. We perform PM3 and DFT calculations for the case of the dumb bell-shaped C140 molecule. We find that the strongest amplitudes are associated with the 11 meV stretch mode, in agreement with experiment. The experimental amplitudes vary from molecule to molecule; indicating that the molecular overlaps are environment dependent. We explore overlaps in the presence of external electric fields from image charges and counter ions.
Quantum-biological control of energy transfer in hybrid quantum dot-metallic nanoparticle systems
NASA Astrophysics Data System (ADS)
Sadeghi, Seyed M.; Hood, Brady; Patty, Kira
2016-09-01
We show theoretically that when a semiconductor quantum dot and metallic nanoparticle system interacts with a laser field, quantum coherence can introduce a new landscape for the dynamics of Forster resonance energy transfer (FRET). We predict adsorption of biological molecules to such a hybrid system can trigger dramatic changes in the way energy is transferred, blocking FRET while the distance between the quantum dot and metallic nanoparticle (R) and other structural specifications remain unchanged. We study the impact of variation of R on the FRET rate in the presence of quantum coherence and its ultrafast decay, offering a characteristically different dependency than the standard 1/R6. Application of the results for quantum nanosensors is discussed.
Strong polygamy of quantum correlations in multi-party quantum systems
NASA Astrophysics Data System (ADS)
Kim, Jeong San
2014-10-01
We propose a new type of polygamy inequality for multi-party quantum entanglement. We first consider the possible amount of bipartite entanglement distributed between a fixed party and any subset of the rest parties in a multi-party quantum system. By using the summation of these distributed entanglements, we provide an upper bound of the distributed entanglement between a party and the rest in multi-party quantum systems. We then show that this upper bound also plays as a lower bound of the usual polygamy inequality, therefore the strong polygamy of multi-party quantum entanglement. For the case of multi-party pure states, we further show that the strong polygamy of entanglement implies the strong polygamy of quantum discord.
NASA Astrophysics Data System (ADS)
Brown, Matthew J.
2014-02-01
The framework of quantum frames can help unravel some of the interpretive difficulties i the foundation of quantum mechanics. In this paper, I begin by tracing the origins of this concept in Bohr's discussion of quantum theory and his theory of complementarity. Engaging with various interpreters and followers of Bohr, I argue that the correct account of quantum frames must be extended beyond literal space-time reference frames to frames defined by relations between a quantum system and the exosystem or external physical frame, of which measurement contexts are a particularly important example. This approach provides superior solutions to key EPR-type measurement and locality paradoxes.
A real-time spectrum acquisition system design based on quantum dots-quantum well detector
NASA Astrophysics Data System (ADS)
Zhang, S. H.; Guo, F. M.
2016-01-01
In this paper, we studied the structure characteristics of quantum dots-quantum well photodetector with response wavelength range from 400 nm to 1000 nm. It has the characteristics of high sensitivity, low dark current and the high conductance gain. According to the properties of the quantum dots-quantum well photodetectors, we designed a new type of capacitive transimpedence amplifier (CTIA) readout circuit structure with the advantages of adjustable gain, wide bandwidth and high driving ability. We have implemented the chip packaging between CTIA-CDS structure readout circuit and quantum dots detector and tested the readout response characteristics. According to the timing signals requirements of our readout circuit, we designed a real-time spectral data acquisition system based on FPGA and ARM. Parallel processing mode of programmable devices makes the system has high sensitivity and high transmission rate. In addition, we realized blind pixel compensation and smoothing filter algorithm processing to the real time spectrum data by using C++. Through the fluorescence spectrum measurement of carbon quantum dots and the signal acquisition system and computer software system to realize the collection of the spectrum signal processing and analysis, we verified the excellent characteristics of detector. It meets the design requirements of quantum dot spectrum acquisition system with the characteristics of short integration time, real-time and portability.
Numerical simulation of quantum systems using the Particle-In-Cell method
NASA Astrophysics Data System (ADS)
Dirkmann, Sven; Youssef, Ziad; Hemke, Torben; Mussenbrock, Thomas
2014-10-01
The Particle-In-Cell (PIC) method is a very powerful method for studying the dynamics of plasmas. It has been primarily developed for tracking the charged particle trajectories subject to selfconsistent and external electromagnetic fields. Exploiting the power of modern computers, one is able to track the classical paths of tens of millions of particles at the same time. In the late 1980th, it was Dawson (and later Dauger) who had the idea to apply the PIC method to the classical part in the semiclassical approach to quantum systems via path integral methods. One could estimate that if a thousands of classical paths are sufficient to describe the dynamics of one quantum particle, then millions classical paths could describe the dynamics of a quantum particle system. A PIC code in the frame of a semiclassical approach would therefore enable the investigation of a number of quantum phenomena, e.g., optical properties, electrical properties, and, ultimately, chemical reactions. In this contribution we explain the use of the PIC code yapic (developed by the authors) in the frame of the path integral method and discuss the numerical results for simple quantum phenomena, i.e., the quantum harmonic oscillator and quantum tunneling. This work is supported by the German Research Foundation in the frame of FOR 2093.
Nonequilibrium dynamical mean-field theory: an auxiliary quantum master equation approach.
Arrigoni, Enrico; Knap, Michael; von der Linden, Wolfgang
2013-02-22
We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.
Advanced-Retarded Differential Equations in Quantum Photonic Systems
NASA Astrophysics Data System (ADS)
Alvarez-Rodriguez, Unai; Perez-Leija, Armando; Egusquiza, Iñigo L.; Gräfe, Markus; Sanz, Mikel; Lamata, Lucas; Szameit, Alexander; Solano, Enrique
2017-02-01
We propose the realization of photonic circuits whose dynamics is governed by advanced-retarded differential equations. Beyond their mathematical interest, these photonic configurations enable the implementation of quantum feedback and feedforward without requiring any intermediate measurement. We show how this protocol can be applied to implement interesting delay effects in the quantum regime, as well as in the classical limit. Our results elucidate the potential of the protocol as a promising route towards integrated quantum control systems on a chip.
Advanced-Retarded Differential Equations in Quantum Photonic Systems
Alvarez-Rodriguez, Unai; Perez-Leija, Armando; Egusquiza, Iñigo L.; Gräfe, Markus; Sanz, Mikel; Lamata, Lucas; Szameit, Alexander; Solano, Enrique
2017-01-01
We propose the realization of photonic circuits whose dynamics is governed by advanced-retarded differential equations. Beyond their mathematical interest, these photonic configurations enable the implementation of quantum feedback and feedforward without requiring any intermediate measurement. We show how this protocol can be applied to implement interesting delay effects in the quantum regime, as well as in the classical limit. Our results elucidate the potential of the protocol as a promising route towards integrated quantum control systems on a chip. PMID:28230090
Quantum interference in an electron-hole graphene ring system
Smirnov, D.; Schmidt, H.; Haug, R. J.
2013-12-04
Quantum interference is observed in a graphene ring system via the Aharonov Bohm effect. As graphene is a gapless semiconductor, this geometry allows to study the unique situation of quantum interference between electrons and holes in addition to the unipolar quantum interference. The period and amplitude of the observed Aharonov-Bohm oscillations are independent of the sign of the applied gate voltage showing the equivalence between unipolar and dipolar interference.
