Combinatorial Approach to Modeling Quantum Systems
NASA Astrophysics Data System (ADS)
Kornyak, Vladimir V.
2016-02-01
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers and unitarity in the formalism of the quantum mechanics. In our approach, the quantum behavior can be explained by the fundamental impossibility to trace the identity of the indistinguishable objects in their evolution. Any observation only provides information about the invariant relations between such objects. The trajectory of a quantum system is a sequence of unitary evolutions interspersed with observations—non-unitary projections. We suggest a scheme to construct combinatorial models of quantum evolution. The principle of selection of the most likely trajectories in such models via the large numbers approximation leads in the continuum limit to the principle of least action with the appropriate Lagrangians and deterministic evolution equations
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
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.
A perturbative probabilistic approach to quantum many-body systems
NASA Astrophysics Data System (ADS)
Di Stefano, Andrea; Ostilli, Massimo; Presilla, Carlo
2013-04-01
In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the potential and hopping (amplitude and phase) values recorded during an infinitely lengthy evolution. We introduce a perturbative expansion of this probability distribution which conserves, at any order, a multinomial-like structure, typical of uncorrelated systems, but includes, order by order, the statistical correlations provided by the cumulant expansion. The proposed perturbative scheme is successfully tested in the case of pseudo-spin 1/2 hard-core boson Hubbard models also when affected by a phase problem due to an applied magnetic field.
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.
Merz, Kenneth M
2014-09-16
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
On the approach to thermal equilibrium of macroscopic quantum systems
Goldstein, Sheldon; Tumulka, Roderich
2011-03-24
In joint work with J. L. Lebowitz, C. Mastrodonato, and N. Zanghi[2, 3, 4], we considered an isolated, macroscopic quantum system. Let H be a micro-canonical 'energy shell', i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E+{delta}E. The thermal equilibrium macro-state at energy E corresponds to a subspace H{sub eq} of H such that dimHeq/dimH is close to 1. We say that a system with state vector {psi}{epsilon}H is in thermal equilibrium if {psi} is 'close' to H{sub eq}. We argue that for 'typical' Hamiltonians, all initial state vectors {psi}{sub 0} evolve in such a way that {psi}{sub t} is in thermal equilibrium for most times t. This is closely related to von Neumann's quantum ergodic theorem of 1929.
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
Entanglement transfer from electrons to photons in quantum dots: an open quantum system approach.
Budich, Jan C; Trauzettel, Björn
2010-07-01
We investigate entanglement transfer from a system of two spin-entangled electron-hole pairs, each placed in a separate single mode cavity, to the photons emitted due to cavity leakage. Dipole selection rules and a splitting between the light hole and the heavy hole subbands are the crucial ingredients establishing a one-to-one correspondence between electron spins and circular photon polarizations. To account for the measurement of the photons as well as dephasing effects, we choose a stochastic Schrödinger equation and a conditional master equation approach, respectively. The influence of interactions with the environment as well as asymmetries in the coherent couplings on the photon entanglement is analysed for two concrete measurement schemes. The first one is designed to violate the Clauser-Horne-Shimony-Holt (CHSH) inequality, while the second one employs the visibility of interference fringes to prove the entanglement of the photons. Because of the spatial separation of the entangled electronic system over two quantum dots, a successful verification of entangled photons emitted by this system would imply the detection of nonlocal spin entanglement of massive particles in a solid state structure. PMID:20571188
Exact analysis of the response of quantum systems to two-photons using a QSDE approach
NASA Astrophysics Data System (ADS)
Pan, Yu; Dong, Daoyi; Zhang, Guofeng
2016-03-01
We introduce the quantum stochastic differential equation (QSDE) approach to exactly analyze the response of quantum systems to a continuous-mode two-photon input. The QSDE description of the two-photon process allows us to integrate the input-output analysis with the quantum network theory, and so the analytical computability of the output state of a general quantum system can be addressed within this framework. We show that the time-domain two-photon output states can be exactly calculated for a large class of quantum systems including passive linear networks, optomechanical oscillators and two-level emitter in waveguide systems. In particular, we propose to utilise the results for the exact simulation of the stimulated emission as well as the study of the scattering of two-mode photon wave packets.
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. PMID:27341253
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.
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. PMID:27627265
Thermofield-based chain-mapping approach for open quantum systems
NASA Astrophysics Data System (ADS)
de Vega, Inés; Bañuls, Mari-Carmen
2015-11-01
We consider a thermofield approach to analyze the evolution of an open quantum system coupled to an environment at finite temperature. In this approach, the finite-temperature environment is exactly mapped onto two virtual environments at zero temperature. These two environments are then unitarily transformed into two different chains of oscillators, leading to a one-dimensional structure that can be numerically studied using tensor network techniques. Compared to previous approaches using a single chain mapping, our strategy offers the advantage of an exact description of the initial state at arbitrary temperatures, which results in a gain in computational efficiency and a reduced truncation error.
Operational approach to fluctuations of thermodynamic variables in finite quantum systems
Jahnke, T.; Lanery, S.; Mahler, G.
2011-01-15
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 {Delta}T{sup 2}=(k{sub B}T{sup 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.
Time Scales in the Approach to Equilibrium of Macroscopic Quantum Systems
NASA Astrophysics Data System (ADS)
Goldstein, Sheldon; Hara, Takashi; Tasaki, Hal
2013-10-01
We prove two theorems concerning the time evolution in general isolated quantum systems. The theorems are relevant to the issue of the time scale in the approach to equilibrium. The first theorem shows that there can be pathological situations in which the relaxation takes an extraordinarily long time, while the second theorem shows that one can always choose an equilibrium subspace, the relaxation to which requires only a short time for any initial state.
Quantum chaos: An entropy approach
NASA Astrophysics Data System (ADS)
Sl/omczyński, Wojciech; Życzkowski, Karol
1994-11-01
A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov-Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ``Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.'' John Milton, Paradise Lost, Book II
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
NASA Astrophysics Data System (ADS)
Purkayastha, Archak; Dhar, Abhishek; Kulkarni, Manas
2016-06-01
We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of N sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the N =2 case, we show that RQME gives results which agree with exact analytical results for steady-state properties and with exact numerics for time-dependent properties over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in nonequilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed-form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED, and far-from-equilibrium quantum dot experiments.
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.
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
Simulation of n-qubit quantum systems: A computer-algebraic approach
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.; Surzhykov, A.
2007-03-01
During the last decade, the field of quantum computation has attracted a lot of interest and motivated many theoretical and experimental studies of n-qubit quantum systems. But apart from the promise of more efficient quantum algorithms, these investigations also revealed a number of obstacles which still have to be overcome in practice. In this context, the use of simulation programs has proved to be an appropriate method. In order to facilitate the simulation of n-qubit quantum systems, we present the Feynman software program to provide the necessary tools to define and to deal with quantum registers as well as the operators acting on them. Using an interactive design within the framework of the computer algebra system Maple, we hope that the Feynman software program will be useful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future.
NASA Astrophysics Data System (ADS)
Okunishi, Takuma; Clark, Richard; Takeda, Kyozaburo; Kusakabe, Koichi; Tomita, Norikazu
2013-02-01
We extend the static multireference description (resonant unrestricted Hartree-Fock) to a dynamical system in order to include the correlation effect dynamically. The resulting time-dependent (TD) Schrödinger equation is simplified into the time-developed rate equation (TD-CI), where the TD external field \\hatH‧(t) is taken into account directly in the Hamiltonian without any approximations. This TD-CI approach also has an advantage in that it takes into account the electron correlation by narrowing down the number of employed Slater determinants. We apply our TD-CI approach to the case of two electrons confined in the square quantum dot (QD) having the spin singlet multiplicity, and study theoretically the spatial and temporal fluctuation of the two-electron ground state under photon injection and pulse field application.
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.
NASA Astrophysics Data System (ADS)
Shnirman, A.; Saha, A.; Burmistrov, I. S.; Kiselev, M. N.; Altland, A.; Gefen, Y.
2016-03-01
There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira-Leggett and Ambegaokar-Eckern-Schön approaches. Here, we recall the differences between them and explain the consequences of applying each to a zero-dimensional spin (having an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).
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.
A unified approach to quantum and classical TTW systems based on factorizations
NASA Astrophysics Data System (ADS)
Celeghini, E.; Kuru, Ş.; Negro, J.; del Olmo, M. A.
2013-05-01
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.
A unified approach to quantum and classical TTW systems based on factorizations
NASA Astrophysics Data System (ADS)
Celeghini, E.; Kuru, Ş.; Negro, J.; del Olmo, M. A.
2012-05-01
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.
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.
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.
Soares-Pinto, D. O.; Moussa, M. H. Y.; Azevedo, E. R. de; Bonagamba, T. J.; Maziero, J.; Serra, R. M.; Celeri, L. C.
2011-06-15
We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T{sub 1} and T{sub 2} (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T{sub 1}). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.
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.
NASA Astrophysics Data System (ADS)
Tosto, Sebastiano
1997-04-01
The presentation aims to show the basic features of an "ab initio" approach to calculate the energy levels of quantum systems. The purpose of the model is not to furtherly increase the accuracy of some already existing computational method or to develop a new mathematical algorithm but rather to examine the consequences of introducing since the beginning the quantum uncertainty in the energy equations of atoms and molecules. Without any hypothesis on the state of motion of the electrons but merely concerning the number of states allowed in the phase space as a function of momentum and space uncertainty ranges, one obtains simple formulae enabling to calculate the enegy levels of multielectron atoms in a good agreement with the experimental data. The same theoretical approach has been also utilized to describe the diatomic molecules in terms of anharmonic oscillators. Also in this case, simple formulae enable to correlate dissociation energy, vibrational frequency and bond length in a good agreement with the experimental data
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.
