The non-Markovian quantum behavior of open systems

It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo wave function method that enables the stochastic treatment of the full non-Markovian behavior of open quantum systems. Numerical simulations are carried out which demonstrate that the method is applicable to open systems strongly coupled to a bosonic reservoir, as well as to the interaction with a spin bath. Full details of the simulation algorithms are given, together with an investigation of the dynamics of fluctuations. Several potential generalizations of the method are outlined.Received: 29 October 2003, Published online: 10 February 2004PACS: 03.65.Yz Decoherence; open systems; quantum statistical methods - 02.70.Ss Quantum Monte Carlo methods - 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)     

Monte Carlo techniques for real-time quantum dynamics

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the “weight”, and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithms are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.     

Demonstration of essentiality of entanglement in a Deutsch-like quantum algorithm

Quantum algorithms can be used to efficiently solve certain classically intractable problems by exploiting quantum parallelism. However, the effectiveness of quantum entanglement in quantum computing remains a question of debate. This study presents a new quantum algorithm that shows entanglement could provide advantages over both classical algorithms and quantum algo- rithms without entanglement. Experiments are implemented to demonstrate the proposed algorithm using superconducting qubits. Results show the viability of the algorithm and suggest that entanglement is essential in obtaining quantum speedup for certain problems in quantum computing. The study provides reliable and clear guidance for developing useful quantum algorithms.     

Quantum statistical monte carlo methods and applications to spin systems

A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem⁽¹⁾ thatd-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this geneal appoach to quantum spin systems are reviewed. A new Monte Carlo method, “thermo field Monte Carlo method,” is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures. Invited talk presented at “Frontiers of Quantum Monte Carlo,” Los Alamos National Laboratory, September 3–6, 1985.     

Quantum Parallelism in Quantum Information Processing

We investigate distinguishability (measured by fidelity) of the initial and the final state of a qubit, which is an object of the so-called nonideal quantum measurement of the first kind. We show that the fidelity of a nonideal measurement can be greater than the fidelity of the corresponding ideal measurement. This result is somewhat counterintuitive, and can be traced back to the quantum parallelism in quantum operations, in analogy with the quantum parallelism manifested in the quantum computing theory. In particular, as the quantum parallelism in quantum computing underlies efficient quantum algorithms, the quantum parallelism in quantum information theory underlies the classically unexpected increase of fidelity.     

Quantum Monte Carlo Study of Frustrated Spin Chain Under External Field

In this paper a stochastic series expansion quantum Monte Carlo algorithm is used to study a frustrated spin chain with diagonal next-nearest-neighbor interactions. The detailed balance conditions are carefully analyzed to improve the efficiency of simulation process. As an application of this algothrim, the total magnetization, the static structure factor and spin-stiffness arecalculated for a certain set of system parameters as a function of external field strength.     

量子信息与计算

量子信息与计算是物理学目前研究的热门领域 .本文简要地介绍量子计算的一些基本概念 :量子纠缠、量子位、量子寄存器、量子并行计算和量子纠错 .并介绍两种典型的量子信息技术 :量子密码和量子传物 .     

量子计算的研究进展

量子计算由于其强大的并行计算能力和可以有效的模拟量子行为的能力而日益受到人们的关注。本文介绍了量子计算的基本原理、实现量子计算的基本要求、量子计算的根本困难、可能的解决办法，以及当前的几个有希望实现量子计算的物理系统。最后介绍了我们课题组在分布式量子计算和基于固有耦合的编码量子计算的实验与理论方面的工作。     

Event-enhanced quantum theory and piecewise deterministic dynamics

The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave-function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID-tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment-induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.     

Accelerated Monte Carlo for Optimal Estimation of Time Series

Asbstract By casting stochastic optimal estimation of time series in path integral form, one can apply analytical and computational techniques of equilibrium statistical mechanics. In particular, one can use standard or accelerated Monte Carlo methods for smoothing, filtering and/or prediction. Here we demonstrate the applicability and efficiency of generalized (nonlocal) hybrid Monte Carlo and multigrid methods applied to optimal estimation, specifically smoothing. We test these methods on a stochastic diffusion dynamics in a bistable potential. This particular problem has been chosen to illustrate the speedup due to the nonlocal sampling technique, and because there is an available optimal solution which can be used to validate the solution via the hybrid Monte Carlo strategy. In addition to showing that the nonlocal hybrid Monte Carlo is statistically accurate, we demonstrate a significant speedup compared with other strategies, thus making it a practical alternative to smoothing/filtering and data assimilation on problems with state vectors of fairly large dimensions, as well as a large total number of time steps.     

(3 1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator

In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1 1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3 1)-dimensional harmonic oscillator.``     

Transition Matrix Monte Carlo Method

We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss the performance of the methods. The results are compared with single histogram method, multi-canonical method, and other methods. In many aspects, the present method is an improvement over the previous methods.     

Simulations: A tool for studying quantum condensed matter systems

Quantum Monte Carlo techniques provide a new method for studying the properties of condensed matter systems. A review of this approach and the type of information which it can provide is given. Talk presented at the Frontiers of Monte Carlo Meeting, Los Alamos National Laboratory, September, 1985.     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Perspectives on relativistic quantum chaos

Quantum Chaos has been investigated for about a half century.It is an old yet vigorous interdisciplinary field with new concepts and interesting topics emerging constantly.Recent years have witnessed a growing interest in quantum chaos in relativistic quantum systems,leading to the still developing field of relativistic quantum chaos.The purpose of this paper is not to provide a thorough review of this area,but rather to outline the basics and introduce the key concepts and methods in a concise way.A few representative topics are discussed,which may help the readers to quickly grasp the essentials of relativistic quantum chaos.A brief overview of the general topics in quantum chaos has also been provided with rich references.     

The Large Hadron Collider: A Marvel of Technology,edited by Lyndon Evans

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessible way, and discusses the potential of a future theory of quantum learning.     

Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.