Quantum and classical operational complementarity for single systems
Luis, Alfredo
2005-07-15
We investigate duality relations between conjugate observables after measurements performed on a single realization of the system. The application of standard inference methods implies the existence of duality relations for single systems when using classical as well as quantum physics.
Causo, Maria Serena; Ciccotti, Giovanni; Montemayor, Daniel; Bonella, Sara; Coker, David F
2005-04-14
We generalize the linearized path integral approach to evaluate quantum time correlation functions for systems best described by a set of nuclear and electronic degrees of freedom, restricting ourselves to the adiabatic approximation. If the operators in the correlation function are nondiagonal in the electronic states, then this adiabatic linearized path integral approximation for the thermal averaged quantum dynamics presents interesting and distinctive features, which we derive and explore in this paper. The capability of these approximations to accurately reproduce the behavior of physical systems is demonstrated by calculating the diffusion constant for an excess electron in a metal-molten salt solution.
Spectral properties of a double-quantum-dot structure: A causal Green's function approach
NASA Astrophysics Data System (ADS)
You, J. Q.; Zheng, Hou-Zhi
1999-09-01
Spectral properties of a double quantum dot (QD) structure are studied by a causal Green's function (GF) approach. The double QD system is modeled by an Anderson-type Hamiltonian in which both the intra- and interdot Coulomb interactions are taken into account. The GF's are derived by an equation-of-motion method and the real-space renormalization-group technique. The numerical results show that the average occupation number of electrons in the QD exhibits staircase features and the local density of states depends appreciably on the electron occupation of the dot.
Hexagonal-shaped monolayer-bilayer quantum disks in graphene: A tight-binding approach
NASA Astrophysics Data System (ADS)
da Costa, D. R.; Zarenia, M.; Chaves, Andrey; Pereira, J. M.; Farias, G. A.; Peeters, F. M.
2016-07-01
Using the tight-binding approach, we investigate confined states in two different hybrid monolayer-bilayer systems: (i) a hexagonal monolayer area surrounded by bilayer graphene in the presence of a perpendicularly applied electric field and (ii) a hexagonal bilayer graphene dot surrounded by monolayer graphene. The dependence of the energy levels on dot size and external magnetic field is calculated. We find that the energy spectrum for quantum dots with zigzag edges consists of states inside the gap which range from dot-localized states, edge states, to mixed states coexisting together, whereas for dots with armchair edges, only dot-localized states are observed.
Adiabatic response and quantum thermoelectrics for ac-driven quantum systems
NASA Astrophysics Data System (ADS)
Ludovico, María Florencia; Battista, Francesca; von Oppen, Felix; Arrachea, Liliana
2016-02-01
We generalize the theory of thermoelectrics to include coherent electron systems under adiabatic ac driving, accounting for quantum pumping of charge and heat, as well as for the work exchanged between the electron system and driving potentials. We derive the relevant response coefficients in the adiabatic regime and show that they obey generalized Onsager reciprocity relations. We analyze the consequences of our generalized thermoelectric framework for quantum motors, generators, heat engines, and heat pumps, characterizing them in terms of efficiencies and figures of merit. We illustrate these concepts in a model for a quantum pump.
A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators.
Ochoa, Maicol A; Galperin, Michael; Ratner, Mark A
2014-11-12
We consider a projection operator approach to the non-equilibrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.
Control of quantum correlations in solid state systems
NASA Astrophysics Data System (ADS)
Berrada, K.
2015-11-01
The quantum correlations between two independent qubits immersed in an anisotropic and isotropic photonic band-gab (PBG) crystal have been studied without Born or Markovian approximation. We show that the amount of the entanglement and quantum discord between the qubits in the photonic crystal is greatly different from that of qubits in vacuum or that subjected to the usual non-Markovian reservoir. The results also show that, for PBG materials as environment, high values of quantum correlation trapping can be achieved and thus prevention of correlation sudden drop occurs, which seriously enhances the coherence and increase the amount of the correlations. Moreover, we show that the quantum correlations in the isotropic PBG are more easily preserved than that in the anisotropic PBG under the same condition. These features make the quantum systems in PBG materials as a good candidate for implementation of different schemes of quantum optics and information with high performance.
Perturbative approach to continuous-time quantum error correction
NASA Astrophysics Data System (ADS)
Ippoliti, Matteo; Mazza, Leonardo; Rizzi, Matteo; Giovannetti, Vittorio
2015-04-01
We present a discussion of the continuous-time quantum error correction introduced by J. P. Paz and W. H. Zurek [Proc. R. Soc. A 454, 355 (1998), 10.1098/rspa.1998.0165]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the three-qubit and five-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame features a short initial transient in which error correction is ineffective, followed by a slow decay of the information content consistent with the known facts about discrete-time error correction in the limit of fast operations. This behavior is explained in the two case studies through a geometric description of the continuous transformation of the state space induced by the combined action of noise and error correction.
Illustrating the quantum approach with an Earth magnetic field MRI
NASA Astrophysics Data System (ADS)
Pars Benli, Kami; Dillmann, Baudouin; Louelh, Ryma; Poirier-Quinot, Marie; Darrasse, Luc
2015-05-01
Teaching imaging of magnetic resonance (MR) today is still as challenging as it has always been, because it requires admitting that we cannot express fundamental questions of quantum mechanics with straightforward language or without using extensive theory. Here we allow students to face a real MR setup based on the Earth's magnetic field. We address the applied side of teaching MR using a device that is affordable and that proves to be sufficiently robust, at universities in Orsay, France, and San Sebastian, Spain, in experimental practicals at undergraduate and graduate levels. We specifically present some of the advantages of low field for measuring R2 relaxation rates, reaching a power of separation of 1.5 μmol on Mn(II) ions between two water bottles each of half a liter. Finally we propose key approaches for the lecturers to adopt when they are asked to pass from theoretical knowledge to teachable knowhow. The outcomes are fast calibration and the MR acquisition protocols, demonstrating the reproducibility of energy transfer during the saturation pulses, and the quantitative nature of MR, with water protons and a helium-3 sample.
Chimera: A hybrid numerical approach for isotropic loop quantum cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter; Gupt, Brajesh; Singh, Parampreet
2013-04-01
Loop quantum cosmology (LQC) is one approach to the resolution of the problem of singularities in classical cosmologies. The evolution of a cosmological model in LQC is governed by a set difference equations. In the isotropic cosmology (1+1 dimensions) the discretization is uniform in the spatial dimension. The stable simulation of a widely spread semi-classical state requires a very large computational domain and would therefore be computationally very expensive. In this talk we present an efficient hybrid numerical scheme based on the fact that the difference equations can be approximated by a set of partial differential equations (PDE's) in the limit of large spatial volume. We therefore introduce a hybrid scheme where we solve the LQC difference equations in the small volume and the PDE's in the large volume regime. By a simple change of coordinates in the large volume regime, we can significantly reduce the computational cost and explore regions of parameter space previously unachievable. We will describe the numerical implementation, present selected results and discuss the extension of the scheme to other models.
Alternative Hamiltonian description for quantum systems
Dubrovin, B.A. ); Marno, G.; Simoni, A. )
1990-06-20
The existence of time-invariant Kahler structures is analyzed in both Classical and Quantum Mechanics. In Quantum Mechanics, a family of such Kahler structures is found, in the finite-dimensional case it is proven that this family is complete.