Velocity operator approach to quantum fluid dynamics in a three-dimensional neutron-proton system
NASA Astrophysics Data System (ADS)
Nishiyama, Seiya; da Providência, João
2016-07-01
In the preceeding paper, introducing isospin-dependent density operators and defining exact momenta (collective variables), we could get an exact canonically momenta approach to a one-dimensional (1D) neutron-proton (NP) system. In this paper, we attempt at a velocity operator approach to a 3D NP system. Following Sunakawa, after introducing momentum density operators, we define velocity operators, denoting classical fluid velocities. We derive a collective Hamiltonian in terms of the collective variables.
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.
NASA Astrophysics Data System (ADS)
Tiwari, M.; Kenkre, V. M.
2014-04-01
The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effects of interaction with a reservoir. One stems from the randomization of phases and the other from phase space considerations. Even the meaning of the word `phase' differs drastically in the two instances in which it appears in the previous statement. In the first case it normally refers to quantum phases whereas in the second it describes the multiplicity of reservoir states that corresponds to each system state. The generalized master equation theory for the time evolution of such systems is here developed in a transparent manner and both effects of reservoir interactions are addressed in a unified fashion. The formalism is illustrated in simple cases including in the standard spin-boson situation wherein a quantum dimer is in interaction with a bath consisting of harmonic oscillators. The theory has been constructed for application in energy transfer in molecular aggregates and in photosynthetic reaction centers.
Andreev, P. A.; Kuzmenkov, L. S.; Trukhanova, M. I.
2011-12-15
In this paper, we explicate a method of quantum hydrodynamics (QHD) for the study of the quantum evolution of a system of polarized particles. Although we focused primarily on the two-dimensional (2D) physical systems, the method is valid for three-dimensional (3D) and one-dimensional (1D) systems too. The presented method is based upon the Schroedinger equation. Fundamental QHD equations for charged and neutral particles were derived from the many-particle microscopic Schroedinger equation. The fact that particles possess the electric dipole moment (EDM) was taken into account. The explicated QHD approach was used to study dispersion characteristics of various physical systems. We analyzed dispersion of waves in a two-dimensional ion and hole gas placed into an external electric field, which is orthogonal to the gas plane. Elementary excitations in a system of neutral polarized particles were studied for 1D, 2D, and 3D cases. The polarization dynamics in systems of both neutral and charged particles is shown to cause formation of a new type of waves as well as changes in the dispersion characteristics of already known waves. We also analyzed wave dispersion in 2D exciton systems, in 2D electron-ion plasma, and in 2D electron-hole plasma. Generation of waves in 3D-system neutral particles with EDM by means of the beam of electrons and neutral polarized particles is investigated.
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
Sorting quantum systems efficiently
NASA Astrophysics Data System (ADS)
Ionicioiu, Radu
2016-05-01
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.
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)
Anders, Frithjof B.
2008-08-01
We propose a numerical renormalization group (NRG) approach to steady-state currents through nanodevices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce two degenerate Wilson chains for current carrying left- and right-moving electrons reflecting time-reversal symmetry in the absence of a finite bias V. We employ the time-dependent NRG to evolve the known steady-state density operator for a noninteracting junction into the density operator of the fully interacting nanodevice at finite bias. We calculate the differential conductance as function of V, T, and the external magnetic field.
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.
Quantum coherence and correlations in quantum system
Xi, Zhengjun; Li, Yongming; Fan, Heng
2015-01-01
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem. PMID:26094795
Measurement understood through the quantum potential approach
NASA Astrophysics Data System (ADS)
Bohm, D.; Hiley, B. J.
1984-03-01
We review briefly the quantum potential approach to quantum theory, and show that it yields a completely consistent account of the measurement process, including especially what has been called the “collapse of the wave function.” This is done with the aid of a new concept of active information, which enables us to describe the evolution of a physical system as a unique actuality, in principle independent of any observer (so that we can, for example, provide a simple and coherent answer to the Schrödinger cat paradox). Finally, we extend this approach to relativistic quantum field theories, and show that it leads to results that are consistent with all the known experimental implications of the theory of relativity, despite the nonlocality which this approach entails.
NASA Astrophysics Data System (ADS)
Shi, Qiang; Geva, Eitan
2003-12-01
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics. The standard approach is based on using a perturbative treatment of the system-bath coupling for calculating this kernel, and is therefore restricted to systems weakly coupled to the bath. In this paper, we propose a new approach for calculating the memory kernel for an arbitrary system-bath coupling. The memory kernel is obtained by solving a set of two coupled integral equations that relate it to a new type of two-time system-dependent bath correlation functions. The feasibility of the method is demonstrated in the case of an asymetrical two-level system linearly coupled to a harmonic bath.
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
NASA Astrophysics Data System (ADS)
Dušek, Miloslav; Haderka, Ondřej; Hendrych, Martin; Myška, Robert
1999-07-01
A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and sequences are ``refueled'' from a shared provably secret key transferred through the quantum channel. Two identification protocols are devised. The first protocol can be applied when legitimate users have an unjammable public channel at their disposal. The deception probability is derived for the case of a noisy quantum channel. The second protocol employs unconditionally secure authentication of information sent over the public channel, and thus can be applied even in the case when an adversary is allowed to modify public communications. An experimental realization of a quantum identification system is described.
Quantum pharmacology for infectious diseases: a molecular connectivity approach.
Singh, Shailza
2012-09-01
Infectious diseases are a major cause of global health, economic and social problems. Relationship between the infectious diseases and drugs designed to combat them can be understood by the Quantum Pharmacology approach. Quantum pharmacology which is an amalgamation of chemistry, quantum mechanics and computer modeling aims to understand the structure activity relationship of a drug. As compared to the classical MM, the hybrid QM/MM approach which takes into account the quantum mechanics along with the molecular mechanics facilitates the simulation of biological structures with greater accuracy and speed. This review highlights the importance of quantum mechanics for a better understanding of molecular systems and QSAR studies. PMID:22738083
NASA Astrophysics Data System (ADS)
Srisangyingcharoen, P.; Klinkla, R.; Boonchui, S.
2015-11-01
The quantum history approach is applied to investigate the first-photon emission of a quantum dot induced by propagating surface plasmons. The dynamics of the emission is described through the partitioning dynamics of a quantum system. The extended probability distribution which correspond to the photon emission rate is directly calculated. In the case that the Markov's approximation is satisfied, the well known double decay character of the first-photon emission is obtained accompanying with the analytic expression of decay amplitudes which has never been derived before. This is a merit of our approach which allows us to analytically investigate this interacting quantum system and goes beyond the master equation approach.
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.
NASA Astrophysics Data System (ADS)
Arrachea, Liliana
2007-01-01
We present an efficient method and a fast algorithm to exactly calculate spectral functions and one-body observables of open quantum systems described by lattice Hamiltonians with harmonically time-dependent terms and without many-body interactions. The theoretical treatment is based in Keldysh nonequilibrium Green’s function formalism. We illustrate the implementation of the technique in a paradigmatic model of a quantum pump driven by local fields oscillating in time with one and two harmonic components.
NASA Astrophysics Data System (ADS)
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.
Ye Jinwu
2008-03-15
We use both Mutual Composite Fermion (MCF) and Composite Boson (CB) approach to study balanced and imbalanced Bi-layer Quantum Hall systems (BLQH) and make critical comparisons between the two approaches. We find the CB approach is superior to the MCF approach in studying ground states with different kinds of broken symmetries. In the phase representation of the CB theory, we first study the Excitonic superfluid (ESF) state. The theory puts spin and charge degree freedoms in the same footing, explicitly bring out the spin-charge connection and classify all the possible excitations in a systematic way. Then in the dual density representation of the CB theory, we study possible intermediate phases as the distance increases. We propose there are two critical distances d{sub c1} < d{sub c2} and three phases as the distance increases. When 0 < d < d{sub c1}, the system is in the ESF state which breaks the internal U(1) symmetry, when d{sub c1} < d < d{sub c2}, the system is in an pseudo-spin density wave (PSDW) state which breaks the translational symmetry, there is a first-order transition at d{sub c1} driven by the collapsing of magneto-roton minimum at a finite wavevector in the pseudo-spin channel. When d{sub c2} < d < {infinity}, the system becomes two weakly coupled {nu} = 1/2 Composite Fermion Fermi Liquid (FL) state. There is also a first-order transition at d = d{sub c2}. We construct a quantum Ginzburg Landau action to describe the transition from ESF to PSDW which break the two completely different symmetries. By using the QGL action, we explicitly show that the PSDW takes a square lattice and analyze in detail the properties of the PSDW at zero and finite temperature. We also suggest that the correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature-dependent drag consistent with the experimental data. Then we study the effects of imbalance on both ESF and PSDW. In the ESF side, the system supports
Quantum information approach to the azurite mineral frustrated quantum magnet
NASA Astrophysics Data System (ADS)
Batle, J.; Ooi, C. H. Raymond; Abutalib, M.; Farouk, Ahmed; Abdalla, S.
2016-07-01
Quantum correlations are almost impossible to address in bulk systems. Quantum measures extended only to a few number of parties can be discussed in practice. In the present work, we study nonlocality for a cluster of spins belonging to a mineral whose structure is that of a quantum magnet. We reproduce at a much smaller scale the experimental outcomes, and then, we study the role of quantum correlations there. A macroscopic entanglement witness has been introduced in order to reveal nonlocal quantum correlations between individual constituents of the azurite mineral at nonzero temperatures. The critical point beyond which entanglement is zero is found at T_c < 1 K.
Quantum information approach to the azurite mineral frustrated quantum magnet
NASA Astrophysics Data System (ADS)
Batle, J.; Ooi, C. H. Raymond; Abutalib, M.; Farouk, Ahmed; Abdalla, S.
2016-04-01
Quantum correlations are almost impossible to address in bulk systems. Quantum measures extended only to a few number of parties can be discussed in practice. In the present work, we study nonlocality for a cluster of spins belonging to a mineral whose structure is that of a quantum magnet. We reproduce at a much smaller scale the experimental outcomes, and then, we study the role of quantum correlations there. A macroscopic entanglement witness has been introduced in order to reveal nonlocal quantum correlations between individual constituents of the azurite mineral at nonzero temperatures. The critical point beyond which entanglement is zero is found at T_c < 1 K.