Security proof for quantum key distribution using qudit systems
Sheridan, Lana; Scarani, Valerio
2010-09-15
We provide security bounds against coherent attacks for two families of quantum key distribution protocols that use d-dimensional quantum systems. In the asymptotic regime, both the secret key rate for fixed noise and the robustness to noise increase with d. The finite key corrections are found to be almost insensitive to d < or approx. 20.
Photon nonlinear mixing in subcarrier multiplexed quantum key distribution systems.
Capmany, José
2009-04-13
We provide, for the first time to our knowledge, an analysis of the influence of nonlinear photon mixing on the end to end quantum bit error rate (QBER) performance of subcarrier multiplexed quantum key distribution systems. The results show that negligible impact is to be expected for modulation indexes in the range of 2%.
Quantum-Classical Connection for Hydrogen Atom-Like Systems
ERIC Educational Resources Information Center
Syam, Debapriyo; Roy, Arup
2011-01-01
The Bohr-Sommerfeld quantum theory specifies the rules of quantization for circular and elliptical orbits for a one-electron hydrogen atom-like system. This article illustrates how a formula connecting the principal quantum number "n" and the length of the major axis of an elliptical orbit may be arrived at starting from the quantum…
Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis.
Subaşı, Y; Hu, B L
2012-01-01
In this paper we present a first-principles analysis of the nonequilibrium work distribution and the free energy difference of a quantum system interacting with a general environment (with arbitrary spectral density and for all temperatures) based on a well-understood microphysics (quantum Brownian motion) model under the conditions stipulated by the Jarzynski equality [Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and Crooks' fluctuation theorem [Crooks, Phys. Rev. E 60, 2721 (1999)] (in short, fluctuation theorems, FTs). We use the decoherent histories conceptual framework to explain how the notion of trajectories in a quantum system can be made viable and use the environment-induced decoherence scheme to assess the strength of noise that could provide sufficient decoherence to warrant the use of trajectories to define work in open quantum systems. From the solutions to the Langevin equation governing the stochastic dynamics of such systems we were able to produce formal expressions for these quantities entering in the FTs and from them prove explicitly the validity of the FTs at the high temperature limit. At low temperatures our general results would enable one to identify the range of parameters where FTs may not hold or need be expressed differently. We explain the relation between classical and quantum FTs and the advantage of this microphysics open-system approach over the phenomenological modeling and energy-level calculations for substitute closed quantum systems.
Measurements of nanoresonator-qubit interactions in a hybrid quantum electromechanical system.
Rouxinol, F; Hao, Y; Brito, F; Caldeira, A O; Irish, E K; LaHaye, M D
2016-09-09
Experiments to probe the basic quantum properties of motional degrees of freedom of mechanical systems have developed rapidly over the last decade. One promising approach is to use hybrid electromechanical systems incorporating superconducting qubits and microwave circuitry. However, a critical challenge facing the development of these systems is to achieve strong coupling between mechanics and qubits while simultaneously reducing coupling of both the qubit and mechanical mode to the environment. Here we report measurements of a qubit-coupled mechanical resonator system consisting of an ultra-high-frequency nanoresonator and a long coherence-time superconducting transmon qubit, embedded in a superconducting coplanar waveguide cavity. It is demonstrated that the nanoresonator and transmon have commensurate energies and transmon coherence times are one order of magnitude larger than for all previously reported qubit-coupled nanoresonators. Moreover, we show that numerical simulations of this new hybrid quantum system are in good agreement with spectroscopic measurements and suggest that the nanoresonator in our device resides at low thermal occupation number, near its ground state, acting as a dissipative bath seen by the qubit. We also outline how this system could soon be developed as a platform for implementing more advanced experiments with direct relevance to quantum information processing and quantum thermodynamics, including the study of nanoresonator quantum noise properties, reservoir engineering, and nanomechanical quantum state generation and detection.
Measurements of nanoresonator-qubit interactions in a hybrid quantum electromechanical system
NASA Astrophysics Data System (ADS)
Rouxinol, F.; Hao, Y.; Brito, F.; Caldeira, A. O.; Irish, E. K.; LaHaye, M. D.
2016-09-01
Experiments to probe the basic quantum properties of motional degrees of freedom of mechanical systems have developed rapidly over the last decade. One promising approach is to use hybrid electromechanical systems incorporating superconducting qubits and microwave circuitry. However, a critical challenge facing the development of these systems is to achieve strong coupling between mechanics and qubits while simultaneously reducing coupling of both the qubit and mechanical mode to the environment. Here we report measurements of a qubit-coupled mechanical resonator system consisting of an ultra-high-frequency nanoresonator and a long coherence-time superconducting transmon qubit, embedded in a superconducting coplanar waveguide cavity. It is demonstrated that the nanoresonator and transmon have commensurate energies and transmon coherence times are one order of magnitude larger than for all previously reported qubit-coupled nanoresonators. Moreover, we show that numerical simulations of this new hybrid quantum system are in good agreement with spectroscopic measurements and suggest that the nanoresonator in our device resides at low thermal occupation number, near its ground state, acting as a dissipative bath seen by the qubit. We also outline how this system could soon be developed as a platform for implementing more advanced experiments with direct relevance to quantum information processing and quantum thermodynamics, including the study of nanoresonator quantum noise properties, reservoir engineering, and nanomechanical quantum state generation and detection.
Quantum Mechanics Approaches to Drug Research in the Era of Structural Chemogenomics
Ilatovskiy, Andrey V.; Abagyan, Ruben; Kufareva, Irina
2014-01-01
The rapid growth of the available crystallographic information about proteins and binding pockets creates remarkable opportunities for enriching the drug research pipelines with computational prediction of novel protein-ligand interactions. While ab initio quantum mechanical approaches are known to provide unprecedented accuracy in structure-based binding energy calculations, they are limited to only small systems of dozens of atoms. In the structural chemogenomics era, it is critical that new approaches are developed that enable application of QM methodologies to non-covalent interactions in systems as large as protein-ligand complexes and conformational ensembles. This perspective highlights recent advances towards bridging the gap between high accuracy and high volume computations in drug research. PMID:25414519
NANONIS TRAMEA - A Quantum Transport Measurement System
NASA Astrophysics Data System (ADS)
Kampen, Thorsten; Thissen, Andreas; Schaff, Oliver; Pioda, Alessandro
Nanonis Tramea is a quantum leap with respect to increased speed for transport measurements taking research onto a new level. Measurements which took several hours in the past can now be done in minutes without compromising signal quality. Tramea uses its fast, high-resolution, high-precision and ultra-low-noise outputs and inputs to generate and acquire up to 20000 data points per second on 24 channels in parallel. This is not only up to 1000 x faster than typical measurement systems but it is also time deterministic with highest precision. Here, the time separation between points is constant so that artefacts caused by unequal point spacings in non-deterministic measurement systems are avoided. The emphasis here is the real-time relation. Tramea comes with a built-in interface which allows for control of the instruments' basic functions from any programming environment. For users requiring more functionality and higher speeds a full-featured LabVIEW-based programming interface or scripting module are available as add-on modules. Due to the modularity and flexibility of the hardware and software architecture of Tramea upgrades with standardized add-on modules are possible. Non-standard requests can still be handled by the various programming options.
Implementing quantum electrodynamics with ultracold atomic systems
NASA Astrophysics Data System (ADS)
Kasper, V.; Hebenstreit, F.; Jendrzejewski, F.; Oberthaler, M. K.; Berges, J.