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
Curtright, Thomas; Mezincescu, Luca
2007-09-15
Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+{nu}){sup 2}+{sigma}{sub k>0}{mu}{sub k} exp(ikx). In some nontrivial cases, equivalent Hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.
Quantum contextuality in N-boson systems
Benatti, Fabio; Floreanini, Roberto; Genovese, Marco; Olivares, Stefano
2011-09-15
Quantum contextuality in systems of identical bosonic particles is explicitly exhibited via the maximum violation of a suitable inequality of Clauser-Horne-Shimony-Holt type. Unlike the approaches considered so far, which make use of single-particle observables, our analysis involves collective observables constructed using multiboson operators. An exemplifying scheme to test this violation with a quantum optical setup is also discussed.
Tailoring superradiance to design artificial quantum systems.
Longo, Paolo; Keitel, Christoph H; Evers, Jörg
2016-01-01
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. PMID:27009604
Tailoring superradiance to design artificial quantum systems
Longo, Paolo; Keitel, Christoph H.; Evers, Jörg
2016-01-01
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. PMID:27009604
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.
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.
Nonperturbative approach to relativistic quantum communication channels
NASA Astrophysics Data System (ADS)
Landulfo, André G. S.
2016-05-01
We investigate the transmission of both classical and quantum information between two arbitrary observers in globally hyperbolic spacetimes using a quantum field as a communication channel. The field is supposed to be in some arbitrary quasifree state and no choice of representation of its canonical commutation relations is made. Both sender and receiver possess some localized two-level quantum system with which they can interact with the quantum field to prepare the input and receive the output of the channel, respectively. The interaction between the two-level systems and the quantum field is such that one can trace out the field degrees of freedom exactly and thus obtain the quantum channel in a nonperturbative way. We end the paper determining the unassisted as well as the entanglement-assisted classical and quantum channel capacities.
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
Quantum coherence in multipartite systems
NASA Astrophysics Data System (ADS)
Yao, Yao; Xiao, Xing; Ge, Li; Sun, C. P.
2015-08-01
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord, and quantum entanglement in multipartite systems. On this basis, we define a basis-independent measure of quantum coherence and prove that it is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two-qubit unitary gates. Intriguingly, our results demonstrate that nonlocal unitary gates do not necessarily outperform the local unitary gates. Finally, the additivity relationship of quantum coherence in tripartite systems is discussed in detail, where the strong subadditivity of von Neumann entropy plays an essential role.
Equilibration of quantum chaotic systems.
Zhuang, Quntao; Wu, Biao
2013-12-01
The quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. 57, 30 (1929)] and again by Reimann [Phys. Rev. Lett. 101, 190403 (2008)] in a more practical and well-defined form. However, it is not clear whether the theorem applies to quantum chaotic systems. With a rigorous proof still elusive, we illustrate and verify this theorem for quantum chaotic systems with examples. Our numerical results show that a quantum chaotic system with an initial low-entropy state will dynamically relax to a high-entropy state and reach equilibrium. The quantum equilibrium state reached after dynamical relaxation bears a remarkable resemblance to the classical microcanonical ensemble. However, the fluctuations around equilibrium are distinct: The quantum fluctuations are exponential while the classical fluctuations are Gaussian. PMID:24483425
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.
Open fermionic quantum systems
Artacho, E.; Falicov, L.M. Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 )
1993-01-15
A method to treat a quantum system in interaction with a fermionic reservoir is presented. Its most important feature is that the dynamics of the exchange of particles between the system and the reservoir is explicitly included via an effective interaction term in the Hamiltonian. This feature gives rise to fluctuations in the total number of particles in the system. The system is to be considered in its full structure, whereas the reservoir is described only in an effective way, as a source of particles characterized by a small set of parameters. Possible applications include surfaces, molecular clusters, and defects in solids, in particular in highly correlated electronic materials. Four examples are presented: a tight-binding model for an adsorbate on the surface of a one-dimensional lattice, the Anderson model of a magnetic impurity in a metal, a two-orbital impurity with interorbital hybridization (intermediate-valence center), and a two-orbital impurity with interorbital repulsive interactions.
Quantum approach to Bertrand duopoly
NASA Astrophysics Data System (ADS)
Fra¸ckiewicz, Piotr; Sładkowski, Jan
2016-06-01
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.
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.
Realist model approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Hájíček, P.
2013-06-01
The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations can be assumed objective without the difficulties that are encountered by the same assumption about values of observables. The resulting realist interpretation of quantum mechanics is made rigorous by studying the space of quantum states—the convex set of state operators. Prepared states are classified according to their statistical structure into indecomposable and decomposable instead of pure and mixed. Simple objective properties are defined and showed to form a Boolean lattice.
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
Avoiding irreversible dynamics in quantum systems
NASA Astrophysics Data System (ADS)
Karasik, Raisa Iosifovna
2009-10-01
Devices that exploit laws of quantum physics offer revolutionary advances in computation and communication. However, building such devices presents an enormous challenge, since it would require technologies that go far beyond current capabilities. One of the main obstacles to building a quantum computer and devices needed for quantum communication is decoherence or noise that originates from the interaction between a quantum system and its environment, and which leads to the destruction of the fragile quantum information. Encoding into decoherence-free subspaces (DFS) provides an important strategy for combating decoherence effects in quantum systems and constitutes the focus of my dissertation. The theory of DFS relies on the existence of certain symmetries in the decoherence process, which allow some states of a quantum system to be completely decoupled from the environment and thus to experience no decoherence. In this thesis I describe various approaches to DFS that are developed in the current literature. Although the general idea behind various approaches to DFS is the same, I show that different mathematical definitions of DFS actually have different physical meaning. I provide a rigorous definition of DFS for every approach, explaining its physical meaning and relation to other definitions. I also examine the theory of DFS for Markovian systems. These are systems for which the environment has no memory, i.e., any change in the environment affects the quantum system instantaneously. Examples of such systems include many systems in quantum optics that have been proposed for implementation of a quantum computer, such as atomic and molecular gases, trapped ions, and quantum dots. Here I develop a rigorous theory that provides necessary and sufficient conditions for the existence of DFS. This theory allows us to identify a special new class of DFS that was not known before. Under particular circumstances, dynamics of a quantum system can connive together with
Quantum mechanics of open systems
NASA Astrophysics Data System (ADS)
Melikidze, Akakii
In quantum mechanics, there is a set of problems where the system of interest interacts with another system, usually called "environment". This interaction leads to the exchange of energy and information and makes the dynamics of the system of interest essentially non-unitary. Such problems often appeared in condensed matter physics and attracted much attention after recent advances in nanotechnology. As broadly posed as they are, these problems require a variety of different approaches. This thesis is an attempt to examine several of these approaches in applications to different condensed matter problems. The first problem concerns the so-called "Master equation" approach which is very popular in quantum optics. I show that analytic properties of environmental correlators lead to strong restrictions on the applicability of the approach to the strong-coupling regime of interest in condensed matter physics. In the second problem, I use path integrals to treat the localization of particles on attractive short-range potentials when the environment produces an effective viscous friction force. I find that friction changes drastically the localization properties and leads to much stronger localization in comparison to the non-dissipative case. This has implications for the motion of heavy particles in fermionic liquids and, as will be argued below, is also relevant to the problem of high-temperature superconductivity. Finally, the third problem deals with the interplay of geometric phases and energy dissipation which occurs in the motion of vortices in superconductors. It is shown that this interplay leads to interesting predictions for vortex tunneling in high-temperature superconductors which have been partially confirmed by experiments.
Dissipation Assisted Quantum Memory with Coupled Spin Systems
NASA Astrophysics Data System (ADS)
Jiang, Liang; Verstraete, Frank; Cirac, Ignacio; Lukin, Mikhail
2009-05-01
Dissipative dynamics often destroys quantum coherences. However, one can use dissipation to suppress decoherence. A well-known example is the so-called quantum Zeno effect, in which one can freeze the evolution using dissipative processes (e.g., frequently projecting the system to its initial state). Similarly, the undesired decoherence of quantum bits can also be suppressed using controlled dissipation. We propose and analyze the use of this generalization of quantum Zeno effect for protecting the quantum information encoded in the coupled spin systems. This new approach may potentially enhance the performance of quantum memories, in systems such as nitrogen-vacancy color-centers in diamond.
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.
Optimal approach to quantum communication using dynamic programming.
Jiang, Liang; Taylor, Jacob M; Khaneja, Navin; Lukin, Mikhail D
2007-10-30
Reliable preparation of entanglement between distant systems is an outstanding problem in quantum information science and quantum communication. In practice, this has to be accomplished by noisy channels (such as optical fibers) that generally result in exponential attenuation of quantum signals at large distances. A special class of quantum error correction protocols, quantum repeater protocols, can be used to overcome such losses. In this work, we introduce a method for systematically optimizing existing protocols and developing more efficient protocols. Our approach makes use of a dynamic programming-based searching algorithm, the complexity of which scales only polynomially with the communication distance, letting us efficiently determine near-optimal solutions. We find significant improvements in both the speed and the final-state fidelity for preparing long-distance entangled states. PMID:17959783
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. PMID:25768745
NASA Astrophysics Data System (ADS)
Marquette, Ian; Quesne, Christiane
2015-06-01
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.
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.
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
Entanglement and dephasing of quantum dissipative systems
Stauber, T.; Guinea, F.
2006-04-15
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and the quantum harmonic oscillator. In the case of the free particle, the related entanglement of formation shows no nonanalyticity. In the case of the dissipative harmonic oscillator, there is a nonanalyticity at the transition of underdamped to overdamped oscillations. We argue that this might be a general property of dissipative systems. We show that similar features arise in the dissipative two-level system and study different regimes using sub-Ohmic, Ohmic, and super-Ohmic baths, within a scaling approach.
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.
Comparing conductance quantization in quantum wires and quantum Hall systems
NASA Astrophysics Data System (ADS)
Alekseev, Anton Yu.; Cheianov, Vadim V.; Fröhlich, Jürg
1996-12-01
We suggest a means to calculate the dc conductance of a one-dimensional electron system described by the Luttinger model. Our approach is based on the ideas of Landauer and Büttiker on transport in ballistic channels and on the methods of current algebra. We analyze in detail the way in which the system can be coupled to external reservoirs. This determines whether the conductance is renormalized or not. We provide a parallel treatment of a quantum wire and a fractional quantum Hall system on a cylinder with two widely separated edges. Although both systems are described by the same effective theory, the physical electrons are identified with different types of excitations, and hence the coupling to external reservoirs is different. As a consequence, the conductance in the wire is quantized in integer units of e2/h per spin orientation whereas the Hall conductance allows for fractional quantization.
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.
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.
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.
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. PMID:23829722
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
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.
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.
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.
Bosson, Maël; Grudinin, Sergei; Redon, Stephane
2013-03-01
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. PMID:23108532
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
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
Numerical approach for unstructured quantum key distribution
NASA Astrophysics Data System (ADS)
Coles, Patrick J.; Metodiev, Eric M.; Lütkenhaus, Norbert
2016-05-01
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.
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
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.
Incoherent control of locally controllable quantum systems
Dong Daoyi; Zhang Chenbin; Rabitz, Herschel; Pechen, Alexander; Tarn, T.-J.
2008-10-21
An incoherent control scheme for state control of locally controllable quantum systems is proposed. This scheme includes three steps: (1) amplitude amplification of the initial state by a suitable unitary transformation, (2) projective measurement of the amplified state, and (3) final optimization by a unitary controlled transformation. The first step increases the amplitudes of some desired eigenstates and the corresponding probability of observing these eigenstates, the second step projects, with high probability, the amplified state into a desired eigenstate, and the last step steers this eigenstate into the target state. Within this scheme, two control algorithms are presented for two classes of quantum systems. As an example, the incoherent control scheme is applied to the control of a hydrogen atom by an external field. The results support the suggestion that projective measurements can serve as an effective control and local controllability information can be used to design control laws for quantum systems. Thus, this scheme establishes a subtle connection between control design and controllability analysis of quantum systems and provides an effective engineering approach in controlling quantum systems with partial controllability information.
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.
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-01-01
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(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. PMID:27464855
Duality quantum algorithm efficiently simulates open quantum systems
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-01-01
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. PMID:27464855
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.
The SCOP-formalism: an Operational Approach to Quantum Mechanics
NASA Astrophysics Data System (ADS)
D'Hooghe, Bart
2010-05-01
We present the SCOP-formalism, an operational approach to quantum mechanics. If a State—COntext—Property—System (SCOP) satisfies a specific set of `quantum axioms,] it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case N = 2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it. This contrasts sharply with standard quantum mechanics for which Gleason's theorem states the uniqueness of the state transition probability and independent of measurement context. We show that if a SCOP satisfies a Gleason-like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.
The SCOP-formalism: an Operational Approach to Quantum Mechanics
D'Hooghe, Bart
2010-05-04
We present the SCOP-formalism, an operational approach to quantum mechanics. If a State-COntext-Property-System (SCOP) satisfies a specific set of 'quantum axioms,] it fits in a quantum mechanical representation in Hilbert space. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter N. In the case N = 2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N->infinity the system is classical. For the intermediate cases it is impossible to define an orthocomplementation on the set of properties. Another interesting feature is that the probability of a state transition also depends on the context which induces it. This contrasts sharply with standard quantum mechanics for which Gleason's theorem states the uniqueness of the state transition probability and independent of measurement context. We show that if a SCOP satisfies a Gleason-like condition, namely that all state transition probabilities are independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented.
Green-function approach for scattering quantum walks
Andrade, F. M.; Luz, M. G. E. da
2011-10-15
In this work a Green-function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position-dependent quantum amplitudes. By introducing the step and path operators, it is shown how to extract any information about the system from the Green function. The method's relevant features are demonstrated by discussing in detail an example, a general diamond-shaped graph.
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.
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.
Relativistic Quantum Metrology in Open System Dynamics
Tian, Zehua; Wang, Jieci; Fan, Heng; Jing, Jiliang
2015-01-01
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. PMID:25609187
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.
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
Perturbative approach to open circuit QED systems
NASA Astrophysics Data System (ADS)
Li, Andy C. Y.; Petruccione, Francesco; Koch, Jens
2014-03-01
Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The investigation of open systems mostly relies on exact diagonalization of the Liouville superoperator or quantum trajectories. In this approach, the system size is rather limited by current computational capabilities. Analogous to closed-system PT, we develop a PT suitable for open quantum systems. The proposed method is useful in the analytical understanding of open systems as well as in the numerical calculation of system observables, which would otherwise be impractical. This enables us to investigate a variety of open circuit QED systems, including the open Jaynes-Cummings lattice model.
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.
Quantum cloning attacks against PUF-based quantum authentication systems
NASA Astrophysics Data System (ADS)
Yao, Yao; Gao, Ming; Li, Mo; Zhang, Jian
2016-05-01
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.
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.
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. PMID:22163723
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.
The quantum Hall effect in quantum dot systems
NASA Astrophysics Data System (ADS)
Beltukov, Y. M.; Greshnov, A. A.
2014-12-01
It is proposed to use quantum dots in order to increase the temperatures suitable for observation of the integer quantum Hall effect. A simple estimation using Fock-Darwin spectrum of a quantum dot shows that good part of carriers localized in quantum dots generate the intervals of plateaus robust against elevated temperatures. Numerical calculations employing local trigonometric basis and highly efficient kernel polynomial method adopted for computing the Hall conductivity reveal that quantum dots may enhance peak temperature for the effect by an order of magnitude, possibly above 77 K. Requirements to potentials, quality and arrangement of the quantum dots essential for practical realization of such enhancement are indicated. Comparison of our theoretical results with the quantum Hall measurements in InAs quantum dot systems from two experimental groups is also given.
Functional renormalization group - a new approach to frustrated quantum magnetism
NASA Astrophysics Data System (ADS)
Reuther, Johannes
The experimental and theoretical investigation of quantum spin systems has become one of the central disciplines of contemporary condensed matter physics. From an experimental viewpoint, the field has been significantly fueled by the recent synthesis of novel strongly correlated materials with exotic magnetic or quantum paramagnetic ground states. From a theoretical perspective, however, the numerical treatment of realistic models for quantum magnetism in two and three spatial dimensions still constitutes a serious challenge. This particularly applies to frustrated systems, which complicate the employment of established methods. This talk intends to propagate the pseudofermion functional renormalization group (PFFRG) as a novel approach to determine large size ground state correlations of a wide class of spin Hamiltonians. Using a diagrammatic pseudofermion representation for quantum spin models, the PFFRG performs systematic summations in all two-particle fermionic interaction channels, capturing the correct balance between classical magnetic ordering and quantum fluctuations. Numerical results for various frustrated spin models on different 2D and 3D lattices are reviewed, and benchmarked against other methods if available.
Taubman, Matthew S.; Myers, Tanya L.; Bernacki, Bruce E.; Stahl, Robert D.; Cannon, Bret D.; Schiffern, John T.; Phillips, Mark C.
2012-04-01
A multi-channel laser-based chemical sensor platform is presented, in which a modular architecture allows the exchange of complete sensor channels without disruption to overall operation. Each sensor channel contains custom optical and electronics packages, which can be selected to access laser wavelengths, interaction path lengths and modulation techniques optimal for a given application or mission. Although intended primarily to accommodate mid-infrared (MIR) external cavity quantum cascade lasers (ECQCLs)and astigmatic Herriott cells, channels using visible or near infrared (NIR) lasers or other gas cell architectures can also be used, making this a truly versatile platform. Analog and digital resources have been carefully chosen to facilitate small footprint, rapid spectral scanning, ow-noise signal recovery, failsafe autonomous operation, and in-situ chemometric data analysis, storage and transmission. Results from the demonstration of a two-channel version of this platform are also presented.
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.
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.
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.
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.