2017-02-01
We discuss the experimental engineering of model systems for the description of quantum electrodynamics (QED) in one spatial dimension via a mixture of bosonic 23Na and fermionic 6Li atoms. The local gauge symmetry is realized in an optical superlattice, using heteronuclear boson–fermion spin-changing interactions which preserve the total spin in every local collision. We consider a large number of bosons residing in the coherent state of a Bose–Einstein condensate on each link between the fermion lattice sites, such that the behavior of lattice QED in the continuum limit can be recovered. The discussion about the range of possible experimental parameters builds, in particular, upon experiences with related setups of fermions interacting with coherent samples of bosonic atoms. We determine the atomic system’s parameters required for the description of fundamental QED processes, such as Schwinger pair production and string breaking. This is achieved by benchmark calculations of the atomic system and of QED itself using functional integral techniques. Our results demonstrate that the dynamics of one-dimensional QED may be realized with ultracold atoms using state-of-the-art experimental resources. The experimental setup proposed may provide a unique access to longstanding open questions for which classical computational methods are no longer applicable.
The transfer matrix approach to circular graphene quantum dots
NASA Astrophysics Data System (ADS)
Chau Nguyen, H.; Nguyen, Nhung T. T.; Nguyen, V. Lien
2016-07-01
We adapt the transfer matrix (T-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. Similar to one-dimensional problems, we show that the generalized T-matrix contains rich information about the physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasi-bound states of a circular graphene quantum dot and related quantities such as the local density of states and the scattering coefficients are all expressed exactly in terms of the T-matrix for the radial confinement potential. As an example, we use the developed formalism to analyse physical aspects of a graphene quantum dot induced by a trapezoidal radial potential. Among the obtained results, it is in particular suggested that the thermal fluctuations and electrostatic disorders may appear as an obstacle to controlling the valley polarization of Dirac electrons.
Quantum refrigeration cycles using spin-1/2 systems as the working substance.
He, Jizhou; Chen, Jincan; Hua, Ben
2002-03-01
The cycle model of a quantum refrigerator composed of two isothermal and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. Especially, the case at high temperatures is analyzed in detail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of the quantum refrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot refrigerator are derived simply.
Sum Rules, Classical and Quantum - A Pedagogical Approach
NASA Astrophysics Data System (ADS)
Karstens, William; Smith, David Y.
2014-03-01
Sum rules in the form of integrals over the response of a system to an external probe provide general analytical tools for both experiment and theory. For example, the celebrated f-sum rule gives a system's plasma frequency as an integral over the optical-dipole absorption spectrum regardless of the specific spectral distribution. Moreover, this rule underlies Smakula's equation for the number density of absorbers in a sample in terms of the area under their absorption bands. Commonly such rules are derived from quantum-mechanical commutation relations, but many are fundamentally classical (independent of ℏ) and so can be derived from more transparent mechanical models. We have exploited this to illustrate the fundamental role of inertia in the case of optical sum rules. Similar considerations apply to sum rules in many other branches of physics. Thus, the ``attenuation integral theorems'' of ac circuit theory reflect the ``inertial'' effect of Lenz's Law in inductors or the potential energy ``storage'' in capacitors. These considerations are closely related to the fact that the real and imaginary parts of a response function cannot be specified independently, a result that is encapsulated in the Kramers-Kronig relations. Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.
Certifying single-system steering for quantum-information processing
NASA Astrophysics Data System (ADS)
Li, Che-Ming; Chen, Yueh-Nan; Lambert, Neill; Chiu, Ching-Yi; Nori, Franco
2015-12-01
Einstein-Podolsky-Rosen (EPR) steering describes how different ensembles of quantum states can be remotely prepared by measuring one particle of an entangled pair. Here, we investigate quantum steering for single quantum d -dimensional systems (qudits) and devise efficient conditions to certify the steerability therein, which we find are applicable both to single-system steering and EPR steering. In the single-system case our steering conditions enable the unambiguous ruling out of generic classical means of mimicking steering. Ruling out "false-steering" scenarios has implications for securing channels against both cloning-based individual attack and coherent attacks when implementing quantum key distribution using qudits. We also show that these steering conditions also have applications in quantum computation, in that they can serve as an efficient criterion for the evaluation of quantum logic gates of arbitrary size. Finally, we describe how the nonlocal EPR variant of these conditions also function as tools for identifying faithful one-way quantum computation, secure entanglement-based quantum communication, and genuine multipartite EPR steering.
Shakib, Farnaz A; Hanna, Gabriel
2014-07-28
The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions is investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in the molecular dynamics with quantum transitions surface-hopping approach commonly used for simulating PCET reactions. Within this approach, the protonic and electronic coordinates are treated quantum mechanically and the solvent coordinate evolves classically on both single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Both concerted and sequential PCET reactions are studied in detail under various subsystem-bath coupling conditions and insights into the dynamical principles underlying PCET reactions are gained. Notably, an examination of the trajectories reveals that the system spends the majority of its time on the average of two coherently coupled adiabatic surfaces, during which a phase enters into the calculation of an observable. In general, the results of this paper demonstrate the applicability of QCLE-based surface-hopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.
Detecting quantum speedup in closed and open systems
NASA Astrophysics Data System (ADS)
Xu, Zhen-Yu
2016-07-01
We construct a general measure for detecting the quantum speedup in both closed and open systems. The speed measure is based on the changing rate of the position of quantum states on a manifold with appropriate monotone Riemannian metrics. Any increase in speed is a clear signature of dynamical speedup. To clarify the mechanisms for quantum speedup, we first introduce the concept of longitudinal and transverse types of speedup: the former stems from the time evolution process itself with fixed initial conditions, while the latter is a result of adjusting initial conditions. We then apply the proposed measure to several typical closed and open quantum systems, illustrating that quantum coherence (or entanglement) and the memory effect of the environment together can become resources for longitudinally or transversely accelerating dynamical evolution under specific conditions and assumptions.
Contextuality without nonlocality in a superconducting quantum system.
Jerger, Markus; Reshitnyk, Yarema; Oppliger, Markus; Potočnik, Anton; Mondal, Mintu; Wallraff, Andreas; Goodenough, Kenneth; Wehner, Stephanie; Juliusson, Kristinn; Langford, Nathan K; Fedorov, Arkady
2016-10-04
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell-Kochen-Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such models experimentally, since imperfections may introduce loopholes that enable a realist interpretation. Here we use a superconducting qutrit with deterministic, binary-outcome readouts to violate a noncontextuality inequality while addressing the detection, individual-existence and compatibility loopholes. This evidence of state-dependent contextuality also demonstrates the fitness of superconducting quantum circuits for fault-tolerant quantum computation in surface-code architectures, currently the most promising route to scalable quantum computing.
Contextuality without nonlocality in a superconducting quantum system
NASA Astrophysics Data System (ADS)
Jerger, Markus; Reshitnyk, Yarema; Oppliger, Markus; Potočnik, Anton; Mondal, Mintu; Wallraff, Andreas; Goodenough, Kenneth; Wehner, Stephanie; Juliusson, Kristinn; Langford, Nathan K.; Fedorov, Arkady
2016-10-01
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell-Kochen-Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such models experimentally, since imperfections may introduce loopholes that enable a realist interpretation. Here we use a superconducting qutrit with deterministic, binary-outcome readouts to violate a noncontextuality inequality while addressing the detection, individual-existence and compatibility loopholes. This evidence of state-dependent contextuality also demonstrates the fitness of superconducting quantum circuits for fault-tolerant quantum computation in surface-code architectures, currently the most promising route to scalable quantum computing.
Unconventional quantum critical points in systems of strongly interacting bosons
NASA Astrophysics Data System (ADS)
Zaleski, T. A.; Kopeć, T. K.
2014-09-01
Using the combined Bogoliubov method and the quantum rotor approach, we map the Bose-Hubbard Hamiltonian of strongly interacting bosons onto U(1) phase action. By unraveling consequences of the nontrivial topology of the U(1) gauge group and the associated ground state degeneracy we found a close kinship of the zero-temperature divergence of the compressibility and the topological susceptibility at degeneracy points, which marks a novel quantum criticality governed by topological features rather than the Landau principle of the symmetry breaking. We argue that the existence of this new type of the criticality may be instrumental in explaining unconventional quantum critical points observed in superconducting cuprates.
Hemmatiyan, S; Rahimi Movassagh, M; Ghassemi, N; Kargarian, M; Rezakhani, A T; Langari, A
2015-04-22
The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the 'perturbative continuous unitary transformations' approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.
Epilogue: Systems Approaches and Systems Practice
NASA Astrophysics Data System (ADS)
Reynolds, Martin; Holwell, Sue
Each of the five systems approaches discussed in this volume: system dynamics (SD), the viable systems model (VSM), strategic options development and analysis (SODA), soft systems methodology (SSM) and critical systems heuristics (CSH) has a pedigree. Not in the sense of the sometimes absurd spectacle of animals paraded at dog shows. Rather, their pedigree derives from their systems foundations, their capacity to evolve and their flexibility in use. None of the five approaches has developed out of use in restricted and controlled contexts of either low or high levels of complicatedness. Neither has any one of them evolved as a consequence of being applied only to situations with either presumed stakeholder agreement on purpose, or courteous disagreement amongst stakeholders, or stakeholder coercion. The compilation is not a celebration of abstract ‘methodologies', but of theoretically robust approaches that have a genuine pedigree in practice.
Mascarenhas, E.; Marques, B.; Santos, M. Franca; Cavalcanti, D.; Cunha, M. Terra
2010-03-15
We study how to protect quantum information in quantum systems subjected to local dissipation. We show that combining the use of three-level systems, environment monitoring, and local feedback can fully and deterministically protect any available quantum information, including entanglement initially shared by different parties. These results can represent a gain in resources and/or distances in quantum communication protocols such as quantum repeaters and teleportation as well as time for quantum memories. Finally, we show that monitoring local environments physically implements the optimum singlet conversion protocol, which is essential for classical entanglement percolation.
Effective quantum dynamics of interacting systems with inhomogeneous coupling
Lopez, C. E.; Retamal, J. C.; Christ, H.; Solano, E.
2007-03-15
We study the quantum dynamics of a single mode (particle) interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space, where the dynamics takes place. Two relevant examples are given: the inhomogeneous Tavis-Cummings model (e.g., N atomic qubits coupled to a single cavity mode, or to a motional mode in trapped ions) and the inhomogeneous coupling of an electron spin to N nuclear spins in a quantum dot.
Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach.
Antipov, Sergey V; Ye, Ziyu; Ananth, Nandini
2015-05-14
We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.
Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach
Antipov, Sergey V.; Ye, Ziyu; Ananth, Nandini
2015-05-14
We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.
Nano-optics with single quantum systems.
Hecht, Bert
2004-04-15
This paper reviews the recent progress in using single quantum systems, here mainly single fluorescent molecules, as local probes for nano-optical field distributions. We start by discussing the role of the absorption cross-section for the spatial resolution attainable in such experiments and its behaviour for different environmental conditions. It is shown that the spatial distribution of field components in a high-numerical aperture laser focus can be mapped with high precision using single fluorescent molecules embedded in a thin polymer film on glass. With this proof-of-principle experiment as a starting point, the possibility of mapping strongly confined and enhanced nano-optical fields close to material structures, e.g. sharp metal tips, is discussed. The mapping of the spatial distribution of the enhanced field at an etched gold tip using a single molecule is presented as an example. Energy transfer effects and quenching are identified as possible artefacts in this context. Finally, it is demonstrated that the local quenching at a sharp metal structure nevertheless can be exploited as a novel contrast mechanism for ultrahigh-resolution optical microscopy with single-molecule sensitivity.
The Dalton quantum chemistry program system
Aidas, Kestutis; Angeli, Celestino; Bak, Keld L; Bakken, Vebjørn; Bast, Radovan; Boman, Linus; Christiansen, Ove; Cimiraglia, Renzo; Coriani, Sonia; Dahle, Pål; Dalskov, Erik K; Ekström, Ulf; Enevoldsen, Thomas; Eriksen, Janus J; Ettenhuber, Patrick; Fernández, Berta; Ferrighi, Lara; Fliegl, Heike; Frediani, Luca; Hald, Kasper; Halkier, Asger; Hättig, Christof; Heiberg, Hanne; Helgaker, Trygve; Hennum, Alf Christian; Hettema, Hinne; Hjertenæs, Eirik; Høst, Stinne; Høyvik, Ida-Marie; Iozzi, Maria Francesca; Jansík, Branislav; Jensen, Hans Jørgen Aa; Jonsson, Dan; Jørgensen, Poul; Kauczor, Joanna; Kirpekar, Sheela; Kjærgaard, Thomas; Klopper, Wim; Knecht, Stefan; Kobayashi, Rika; Koch, Henrik; Kongsted, Jacob; Krapp, Andreas; Kristensen, Kasper; Ligabue, Andrea; Lutnæs, Ola B; Melo, Juan I; Mikkelsen, Kurt V; Myhre, Rolf H; Neiss, Christian; Nielsen, Christian B; Norman, Patrick; Olsen, Jeppe; Olsen, Jógvan Magnus H; Osted, Anders; Packer, Martin J; Pawlowski, Filip; Pedersen, Thomas B; Provasi, Patricio F; Reine, Simen; Rinkevicius, Zilvinas; Ruden, Torgeir A; Ruud, Kenneth; Rybkin, Vladimir V; Sałek, Pawel; Samson, Claire C M; de Merás, Alfredo Sánchez; Saue, Trond; Sauer, Stephan P A; Schimmelpfennig, Bernd; Sneskov, Kristian; Steindal, Arnfinn H; Sylvester-Hvid, Kristian O; Taylor, Peter R; Teale, Andrew M; Tellgren, Erik I; Tew, David P; Thorvaldsen, Andreas J; Thøgersen, Lea; Vahtras, Olav; Watson, Mark A; Wilson, David J D; Ziolkowski, Marcin; Ågren, Hans
2014-01-01
Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self-consistent-field, Møller–Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms. PMID:25309629
The Dalton quantum chemistry program system.