Investigating non-Markovian dynamics of quantum open systems
NASA Astrophysics Data System (ADS)
Chen, Yusui
Quantum open system coupled to a non-Markovian environment has recently attracted widespread interest for its important applications in quantum information processing and quantum dissipative systems. New phenomena induced by the non-Markovian environment have been discovered in variety of research areas ranging from quantum optics, quantum decoherence to condensed matter physics. However, the study of the non-Markovian quantum open system is known a difficult problem due to its technical complexity in deriving the fundamental equation of motion and elusive conceptual issues involving non-equilibrium dynamics for a strong coupled environment. The main purpose of this thesis is to introduce several new techniques of solving the quantum open systems including a systematic approach to dealing with non-Markovian master equations from a generic quantum-state diffusion (QSD) equation. In the first part of this thesis, we briefly introduce the non-Markovian quantum-state diffusion approach, and illustrate some pronounced non-Markovian quantum effects through numerical investigation on a cavity-QED model. Then we extend the non-Markovian QSD theory to an interesting model where the environment has a hierarchical structure, and find out the exact non-Markovian QSD equation of this model system. We observe the generation of quantum entanglement due to the interplay between the non-Markovian environment and the cavity. In the second part, we show an innovative method to obtain the exact non-Markovian master equations for a set of generic quantum open systems based on the corresponding non-Markovian QSD equations. Multiple-qubit systems and multilevel systems are discussed in details as two typical examples. Particularly, we derive the exact master equation for a model consisting of a three-level atom coupled to an optical cavity and controlled by an external laser field. Additionally, we discuss in more general context the mathematical similarity between the multiple
Hybrid quantum systems with ultracold spins and optomechanics
NASA Astrophysics Data System (ADS)
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Date, Aditya; Schwab, Keith; Meystre, Pierre; Vengalattore, Mukund
2016-05-01
Linear cavity optomechanics has enabled radiation pressure cooling and sensing of mechanical resonators at the quantum limits. However, exciting and unrealized avenues such as generating massive macroscopic nonclassical states, quantum signal transduction, and phonon-based manybody physics each require strong, nonlinear interactions. In our group, we are exploring three approaches to realizing strong optomechanical nonlinearities - i. using atomically thin graphene membranes, ii. coupling optomechanical systems with ultracold atomic spins, and iii. using microtoroidal optomechanical resonators strongly coupled to atoms trapped in their evanescent fields. We describe our progress in each of these efforts and discuss ongoing studies on various aspects of quantum enhanced metrology, nonequilibrium dynamics of open quantum systems and quantum transduction using these novel hybrid quantum systems. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Classical and quantum correlative capacities of quantum systems
Li Nan; Luo Shunlong
2011-10-15
How strongly can one system be correlated with another? In the classical world, this basic question concerning correlative capacity has a very satisfying answer: The ''effective size'' of the marginal system, as quantified by the Shannon entropy, sets a tight upper bound to the correlations, as quantified by the mutual information. Although in the quantum world bipartite correlations, like their classical counterparts, are also well quantified by mutual information, the similarity ends here: The correlations in a bipartite quantum system can be twice as large as the marginal entropy. In the paradigm of quantum discord, the correlations are split into classical and quantum components, and it was conjectured that both the classical and quantum correlations are (like the classical mutual information) bounded above by each subsystem's entropy. In this work, by exploiting the interplay between entanglement of formation, mutual information, and quantum discord, we disprove that conjecture. We further indicate a scheme to restore harmony between quantum and classical correlative capacities. The results illustrate dramatically the asymmetric nature of quantum discord and highlight some subtle and unusual features of quantum correlations.
Adiabaticity in open quantum systems
NASA Astrophysics Data System (ADS)
Venuti, Lorenzo Campos; Albash, Tameem; Lidar, Daniel A.; Zanardi, Paolo
2016-03-01
We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian L (t ) . We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of L (t ) will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time T . In the case of a finite number of level crossings, the scaling becomes T-η with an exponent η that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time T should be long compared to the corresponding minimum inverse gap squared of L (t ) . Our results are illustrated with several examples.
Supersymmetric biorthogonal quantum systems
Curtright, Thomas; Mezincescu, Luca; Schuster, David
2007-09-15
We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V{sub {+-}}(z)=-U(z){sup 2}{+-}z(d/dz)U(z) where U(z){identical_to}{sigma}{sub k>0}{upsilon}{sub k}z{sup k}. In particular, we consider the cases generated by U(z)=z and z/(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.
Exchange fluctuation theorem for correlated quantum systems.
Jevtic, Sania; Rudolph, Terry; Jennings, David; Hirono, Yuji; Nakayama, Shojun; Murao, Mio
2015-10-01
We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem. PMID:26565174
A random walk approach to quantum algorithms.
Kendon, Vivien M
2006-12-15
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems. PMID:17090467
Note on entropies for quantum dynamical systems.
Watanabe, Noboru
2016-05-28
Quantum entropy and channel are fundamental concepts for quantum information theory progressed recently in various directions. We will review the fundamental aspects of mean entropy and mean mutual entropy and calculate them for open system dynamics. PMID:27091165
Current in open quantum systems.
Gebauer, Ralph; Car, Roberto
2004-10-15
We show that a dissipative current component is present in the dynamics generated by a Liouville-master equation, in addition to the usual component associated with Hamiltonian evolution. The dissipative component originates from coarse graining in time, implicit in a master equation, and needs to be included to preserve current continuity. We derive an explicit expression for the dissipative current in the context of the Markov approximation. Finally, we illustrate our approach with a simple numerical example, in which a quantum particle is coupled to a harmonic phonon bath and dissipation is described by the Pauli master equation. PMID:15524960
Optimal protocols for slowly driven quantum systems.
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. PMID:26465432
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.
Enhanced Fault-Tolerant Quantum Computing in d -Level Systems
NASA Astrophysics Data System (ADS)
Campbell, Earl T.
2014-12-01
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 .
Maxwell's demons in multipartite quantum correlated systems
NASA Astrophysics Data System (ADS)
Braga, Helena C.; Rulli, Clodoaldo C.; de Oliveira, Thiago R.; Sarandy, Marcelo S.
2014-10-01
We investigate the extraction of thermodynamic work by a Maxwell's demon in a multipartite quantum correlated system. We begin by adopting the standard model of a Maxwell's demon as a Turing machine, either in a classical or quantum setup depending on its ability to implement classical or quantum conditional dynamics. Then, for an n -partite system (A1,A2,⋯,An) , we introduce a protocol of work extraction that bounds the advantage of the quantum demon over its classical counterpart through the amount of multipartite quantum correlation present in the system, as measured by a thermal version of the global quantum discord. This result is illustrated for an arbitrary n -partite pure state of qubits with Schmidt decomposition, where it is shown that the thermal global quantum discord exactly quantifies the quantum advantage. Moreover, we also consider the work extraction via mixed multipartite states, where examples of tight upper bounds can be obtained.
Quantum state engineering in hybrid open quantum systems
NASA Astrophysics Data System (ADS)
Joshi, Chaitanya; Larson, Jonas; Spiller, Timothy P.
2016-04-01
We investigate a possibility to generate nonclassical states in light-matter coupled noisy quantum systems, namely, the anisotropic Rabi and Dicke models. In these hybrid quantum systems, a competing influence of coherent internal dynamics and environment-induced dissipation drives the system into nonequilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model, the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement, we also find that the full state is entangled. Furthermore, as a natural extension of the anisotropic Rabi model to an infinite spin subsystem, we next explored the NESS of the anisotropic Dicke model. The NESS of this linearized Dicke model is also an inseparable state of light and matter. With an aim to enrich the dynamics beyond the sustainable entanglement found for the NESS of these hybrid quantum systems, we also propose to combine an all-optical feedback strategy for quantum state protection and for establishing quantum control in these systems. Our present work further elucidates the relevance of such hybrid open quantum systems for potential applications in quantum architectures.
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.
Classical versus quantum errors in quantum computation of dynamical systems.
Rossini, Davide; Benenti, Giuliano; Casati, Giulio
2004-11-01
We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum motion when the system's parameters are perturbed or when there are unitary errors in the quantum gates implementing the quantum algorithm. While the first kind of errors has a classical limit, the second one has no classical analog. It is shown that, whereas in the first case ("classical errors") the decay of fidelity is very sensitive to the dynamical regime, in the second case ("quantum errors") it is almost independent of the dynamical behavior of the simulated system. Therefore, the rich variety of behaviors found in the study of the stability of quantum motion under "classical" perturbations has no correspondence in the fidelity of quantum computation under its natural perturbations. In particular, in this latter case it is not possible to recover the semiclassical regime in which the fidelity decays with a rate given by the classical Lyapunov exponent. PMID:15600737
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.
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
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.
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…
New approach to nonperturbative quantum mechanics with minimal length uncertainty
NASA Astrophysics Data System (ADS)
Pedram, Pouria
2012-01-01
The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity, and black-hole physics. In this scenario, all commutation relations are modified and the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP). Here, we present a one-dimensional nonperturbative approach to quantum mechanics with minimal length uncertainty relation which implies X=x to all orders and P=p+(1)/(3)βp3 to first order of GUP parameter β, where X and P are the generalized position and momentum operators and [x,p]=iℏ. We show that this formalism is an equivalent representation of the seminal proposal by Kempf, Mangano, and Mann and predicts the same physics. However, this proposal reveals many significant aspects of the generalized uncertainty principle in a simple and comprehensive form and the existence of a maximal canonical momentum is manifest through this representation. The problems of the free particle and the harmonic oscillator are exactly solved in this GUP framework and the effects of GUP on the thermodynamics of these systems are also presented. Although X, P, and the Hamiltonian of the harmonic oscillator all are formally self-adjoint, the careful study of the domains of these operators shows that only the momentum operator remains self-adjoint in the presence of the minimal length uncertainty. We finally discuss the difficulties with the definition of potentials with infinitely sharp boundaries.
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. PMID:23572581
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).
The decoupling approach to quantum information theory
NASA Astrophysics Data System (ADS)
Dupuis, Frédéric
2010-04-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.
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. PMID:26967399
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.
Multielectron dynamics in the tunneling ionization of correlated quantum systems
NASA Astrophysics Data System (ADS)
Hollstein, Maximilian; Pfannkuche, Daniela
2015-11-01
The importance of multielectron dynamics during the tunneling ionization of a correlated quantum system is investigated. By comparison of the solution of the time-dependent Schrödinger equation with the time-dependent configuration-interaction singles approach, we demonstrate the importance of a multielectron description of the tunneling ionization process especially for weakly confined quantum systems. Within this context, we observe that adiabatic driving by an intense light field can even enhance the correlations between still trapped electrons.
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.
Quasiequilibria in open quantum systems
Walls, Jamie D.
2010-03-15
In this work, the steady-state or quasiequilibrium resulting from periodically modulating the Liouvillian of an open quantum system, L-circumflex-circumflex(t), is investigated. It is shown that differences between the quasiequilibrium and the instantaneous equilibrium occur due to nonadiabatic contributions from the gauge field connecting the instantaneous eigenstates of L-circumflex-circumflex(t) to a fixed basis. These nonadiabatic contributions are shown to result in an additional rotation and/or depolarization for a single spin-1/2 in a time-dependent magnetic field and to affect the thermal mixing of two coupled spins interacting with a time-dependent magnetic field.
A causal net approach to relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Bateson, R. D.
2012-05-01
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.
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.
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.
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.
Avoiding degenerate coframes in an affine gauge approach to quantum gravity
Mielke, E.W.; McCrea, J.D.; Ne`eman, Y.; Hehl, F.W.
1993-04-01
This report discusses the following concepts on quantum gravity: The affine gauge approach; affine gauge transformations versus active differomorphisms; affine gauge approach to quantum gravity with topology change.
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.
Quantum Logic: Approach a Child's Environment from "Inside."
ERIC Educational Resources Information Center
Rhodes, William C.
1987-01-01
With the advent of quantum mechanics, physics has merged with psychology, and cognitive science has been revolutionized. Quantum logic supports the notion of influencing the environment by increasing the child's capacity for cognitive processing. This special educational approach is theoretically more effective than social and political…
Superconductor-Diamond Hybrid Quantum System
NASA Astrophysics Data System (ADS)
Semba, Kouichi; Yoshihara, Fumiki; Johansson, Jan E. S.; Zhu, Xiaobo; Mizuochi, Norikazu; Munro, William J.; Saito, Shiro; Kakuyanagi, Kosuke; Matsuzaki, Yuichiro
This chapter describes recent progress on research into superconducting flux qubit, NV diamond, and superconductor-diamond hybrid quantum systems. First, we describe important physical properties of superconducting macroscopic artificial atoms i.e., the tunability of the qubit energy level spacing, the coherence property, an example of strong coupling to another quantum system such as an LC harmonic oscillator, and qubit state readout through a Josephson bifurcation amplifier. We then introduce the NV center in diamond as an intriguing candidate for quantum information processing, which offers excellent multiple accessibility via visible light, microwaves and magnetic fields. Finally, we describe the superconducting flux qubit - NV centers in a diamond hybrid quantum system.
Uncertainty Relation for a Quantum Open System
NASA Astrophysics Data System (ADS)
Hu, B. L.; Zhang, Yuhong
We derive the uncertainty relation for a quantum open system consisting of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the system. We show that upon contact with the bath (assumed to be ohmic in this paper) the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time in similar models in the discussion of quantum to classical transition. This offers some insight into the physical mechanisms involved in the environment-induced decoherence process. We obtain closed analytic expressions for this generalized uncertainty relation under the conditions of high temperature and weak damping, separately. We also consider under these conditions an arbitrarily squeezed initial state and show how the squeeze parameter enters in the generalized uncertainty relation. Using these results we examine the transition of the system from a quantum pure state to a nonequilibrium quantum statistical state and to an equilibrium quantum statistical state. The three stages are marked by the decoherence time and the relaxation time, respectively. With these observations we explicate the physical conditions under which the two basic postulates of quantum statistical mechanics become valid. We also comment on the inappropriate usage of the word “classicality” in many decoherence studies of quantum to classical transition.
The geometric approach to quantum correlations: computability versus reliability
NASA Astrophysics Data System (ADS)
Tufarelli, Tommaso; MacLean, Tom; Girolami, Davide; Vasile, Ruggero; Adesso, Gerardo
2013-07-01
We propose a modified metric based on the Hilbert-Schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord. Such a measure is found not to suffer from pathological dependence on state purity. Although the employed metric is still non-contractive under quantum operations, we show that the resulting indicator of quantum correlations is in agreement with other bona fide discord measures in a number of physical examples. We present a critical assessment of the requirements of reliability versus computability when approaching the task of quantifying, or measuring, general quantum correlations in a bipartite state.
Approaching chemical accuracy with quantum Monte Carlo.
Petruzielo, F R; Toulouse, Julien; Umrigar, C J
2012-03-28
A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space. PMID:22462844
Quantum kinetic energy densities: An operational approach
Muga, J.G.; Seidel, D.; Hegerfeldt, G.C.
2005-04-15
We propose and investigate a procedure to measure, at least in principle, a positive quantum version of the local kinetic energy density. This procedure is based, under certain idealized limits, on the detection rate of photons emitted by moving atoms which are excited by a localized laser beam. The same type of experiment, but in different limits, can also provide other non-positive-definite versions of the kinetic energy density. A connection with quantum arrival time distributions is discussed.
Real-time nonequilibrium dynamics of quantum glassy systems
NASA Astrophysics Data System (ADS)
Cugliandolo, Leticia F.; Lozano, Gustavo
1999-01-01
We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the p spin glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely, aging, survives the quantum fluctuations. In the subcritical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin glasses and the relevance of the effective temperatures with respect to the understanding of the low-temperature dynamics.
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.
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.
Chebyshev Expansion Applied to Dissipative Quantum Systems.
Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich
2016-05-19
To determine the dynamics of a molecular aggregate under the influence of a strongly time-dependent perturbation within a dissipative environment is still, in general, a challenge. The time-dependent perturbation might be, for example, due to external fields or explicitly treated fluctuations within the environment. Methods to calculate the dynamics in these cases do exist though some of these approaches assume that the corresponding correlation functions can be written as a weighted sum of exponentials. One such theory is the hierarchical equations of motion approach. If the environment, however, is described by a complex spectral density or if its temperature is low, these approaches become very inefficient. Therefore, we propose a scheme based on a Chebyshev decomposition of the bath correlation functions and detail the respective quantum master equations within second-order perturbation theory in the environmental coupling. Similar approaches have recently been proposed for systems coupled to Fermionic reservoirs. The proposed scheme is tested for a simple two-level system and compared to existing results. Furthermore, the advantages and disadvantages of the present Chebyshev approach are discussed. PMID:26845380
Quantum Rotational Effects in Nanomagnetic Systems
NASA Astrophysics Data System (ADS)
O'Keeffe, Michael F.
Quantum tunneling of the magnetic moment in a nanomagnet must conserve the total angular momentum. For a nanomagnet embedded in a rigid body, reversal of the magnetic moment will cause the body to rotate as a whole. When embedded in an elastic environment, tunneling of the magnetic moment will cause local elastic twists of the crystal structure. In this thesis, I will present a theoretical study of the interplay between magnetization and rotations in a variety of nanomagnetic systems which have some degree of rotational freedom. We investigate the effect of rotational freedom on the tunnel splitting of a nanomagnet which is free to rotate about its easy axis. Calculating the exact instanton of the coupled equations of motion shows that mechanical freedom of the particle renormalizes the easy axis anisotropy, increasing the tunnel splitting. To understand magnetization dynamics in free particles, we study a quantum mechanical model of a tunneling spin embedded in a rigid rotor. The exact energy levels for a symmetric rotor exhibit first and second order quantum phase transitions between states with different values the magnetic moment. A quantum phase diagram is obtained in which the magnetic moment depends strongly on the moments of inertia. An intrinsic contribution to decoherence of current oscillations of a flux qubit must come from the angular momentum it transfers to the surrounding body. Within exactly solvable models of a qubit embedded in a rigid body and an elastic medium, we show that slow decoherence is permitted if the solid is macroscopically large. The spin-boson model is one of the simplest representations of a two-level system interacting with a quantum harmonic oscillator, yet has eluded a closed-form solution. I investigate some possible approaches to understanding its spectrum. The Landau-Zener dynamics of a tunneling spin coupled to a torsional resonator show that for certain parameter ranges the system exhibits multiple Landau-Zener transitions
Logic of infinite quantum systems
NASA Astrophysics Data System (ADS)
Mundici, Daniele
1993-10-01
Limits of sequences of finite-dimensional (AF) C *-algebras, such as the CAR algebra for the ideal Fermi gas, are a standard mathematical tool to describe quantum statistical systems arising as thermodynamic limits of finite spin systems. Only in the infinite-volume limit one can, for instance, describe phase transitions as singularities in the thermodynamic potentials, and handle the proliferation of physically inequivalent Hilbert space representations of a system with infinitely many degrees of freedom. As is well known, commutative AF C *-algebras correspond to countable Boolean algebras, i.e., algebras of propositions in the classical two-valued calculus. We investigate the noncommutative logic properties of general AF C *-algebras, and their corresponding systems. We stress the interplay between Gödel incompleteness and quotient structures in the light of the “nature does not have ideals” program, stating that there are no quotient structures in physics. We interpret AF C *-algebras as algebras of the infinite-valued calculus of Lukasiewicz, i.e., algebras of propositions in Ulam's “ twenty questions” game with lies.
Reprint of : A computational approach to quantum noise in time-dependent nanoelectronic devices
NASA Astrophysics Data System (ADS)
Gaury, Benoit; Waintal, Xavier
2016-08-01
We derive simple expressions that relate the noise and correlation properties of a general time-dependent quantum conductor to the wave functions of the system. The formalism provides a practical route for numerical calculations of quantum noise in an externally driven system. We illustrate the approach with numerical calculations of the noise properties associated to a voltage pulse applied on a one-dimensional conductor. The methodology is however fully general and can be used for a large class of mesoscopic conductors.
A computational approach to quantum noise in time-dependent nanoelectronic devices
NASA Astrophysics Data System (ADS)
Gaury, Benoit; Waintal, Xavier
2016-01-01
We derive simple expressions that relate the noise and correlation properties of a general time-dependent quantum conductor to the wave functions of the system. The formalism provides a practical route for numerical calculations of quantum noise in an externally driven system. We illustrate the approach with numerical calculations of the noise properties associated to a voltage pulse applied on a one-dimensional conductor. The methodology is however fully general and can be used for a large class of mesoscopic conductors.
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.
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.
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
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.
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.
Discrete quantum gravity; The Regge calculus approach
Williams, J.W. )
1992-06-01
After a brief introduction to Regge calculus, some examples of its application is quantum gravity are described in this paper. In particular, the earliest such application, by Ponzano and Regge, is discussed in some detail and it is shown how this leads naturally to current work on invariants of three-manifolds.
NASA Technical Reports Server (NTRS)
1975-01-01
The methodology of ECASTAR was presented and a discussion of the application of technology to energy conservation was given. This methodology constitutes an overview and blueprint for the analysis of energy conservation actions, and is subdivided into the following sections: the systems approach, constraints and criteria, application of the method (systems approach display, ECASTAR team, study phases and objectives, requirements and impacts, trade-off, integration, and feedback), an example of the method (technology applications).