Aidas, Kestutis; Angeli, Celestino; Bak, Keld L; Bakken, Vebjørn; Bast, Radovan; Boman, Linus; Christiansen, Ove; Cimiraglia, Renzo; Coriani, Sonia; Dahle, Pål; Dalskov, Erik K; Ekström, Ulf; Enevoldsen, Thomas; Eriksen, Janus J; Ettenhuber, Patrick; Fernández, Berta; Ferrighi, Lara; Fliegl, Heike; Frediani, Luca; Hald, Kasper; Halkier, Asger; Hättig, Christof; Heiberg, Hanne; Helgaker, Trygve; Hennum, Alf Christian; Hettema, Hinne; Hjertenæs, Eirik; Høst, Stinne; Høyvik, Ida-Marie; Iozzi, Maria Francesca; Jansík, Branislav; Jensen, Hans Jørgen Aa; Jonsson, Dan; Jørgensen, Poul; Kauczor, Joanna; Kirpekar, Sheela; Kjærgaard, Thomas; Klopper, Wim; Knecht, Stefan; Kobayashi, Rika; Koch, Henrik; Kongsted, Jacob; Krapp, Andreas; Kristensen, Kasper; Ligabue, Andrea; Lutnæs, Ola B; Melo, Juan I; Mikkelsen, Kurt V; Myhre, Rolf H; Neiss, Christian; Nielsen, Christian B; Norman, Patrick; Olsen, Jeppe; Olsen, Jógvan Magnus H; Osted, Anders; Packer, Martin J; Pawlowski, Filip; Pedersen, Thomas B; Provasi, Patricio F; Reine, Simen; Rinkevicius, Zilvinas; Ruden, Torgeir A; Ruud, Kenneth; Rybkin, Vladimir V; Sałek, Pawel; Samson, Claire C M; de Merás, Alfredo Sánchez; Saue, Trond; Sauer, Stephan P A; Schimmelpfennig, Bernd; Sneskov, Kristian; Steindal, Arnfinn H; Sylvester-Hvid, Kristian O; Taylor, Peter R; Teale, Andrew M; Tellgren, Erik I; Tew, David P; Thorvaldsen, Andreas J; Thøgersen, Lea; Vahtras, Olav; Watson, Mark A; Wilson, David J D; Ziolkowski, Marcin; Agren, Hans
2014-05-01
Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.
NASA Astrophysics Data System (ADS)
Lidar, Daniel A.; Brun, Todd A.
2013-09-01
Prologue; Preface; Part I. Background: 1. Introduction to decoherence and noise in open quantum systems Daniel Lidar and Todd Brun; 2. Introduction to quantum error correction Dave Bacon; 3. Introduction to decoherence-free subspaces and noiseless subsystems Daniel Lidar; 4. Introduction to quantum dynamical decoupling Lorenza Viola; 5. Introduction to quantum fault tolerance Panos Aliferis; Part II. Generalized Approaches to Quantum Error Correction: 6. Operator quantum error correction David Kribs and David Poulin; 7. Entanglement-assisted quantum error-correcting codes Todd Brun and Min-Hsiu Hsieh; 8. Continuous-time quantum error correction Ognyan Oreshkov; Part III. Advanced Quantum Codes: 9. Quantum convolutional codes Mark Wilde; 10. Non-additive quantum codes Markus Grassl and Martin Rötteler; 11. Iterative quantum coding systems David Poulin; 12. Algebraic quantum coding theory Andreas Klappenecker; 13. Optimization-based quantum error correction Andrew Fletcher; Part IV. Advanced Dynamical Decoupling: 14. High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu; 15. Combinatorial approaches to dynamical decoupling Martin Rötteler and Pawel Wocjan; Part V. Alternative Quantum Computation Approaches: 16. Holonomic quantum computation Paolo Zanardi; 17. Fault tolerance for holonomic quantum computation Ognyan Oreshkov, Todd Brun and Daniel Lidar; 18. Fault tolerant measurement-based quantum computing Debbie Leung; Part VI. Topological Methods: 19. Topological codes Héctor Bombín; 20. Fault tolerant topological cluster state quantum computing Austin Fowler and Kovid Goyal; Part VII. Applications and Implementations: 21. Experimental quantum error correction Dave Bacon; 22. Experimental dynamical decoupling Lorenza Viola; 23. Architectures Jacob Taylor; 24. Error correction in quantum communication Mark Wilde; Part VIII. Critical Evaluation of Fault Tolerance: 25. Hamiltonian methods in QEC and fault tolerance Eduardo Novais, Eduardo Mucciolo and
Valence atom with bohmian quantum potential: the golden ratio approach
2012-01-01
Background The alternative quantum mechanical description of total energy given by Bohmian theory was merged with the concept of the golden ratio and its appearance as the Heisenberg imbalance to provide a new density-based description of the valence atomic state and reactivity charge with the aim of clarifying their features with respect to the so-called DFT ground state and critical charge, respectively. Results The results, based on the so-called double variational algorithm for chemical spaces of reactivity, are fundamental and, among other issues regarding chemical bonding, solve the existing paradox of using a cubic parabola to describe a quadratic charge dependency. Conclusions Overall, the paper provides a qualitative-quantitative explanation of chemical reactivity based on more than half of an electronic pair in bonding, and provide new, more realistic values for the so-called “universal” electronegativity and chemical hardness of atomic systems engaged in reactivity (analogous to the atoms-in-molecules framework). PMID:23146157
Nonresonant interaction of ultrashort electromagnetic pulses with multilevel quantum systems
NASA Technical Reports Server (NTRS)
Belenov, E.; Isakov, V.; Nazarkin, A.
1994-01-01
Some features of the excitation of multilevel quantum systems under the action of electromagnetic pulses which are shorter than the inverse frequency of interlevel transitions are considered. It is shown that the interaction is characterized by a specific type of selectivity which is not connected with the resonant absorption of radiation. The simplest three-level model displays the inverse population of upper levels. The effect of an ultrashort laser pulse on a multilevel molecule was regarded as an instant reception of the oscillation velocity by the oscillator and this approach showed an effective excitation and dissociation of the molecule. The estimations testify to the fact that these effects can be observed using modern femtosecond lasers.
Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Freytes, H.; Domenech, G.; de Ronde, C.
2014-12-01
In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
Who is afraid of POV measures? Unified approach to quantum phase observables
Busch, P. |; Grabowski, M.; Lahti, P.J.
1995-01-01
It is shown that introducing phase observables as shift-covariant positive-operator-valued measures yields a coherent unification of various conceptually different approaches to the phase in quantum theory. {copyright} 1995 Academic Press, Inc.
Evolution of Quantum Systems from Microscopic to Macroscopic Scales
Ovchinnikov, Serguei Yurevich; Macek, Joseph H; Sternberg, James; Lee, Teck G; Schultz, David Robert
2009-01-01
Even though the static properties of quantum systems have been known since the early days of quantum mechanics, accurate simulation of dynamical break-up or ionization remains a theoretical challenge despite our complete knowledge of the relevant interactions. The simulations are challenging because of highly oscillatory exponential phase factors in the electronic wave function and the infinitesimally small values of the continuum components of electronic probability density at large times after the collision. The approach we recently developed, so-called, the regularized time-dependent Schrodinger equation method, has addressed these difficulties by removing the diverging phase factors and transforming the time-dependent Schrodinger equation to an expanding space. The evolution of the electronic wave function was followed to internuclear distances of R = 1000,000 a.u. or 5 microns, which is of the order of the diameter of a human hair. Our calculations also revealed unexpected presence of free vortices in the electronic wave function. The discovered vortices also bring new light on the mechanism of transferring of the angular momentum from an external to internal motion. The connection between the observable momentum distribution and the time-dependent wave function implies that vortices in the wave function at large times are imaged in the momentum distribution.