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…
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. PMID:23377293
Multiparticle correlations in quaternionic quantum systems
NASA Astrophysics Data System (ADS)
Brumby, S. P.; Joshi, G. C.; Anderson, R.
1995-02-01
We investigate the outcome of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multiparticle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements.
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.
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
Interpreting Quantum Mechanics according to a Pragmatist Approach
NASA Astrophysics Data System (ADS)
Bächtold, Manuel
2008-09-01
The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.
Local shortcut to adiabaticity for quantum many-body systems
NASA Astrophysics Data System (ADS)
Mukherjee, Victor; Montangero, Simone; Fazio, Rosario
2016-06-01
We study the environmentally assisted local transitionless dynamics in closed spin systems driven through quantum critical points. In general the shortcut to adaiabaticity (STA) in quantum critical systems requires highly nonlocal control Hamiltonians. In this work we develop an approach to achieve local shortcuts to adiabaticity (LSTA) in spin chains, using local control fields which scale polynomially with the system size, following universal critical exponents. We relate the control fields to reduced fidelity susceptibility and use the transverse Ising model in one dimension to exemplify our generic results. We also extend our analysis to achieve LSTA in central spin models.
Quantum correlations in a clusterlike system
Chen Yixin; Li Shengwen; Yin Zhi
2010-11-15
We discuss a clusterlike one-dimensional system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system and is well protected against external local perturbations. All these facts show that the system is topologically ordered. We also find a string order parameter to characterize the quantum phase transition. Besides, we investigate two-site correlations including entanglement, quantum discord, and mutual information. We study the different divergence behaviors of the correlations. The quantum correlation decays exponentially in both topological and magnetic phases, and diverges in reversed power law at the critical point. And we find that in topological order systems, the global difference of topology induced by dimension can be reflected in local quantum correlations.
Chapter 2 A Single Quantum System
NASA Astrophysics Data System (ADS)
Toschek, Peter E.
The evolution of quantum mechanics has followed the critical analysis of "gedanken" experiments. Many of these concrete speculations can become implemented today in the laboratory--thanks to now available techniques. A key experiment is concerned with the time evolution of a quantum system under repeated or continuing observation. Here, three problems overlap: (1) The microphysical measurement by a macroscopic device, (2) the system's temporal evolution, and (3) the emergence of macroscopic reality out of the microcosmos. A well-known calculation shows the evolution of a quantum system being slowed down, or even obstructed, when the system is merely observed. An experiment designed to demonstrate this "quantum Zeno effect" and performed in the late eighties on an ensemble of identical atomic ions confirmed its quantum description, but turned out inconclusive with respect to the very origin of the impediment of evolution. During the past years, experiments on individual electrodynamically stored and laser-cooled ions have been performed that unequivocally demonstrate the observed system's quantum evolution being impeded. Strategy and results exclude any physical reaction on the measured object, but reveal the effect of the gain of information as put forward by the particular correlation of the ion state with the detected signal. They shed light on the process of measurement as well as on the quantum evolution and allow an epistemological interpretation.
A synthetic approach to the transfer matrix method in classical and quantum physics
NASA Astrophysics Data System (ADS)
Pujol, O.; Pérez, J. P.
2007-07-01
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 would benefit by using the abcd-matrix which in addition is easy to implement on a personal computer.
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. PMID:27419233
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
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.
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.
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.
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.
Novel systems and methods for quantum communication, quantum computation, and quantum simulation
NASA Astrophysics Data System (ADS)
Gorshkov, Alexey Vyacheslavovich
Precise control over quantum systems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators that can elucidate the physics of complex condensed matter systems. However, the fragility of quantum effects makes it very difficult to harness the power of quantum mechanics. In this thesis, we present novel systems and tools for gaining fundamental insights into the complex quantum world and for bringing practical applications of quantum mechanics closer to reality. We first optimize and show equivalence between a wide range of techniques for storage of photons in atomic ensembles. We describe experiments demonstrating the potential of our optimization algorithms for quantum communication and computation applications. Next, we combine the technique of photon storage with strong atom-atom interactions to propose a robust protocol for implementing the two-qubit photonic phase gate, which is an important ingredient in many quantum computation and communication tasks. In contrast to photon storage, many quantum computation and simulation applications require individual addressing of closely-spaced atoms, ions, quantum dots, or solid state defects. To meet this requirement, we propose a method for coherent optical far-field manipulation of quantum systems with a resolution that is not limited by the wavelength of radiation. While alkali atoms are currently the system of choice for photon storage and many other applications, we develop new methods for quantum information processing and quantum simulation with ultracold alkaline-earth atoms in optical lattices. We show how multiple qubits can be encoded in individual alkaline-earth atoms and harnessed for quantum computing and precision measurements applications. We also demonstrate that alkaline-earth atoms can be used to simulate highly symmetric systems exhibiting spin-orbital interactions and capable of providing valuable insights into strongly
Spectrum analysis with quantum dynamical systems
NASA Astrophysics Data System (ADS)
Ng, Shilin; Ang, Shan Zheng; Wheatley, Trevor A.; Yonezawa, Hidehiro; Furusawa, Akira; Huntington, Elanor H.; Tsang, Mankei
2016-04-01
Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future technology, especially in optomechanics for temperature, stochastic gravitational wave, and decoherence measurements. Motivated by this concern, here we prove a measurement-independent quantum limit to the accuracy of estimating the spectrum parameters of a classical stochastic process coupled to a quantum dynamical system. We demonstrate our results by analyzing the data from a continuous-optical-phase-estimation experiment and showing that the experimental performance with homodyne detection is close to the quantum limit. We further propose a spectral photon-counting method that can attain quantum-optimal performance for weak modulation and a coherent-state input, with an error scaling superior to that of homodyne detection at low signal-to-noise ratios.
Work, heat and entropy production in bipartite quantum systems
NASA Astrophysics Data System (ADS)
Hossein-Nejad, Hoda; O'Reilly, Edward J.; Olaya-Castro, Alexandra
2015-07-01
In bipartite quantum systems commutation relations between the Hamiltonian of each subsystem and the interaction impose fundamental constraints on the dynamics of each partition. Here we investigate work, heat and entropy production in bipartite systems characterized by particular commutators between their local Hamiltonians and the interaction operator. We consider the formalism of (Weimer et al 2008 Europhys. Lett. 83 30008), in which heat (work) is identified with energy changes that (do not) alter the local von Neumann entropy, as observed in an effective local measurement basis. We demonstrate the consequences of the commutation relations on the work and heat fluxes into each partition, and extend the formalism to open quantum systems where one, or both, partitions are subject to a Markovian thermal bath. We also discuss the relation between heat and entropy in bipartite quantum systems out of thermal equilibrium, and reconcile the aforementioned approach with the second law of thermodynamics.
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.
Quantum Mechanical Scattering in Nanoscale Systems
NASA Astrophysics Data System (ADS)
Gianfrancesco, A. G.; Ilyashenko, A.; Boucher, C. R.; Ram-Mohan, L. R.
2012-02-01
We investigate quantum scattering using the finite element method. Unlike textbook treatments employing asymptotic boundary conditions (BCs), we use modified BCs, which permits computation close to the near-field region and reduces the Cauchy BCs to Dirichlet BCs, greatly simplifying the analysis. Scattering from any finite quantum mechanical potential can be modeled, including scattering in a finite waveguide geometry and in the open domain. Being numerical, our analysis goes beyond the Born Approximation, and the finite element approach allows us to transcend geometric constraints. Results of the formulation will be presented with several case studies, including spin dependent scattering, demonstrating the high accuracy and flexibility attained in this approach.
Levy distribution in many-particle quantum systems
Ponomarev, A. V.; Denisov, S.; Haenggi, P.
2010-04-15
The Levy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grand-canonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas - a one-dimensional gas of N impenetrable (hard-core) bosons-harmonically confined on a lattice at finite temperatures obeys a Levy distribution. Finally, we extend our analysis to different confinement setups and demonstrate that the tunable Levy distribution properly reproduces momentum profiles in experimentally accessible regions. Our finding allows for calibration of complex many-body quantum states by using a unique scaling exponent.
Entanglement in algebraic quantum mechanics: Majorana fermion systems
NASA Astrophysics Data System (ADS)
Benatti, F.; Floreanini, R.
2016-07-01
Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows a complete characterization of non-separable Majorana fermion states to be obtained. These results may have direct application in quantum metrology: using Majorana systems, sub-shot-noise accuracy in parameter estimations can be achieved without preliminary resource-consuming, state entanglement operations.
Superconducting circuitry for quantum electromechanical systems
NASA Astrophysics Data System (ADS)
LaHaye, Matthew D.; Rouxinol, Francisco; Hao, Yu; Shim, Seung-Bo; Irish, Elinor K.
2015-05-01
Superconducting systems have a long history of use in experiments that push the frontiers of mechanical sensing. This includes both applied and fundamental research, which at present day ranges from quantum computing research and e orts to explore Planck-scale physics to fundamental studies on the nature of motion and the quantum limits on our ability to measure it. In this paper, we first provide a short history of the role of superconducting circuitry and devices in mechanical sensing, focusing primarily on efforts in the last decade to push the study of quantum mechanics to include motion on the scale of human-made structures. This background sets the stage for the remainder of the paper, which focuses on the development of quantum electromechanical systems (QEMS) that incorporate superconducting quantum bits (qubits), superconducting transmission line resonators and flexural nanomechanical elements. In addition to providing the motivation and relevant background on the physical behavior of these systems, we discuss our recent efforts to develop a particular type of QEMS that is based upon the Cooper-pair box (CPB) and superconducting coplanar waveguide (CPW) cavities, a system which has the potential to serve as a testbed for studying the quantum properties of motion in engineered systems.
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.
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.
Quantum algebraic approach to refined topological vertex
NASA Astrophysics Data System (ADS)
Awata, H.; Feigin, B.; Shiraishi, J.