Evolution of Quantum Systems from Microscopic to Macroscopic Scales
NASA Astrophysics Data System (ADS)
Ovchinnikov, Sergey Y.; Macek, Joseph H.; Sternberg, James S.; Lee, Teck-Ghee; Schultz, David R.
2009-03-01
Even though the static properties of quantum systems have been known since the early days of quantum mechanics, accurate simulation of the dynamical break-up or ionization remains a theoretical challenge despite our complete knowledge of the relevant interactions. Simulations are challenging because of highly oscillatory exponential phase factors in the electronic wave function and the infinitesimally small values of the continuum components of electronic probability density at large times after the collision. The approach we recently developed, the regularized time-dependent Schrödinger equation method, has addressed these difficulties by removing the diverging phase factors and transforming the time-dependent Schrödinger equation to an expanding space. The evolution of the electronic wave function was followed to internuclear distances of R = 100,000 a.u. or 5 microns, which is of the order of the diameter of a human hair. Our calculations also revealed unexpected presence of free vortices in the electronic wave function. The discovered vortices also bring new light on the mechanism of transferring of the angular momentum from an external to internal motion. The connection between the observable momentum distribution and the time-dependent wave function implies that vortices in the wave function at large times are imaged in the momentum distribution.
Evolution of Quantum Systems from Microscopic to Macroscopic Scales
Ovchinnikov, Sergey Y.; Macek, Joseph H.; Sternberg, James S.; Lee, Teck-Ghee; Schultz, David R.
2009-03-10
Even though the static properties of quantum systems have been known since the early days of quantum mechanics, accurate simulation of the dynamical break-up or ionization remains a theoretical challenge despite our complete knowledge of the relevant interactions. Simulations are challenging because of highly oscillatory exponential phase factors in the electronic wave function and the infinitesimally small values of the continuum components of electronic probability density at large times after the collision. The approach we recently developed, the regularized time-dependent Schroedinger equation method, has addressed these difficulties by removing the diverging phase factors and transforming the time-dependent Schroedinger equation to an expanding space. The evolution of the electronic wave function was followed to internuclear distances of R = 100,000 a.u. or 5 microns, which is of the order of the diameter of a human hair. Our calculations also revealed unexpected presence of free vortices in the electronic wave function. The discovered vortices also bring new light on the mechanism of transferring of the angular momentum from an external to internal motion. The connection between the observable momentum distribution and the time-dependent wave function implies that vortices in the wave function at large times are imaged in the momentum distribution.
Quantum modeling of nonlinear dynamics of stock prices: Bohmian approach
NASA Astrophysics Data System (ADS)
Choustova, O.
2007-08-01
We use quantum mechanical methods to model the price dynamics in the financial market mathematically. We propose describing behavioral financial factors using the pilot-wave (Bohmian) model of quantum mechanics. The real price trajectories are determined (via the financial analogue of the second Newton law) by two financial potentials: the classical-like potential V (q) (“hard” market conditions) and the quantumlike potential U(q) (behavioral market conditions).
Quantum Correlations, Separability, and Quantum Coherence Length in Equilibrium Many-Body Systems
NASA Astrophysics Data System (ADS)
Malpetti, Daniele; Roscilde, Tommaso
2016-09-01
Nonlocality is a fundamental trait of quantum many-body systems, both at the level of pure states, as well as at the level of mixed states. Because of nonlocality, mixed states of any two subsystems are correlated in a stronger way than what can be accounted for by considering the correlated probabilities of occupying some microstates. In the case of equilibrium mixed states, we explicitly build two-point quantum correlation functions, which capture the specific, superior correlations of quantum systems at finite temperature, and which are directly accessible to experiments when correlating measurable properties. When nonvanishing, these correlation functions rule out a precise form of separability of the equilibrium state. In particular, we show numerically that quantum correlation functions generically exhibit a finite quantum coherence length, dictating the characteristic distance over which degrees of freedom cannot be considered as separable. This coherence length is completely disconnected from the correlation length of the system—as it remains finite even when the correlation length of the system diverges at finite temperature—and it unveils the unique spatial structure of quantum correlations.
Baladrón, Carlos; Khrennikov, Andrei
2016-12-01
The similarities between biological and physical systems as respectively defined in quantum information biology (QIB) and in a Darwinian approach to quantum mechanics (DAQM) have been analysed. In both theories the processing of information is a central feature characterising the systems. The analysis highlights a mutual support on the thesis contended by each theory. On the one hand, DAQM provides a physical basis that might explain the key role played by quantum information at the macroscopic level for bio-systems in QIB. On the other hand, QIB offers the possibility, acting as a macroscopic testing ground, to analyse the emergence of quantumness from classicality in the terms held by DAQM. As an added result of the comparison, a tentative definition of quantum information in terms of classical information flows has been proposed. The quantum formalism would appear from this comparative analysis between QIB and DAQM as an optimal information scheme that would maximise the stability of biological and physical systems at any scale.
Information Theory Density Matrix for a Simple Quantum System.
ERIC Educational Resources Information Center
Titus, William J.
1979-01-01
Derives the density matrix that best describes, according to information theory, a one-dimensional single particle quantum system when the only information available is the values for the linear and quadratic position-momentum moments. (Author/GA)
Phases and phase transitions in disordered quantum systems
NASA Astrophysics Data System (ADS)
Vojta, Thomas
2013-08-01
These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase transitions. We then derive criteria governing under what conditions spatial disorder or randomness can change the properties of a phase transition. After introducing the strong-disorder renormalization group method, we discuss in detail some of the exotic phenomena arising at phase transitions in disordered quantum systems. These include infinite-randomness criticality, rare regions and quantum Griffiths singularities, as well as the smearing of phase transitions. We also present a number of experimental examples.
Quantum-optical nonlinearities induced by Rydberg-Rydberg interactions: A perturbative approach
NASA Astrophysics Data System (ADS)
Grankin, A.; Brion, E.; Bimbard, E.; Boddeda, R.; Usmani, I.; Ourjoumtsev, A.; Grangier, P.
2015-10-01
In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical nonlinearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant thus generalizing our previous results. We can thus investigate quantitatively new features associated with the resonant behavior of the system. We also propose an effective nonlinear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system.
Modelling Systems of Classical/Quantum Identical Particles by Focusing on Algorithms
ERIC Educational Resources Information Center
Guastella, Ivan; Fazio, Claudio; Sperandeo-Mineo, Rosa Maria
2012-01-01
A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…
Quantum Brayton cycle with coupled systems as working substance.
Huang, X L; Wang, L C; Yi, X X
2013-01-01
We explore the quantum version of the Brayton cycle with a composite system as the working substance. The actual Brayton cycle consists of two adiabatic and two isobaric processes. Two pressures can be defined in our isobaric process; one corresponds to the external magnetic field (characterized by F(x)) exerted on the system, while the other corresponds to the coupling constant between the subsystems (characterized by F(y)). As a consequence, we can define two types of quantum Brayton cycle for the composite system. We find that the subsystem experiences a quantum Brayton cycle in one quantum Brayton cycle (characterized by F(x)), whereas the subsystem's cycle is quantum Otto cycle in another Brayton cycle (characterized by F(y)). The efficiency for the composite system equals to that for the subsystem in both cases, but the work done by the total system is usually larger than the sum of the work done by the two subsystems. The other interesting finding is that for the cycle characterized by F(y), the subsystem can be a refrigerator, while the total system is a heat engine. The result in this paper can be generalized to a quantum Brayton cycle with a general coupled system as the working substance.
Geodesic paths and topological charges in quantum systems
NASA Astrophysics Data System (ADS)
Grangeiro Souza Barbosa Lima, Tiago Aecio
This dissertation focuses on one question: how should one drive an experimentally prepared state of a generic quantum system into a different target-state, simultaneously minimizing energy dissipation and maximizing the fidelity between the target and evolved-states? We develop optimal adiabatic driving protocols for general quantum systems, and show that these are geodesic paths. Geometric ideas have always played a fundamental role in the understanding and unification of physical phenomena, and the recent discovery of topological insulators has drawn great interest to topology from the field of condensed matter physics. Here, we discuss the quantum geometric tensor, a mathematical object that encodes geometrical and topological properties of a quantum system. It is related to the fidelity susceptibility (an important quantity regarding quantum phase transitions) and to the Berry curvature, which enables topological characterization through Berry phases. A refined understanding of the interplay between geometry and topology in quantum mechanics is of direct relevance to several emergent technologies, such as quantum computers, quantum cryptography, and quantum sensors. As a demonstration of how powerful geometric and topological ideas can become when combined, we present the results of an experiment that we recently proposed. This experimental work was done at the Google Quantum Lab, where researchers were able to visualize the topological nature of a two-qubit system in sharp detail, a startling contrast with earlier methods. To achieve this feat, the optimal protocols described in this dissertation were used, allowing for a great improvement on the experimental apparatus, without the need for technical engineering advances. Expanding the existing literature on the quantum geometric tensor using notions from differential geometry and topology, we build on the subject nowadays known as quantum geometry. We discuss how slowly changing a parameter of a quantum
Genuine quantum and classical correlations in multipartite systems.
Giorgi, Gian Luca; Bellomo, Bruno; Galve, Fernando; Zambrini, Roberta
2011-11-04
Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.
Entropies and correlations in classical and quantum systems
NASA Astrophysics Data System (ADS)
Man'ko, Margarita A.; Man'ko, Vladimir I.; Marmo, Giuseppe
2016-09-01
We present a review of entropy properties for classical and quantum systems including Shannon entropy, von Neumann entropy, Rényi entropy, and Tsallis entropy. We discuss known and new entropic and information inequalities for classical and quantum systems, both composite and noncomposite. We demonstrate matrix inequalities associated with the entropic subadditivity and strong subadditivity conditions and give a new inequality for matrix elements of unitary matrices.
Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Auffèves, Alexia; Grangier, Philippe
2016-02-01
In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.
Neutron interferometry for precise characterization of quantum systems
NASA Astrophysics Data System (ADS)
Sarenac, Dusan; Shahi, Chandra; Mineeva, Taisiya; Wood, Christopher J.; Huber, Michael G.; Arif, Muhammad; Clark, Charles W.; Cory, David G.; Pushin, Dmitry A.
Neutron interferometry (NI) is among the most precise techniques used to test the postulates of quantum mechanics. It has demonstrated coherent spinor rotation and superposition, gravitationally induced quantum interference, the Aharonov-Casher effect, violation of a Bell-like inequality, and generation of a single-neutron entangled state. As massive, penetrating and neutral particles neutrons now provide unique capabilities in classical imaging applications that we seek to extend to the quantum domain. We present recent results on NI measurements of quantum discord in a bipartite quantum system and neutron orbital angular momentum multiplexing, and review progress on our commissioning of a decoherence-free-subspace NI user facility at the NIST Center for Neutron Research. Supported in part by CERC, CIFAR, NSERC and CREATE.
Godsi, Oded; Peskin, Uri; Collins, Michael A.
2010-03-28
A quantum sampling algorithm for the interpolation of diabatic potential energy matrices by the Grow method is introduced. The new procedure benefits from penetration of the wave packet into classically forbidden regions, and the accurate quantum mechanical description of nonadiabatic transitions. The increased complexity associated with running quantum dynamics is reduced by using approximate low order expansions of the nuclear wave function within a Multi-configuration time-dependent Hartree scheme during the Grow process. The sampling algorithm is formulated and applied for three representative test cases, demonstrating the recovery of analytic potentials by the interpolated ones, and the convergence of a dynamic observable.
Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.
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.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
NASA Astrophysics Data System (ADS)
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
Resonant electronic excitation energy transfer by Dexter mechanism in the quantum dot system
NASA Astrophysics Data System (ADS)
Samosvat, D. M.; Chikalova-Luzina, O. P.; Vyatkin, V. M.; Zegrya, G. G.
2016-11-01
In present work the energy transfer between quantum dots by the exchange (Dexter) mechanism is analysed. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same compound A3B5 and embedded in the matrix of other material creating potential barriers for electron and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found using the Kane model that provides the most adequate description spectra of semiconductors A3B5. Numerical calculations show that the rate of the energy transfer by Dexter mechanism is comparable to the rate of the energy transfer by electrostatic mechanism at the distances approaching to the contact ones.
Controllable multiple-quantum transitions in a T-shaped small quantum dot-ring system
NASA Astrophysics Data System (ADS)
Chen, Xiongwen; Chen, Baoju; Song, Kehui; Zhou, Guanghui
2016-05-01
Based on the tight-binding model and the slave boson mean field approximation, we investigate the electron transport properties in a small quantum dot (QD)-ring system. Namely, a strongly correlated QD not only attaches directly to two normal metallic electrodes, but also forms a magnetic control Aharonov-Bohm quantum ring with a few noninteracting QDs. We show that the parity effect, the Kondo effect, and the multiple Fano effects coexist in our system. Moreover, the parities, defined by the odd- and even-numbered energy levels in this system, can be switched by adjusting magnetic flux phase ϕ located at the center of the quantum ring, which induces multiple controllable Fano-interference energy pathways. Therefore, the constructive and destructive multi-Fano interference transition, the Kondo and Fano resonance transition at the Fermi level, the Fano resonance and ani-resonance transition are realized in the even parity system. They can also be observed in the odd parity system when one adjusts the phase ϕ and the gate voltage Vg applied to the noninteracting QDs. The multi-quantum transitions determine some interesting transport properties such as the current switch and its multi-flatsteps, the differential conductance switch at zero bias voltage and its oscillation or quantization at the low bias voltage. These results may be useful for the observation of multiple quantum effect interplays experimentally and the design of controllable QD-based device.
Mixed quantum-classical versus full quantum dynamics: Coupled quasiparticle-oscillator system
NASA Astrophysics Data System (ADS)
Schanz, Holger; Esser, Bernd
1997-05-01
The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.
Quantum bio-nanosensors based on quantum dot-metallic nanoparticle systems
NASA Astrophysics Data System (ADS)
Sadeghi, S. M.
2013-03-01
When metallic nanoparticles are put in the vicinity of semiconductor quantum dots and driven by a coherent light source, their intrinsic plasmonic fields can be replaced with a new type of fields (coherent-plasmonic fields). These fields are generated via coherent coupling of excitons in quantum dots and localized surface plasmon resonances (LSPRs). We show the coherent-plasmonic field of a metallic nanoparticle can lead to a significantly larger field enhancement than that caused by its LSPR. Utilizing this, we investigate how such a coherent field enhancement can improve the sensitivities plasmonic nanosensors for detection single biological molecules. The results demonstrate application of quantum coherence in quantum dot-metallic nanoparticle systems for chemical and biological sensing applications.