2012-03-01
We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W 1+∞ introduced by Miki. Our construction involves trivalent intertwining operators Φ and Φ* associated with triples of the bosonic Fock modules. Resembling the topological vertex, a triple of vectors ∈ {mathbb{Z}^2} is attached to each intertwining operator, which satisfy the Calabi-Yau and smoothness conditions. It is shown that certain matrix elements of Φ and Φ* give the refined topological vertex C λ μν ( t, q) of Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined topological vertex C λ μ ν ( q, t) of Awata-Kanno. The gluing factors appears correctly when we consider any compositions of Φ and Φ*. The spectral parameters attached to Fock spaces play the role of the Kähler parameters.
A geometric approach to quantum state separation
NASA Astrophysics Data System (ADS)
Bagan, E.; Yerokhin, V.; Shehu, A.; Feldman, E.; Bergou, J. A.
2015-12-01
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure states in the general case where the known states have arbitrary a priori probabilities. The problem is formulated from a geometric perspective and shown to be equivalent to the problem of finding tangent curves within two families of conics that represent the unitarity constraints and the objective functions to be optimized, respectively. We present the corresponding analytical solutions in various forms. In the limit of perfect state separation, which is equivalent to unambiguous state discrimination, the solution exhibits a phenomenon analogous to a second order symmetry breaking phase transition. We also propose a linear optics implementation of separation which is based on the dual rail representation of qubits and single-photon multiport interferometry.
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.
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. PMID:24320365
Equilibration of quantum systems and subsystems
NASA Astrophysics Data System (ADS)
Short, Anthony J.
2011-05-01
We unify two recent results concerning equilibration in quantum theory. We first generalize a proof of Reimann (2008 Phys. Rev. Lett. 101 190403), that the expectation value of 'realistic' quantum observables will equilibrate under very general conditions, and discuss its implications for the equilibration of quantum systems. We then use this to re-derive an independent result of Linden et al (2009 Phys. Rev. E 79 061103), showing that small subsystems generically evolve to an approximately static equilibrium state. Finally, we consider subspaces in which all initial states effectively equilibrate to the same state.
ERIC Educational Resources Information Center
British Gas, London (England). Training and Development Dept.
This pamphlet is intended to assist managers and professional trainers alike in using a systems approach to training. Addressed in the individual sections of the guide are the following topics: identifying the training need (the main job objectives, the conditions under which the job is performed, and the responsibilities it involves); analyzing…
Quantum Chemical Approach to Estimating the Thermodynamics of Metabolic Reactions
NASA Astrophysics Data System (ADS)
Jinich, Adrian; Rappoport, Dmitrij; Dunn, Ian; Sanchez-Lengeling, Benjamin; Olivares-Amaya, Roberto; Noor, Elad; Even, Arren Bar; Aspuru-Guzik, Alán
2014-11-01
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.
Quantum optical properties in plasmonic systems
Ooi, C. H. Raymond
2015-04-24
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.
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.
Quantum coherence and entanglement control for atom-cavity systems
NASA Astrophysics Data System (ADS)
Shu, Wenchong
consistently solved the control dynamics of open quantum systems using this stochastic QSD approach. By implementing the QSD equation, our numerical results have revealed that how the control efficacy depends on the designed time points and shapes of the applied control pulses, and the environment memory time scale.
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.
New Results in the Quantum Statistical Approach to Parton Distributions
NASA Astrophysics Data System (ADS)
Soffer, Jacques; Bourrely, Claude; Buccella, Franco
2015-02-01
We will describe the quantum statistical approach to parton distributions allowing to obtain simultaneously the unpolarized distributions and the helicity distributions. We will present some recent results, in particular related to the nucleon spin structure in QCD. Future measurements are challenging to check the validity of this novel physical framework.
Quantum Information with Continuous Variable systems
NASA Astrophysics Data System (ADS)
Rodó, Carles
2010-05-01
This thesis deals with the study of quantum communication protocols with Continuous Variable (CV) systems. Continuous Variable systems are those described by canonical conjugated coordinates x and p endowed with infinite dimensional Hilbert spaces, thus involving a complex mathematical structure. A special class of CV states, are the so-called Gaussian states. With them, it has been possible to implement certain quantum tasks as quantum teleportation, quantum cryptography and quantum computation with fantastic experimental success. The importance of Gaussian states is two-fold; firstly, its structural mathematical description makes them much more amenable than any other CV system. Secondly, its production, manipulation and detection with current optical technology can be done with a very high degree of accuracy and control. Nevertheless, it is known that in spite of their exceptional role within the space of all Continuous Variable states, in fact, Gaussian states are not always the best candidates to perform quantum information tasks. Thus non-Gaussian states emerge as potentially good candidates for communication and computation purposes.
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.
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
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. PMID:18518481
Superconducting Quantum Arrays for Broadband RF Systems
NASA Astrophysics Data System (ADS)
Kornev, V.; Sharafiev, A.; Soloviev, I.; Kolotinskiy, N.; Mukhanov, O.
2014-05-01
Superconducting Quantum Arrays (SQAs), homogenous arrays of Superconducting Quantum Cells, are developed for implementation of broadband radio frequency (RF) systems capable of providing highly linear magnetic signal to voltage transfer with high dynamic range, including active electrically small antennas (ESAs). Among the proposed quantum cells which are bi-SQUID and Differential Quantum Cell (DQC), the latter delivered better performance for SQAs. A prototype of the transformer-less active ESA based on a 2D SQA with nonsuperconducting electric connection of the DQCs was fabricated using HYPRES niobium process with critical current density 4.5 kA/cm2. The measured voltage response is characterized by a peak-to-peak swing of ~100 mV and steepness of ~6500 μV/μT.
Locality, entanglement, and thermalization of isolated quantum systems
NASA Astrophysics Data System (ADS)
Khlebnikov, S.; Kruczenski, M.
2014-11-01
A way to understand thermalization in an isolated system is to interpret it as an increase in entanglement between subsystems. Here we test this idea through a combination of analytical and Krylov-subspace-based numerical methods applied to a quantum gas of bosons. We find that the entanglement entropy of a subsystem is rapidly generated at the initial state of the evolution, to quickly approach the thermal value. Our results also provide an accurate numerical test of the eigenstate thermalization hypothesis (ETH), according to which a single energy eigenstate of an isolated system behaves in certain respects as a thermal state. In the context of quantum black holes, we propose that the ETH is a quantum version of the classical no-hair theorem.
Double-Slit Interference Pattern for a Macroscopic Quantum System
NASA Astrophysics Data System (ADS)
Naeij, Hamid Reza; Shafiee, Afshin
2016-07-01
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.
Locality, entanglement, and thermalization of isolated quantum systems.
Khlebnikov, S; Kruczenski, M
2014-11-01
A way to understand thermalization in an isolated system is to interpret it as an increase in entanglement between subsystems. Here we test this idea through a combination of analytical and Krylov-subspace-based numerical methods applied to a quantum gas of bosons. We find that the entanglement entropy of a subsystem is rapidly generated at the initial state of the evolution, to quickly approach the thermal value. Our results also provide an accurate numerical test of the eigenstate thermalization hypothesis (ETH), according to which a single energy eigenstate of an isolated system behaves in certain respects as a thermal state. In the context of quantum black holes, we propose that the ETH is a quantum version of the classical no-hair theorem. PMID:25493719
Quantum Bound States in a C-C60 System
NASA Astrophysics Data System (ADS)
Adam, R. M.; Sofianos, S. A.
2015-03-01
We investigate the quantum mechanical system of a carbon "test atom" in the proximity of a C60 molecule, both inside and outside the fullerene "cage". Two sets of bound states are found to exist, a deeply bound set inside the cage and another weakly bound set outside it. Tunnelling between these regions is highly unlikely to happen because of the extreme height and width of the potential barrier. However, we predict that a layer of atoms could be adsorbed onto C60 by forming a quantum mechanical bound state, with the adsorbed atoms being concentrated above the "panels" of the buckyball, consistent with "bucky onions" observed experimentally. Until now analysis of such fullerene systems has been via classical mechanics, but a quantum approach reveals new insights.
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. PMID:22669908
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.
Distribution of Quantum Coherence in Multipartite Systems.
Radhakrishnan, Chandrashekar; Parthasarathy, Manikandan; Jambulingam, Segar; Byrnes, Tim
2016-04-15
The distribution of coherence in multipartite systems is examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or is distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence. PMID:27127948
Distribution of Quantum Coherence in Multipartite Systems
NASA Astrophysics Data System (ADS)
Radhakrishnan, Chandrashekar; Parthasarathy, Manikandan; Jambulingam, Segar; Byrnes, Tim
2016-04-01
The distribution of coherence in multipartite systems is examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or is distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the X X Z Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence.
Quantum cognition: a new theoretical approach to psychology.
Bruza, Peter D; Wang, Zheng; Busemeyer, Jerome R
2015-07-01
What type of probability theory best describes the way humans make judgments under uncertainty and decisions under conflict? Although rational models of cognition have become prominent and have achieved much success, they adhere to the laws of classical probability theory despite the fact that human reasoning does not always conform to these laws. For this reason we have seen the recent emergence of models based on an alternative probabilistic framework drawn from quantum theory. These quantum models show promise in addressing cognitive phenomena that have proven recalcitrant to modeling by means of classical probability theory. This review compares and contrasts probabilistic models based on Bayesian or classical versus quantum principles, and highlights the advantages and disadvantages of each approach. PMID:26058709
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. PMID:27482736
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.
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
Quantum temporal probabilities in tunneling systems
NASA Astrophysics Data System (ADS)
Anastopoulos, Charis; Savvidou, Ntina
2013-09-01
We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines 'classical' time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlation functions of the quantum field associated with tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects of the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region. Finally, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems.
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.
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
Molecular dynamics of large systems with quantum corrections for the nuclei
NASA Astrophysics Data System (ADS)
Gu, Bing; Garashchuk, Sophya
2015-12-01
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, C37H15 and a calculation of the ground state of solid 4He simulated by a cell 180-atoms.