Quantum coupled oscillators in two-dimensional systems

Quantum coupled one- and two-well oscillators describing a single-electron dynamics in two-dimensional systems have been investigated. Time realizations for mean position and velocity of wave packet, frequency spectra and signal transmission are discussed in detail.     

Dynamical behavior of quantum correlations between two qubits coupled to an external environment

We investigate the dynamics of quantum correlations of a two-qubit system coupled to an external environment. We have considered both cases: a spin environment and a bosonic environment. In all cases, we have chosen the Bell-diagonal state as the initial state and computed the evolution of quantum correlations in terms of entanglement, quantum discord and trace distance geometric quantum discord. Special attention is paid to the singular quantum phenomena, such as entanglement sudden death, sudden transition and double sudden transitions from classical to quantum decoherence, which all depend on the initial state and the parameters related to the system and the environment. We find the trace distance geometric quantum discord has a good robustness in resisting the spin and bosonic environmental noise.     

Quantifying quantum correlations in fermionic systems using witness operators

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entanglement witness of a state with a class of problems known as semidefinite programs, which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robustness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann concurrence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.     

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

For the global stabilization of a family of feedforward nonlinear time‐delay systems whose linearized systems consist of a chain of identical oscillators, a saturated feedback control is established based on a special canonical form. The proposed control laws use not only the current states but also the delayed states for feedback, which helps maintain the decoupling property in the recursive design. Moreover, explicit conditions guaranteeing the stability of the closed‐loop system are provided. When the nonlinear terms vanish and even the oscillators are distinct, a modified saturated feedback control can still be established for the corresponding global stabilization problem. Two numerical examples are given to illustrate the effectiveness of the proposed approaches.     

Protection of quantum Fisher information for multiple phases in open quantum systems

We study the protection of quantum Fisher information (QFI) of two phases encoded in an open V-type three-level atom embedded in a zero-temperature bosonic reservoir and driven by a classical field. By transforming the problem into the model of an open driving-free V-type atom, we can then solve the dynamics analytically and study the evolution of QFI numerically. It is found that the QFI of both of the two phases can be protected effectively when the strength of the driving field is adequate. The protective effect enhances with the decrease in detuning between the frequency of the classical driving field and the frequency of the atomic transitions. Narrow width of the environmental spectrum is also beneficial for the protection of QFI of the phases.     

Computable measure of total quantum correlations of multipartite systems

Quantum discord as a measure of the quantum correlations cannot be easily computed for most of density operators. In this paper, we present a measure of the total quantum correlations that is operationally simple and can be computed effectively for an arbitrary mixed state of a multipartite system. The measure is based on the coherence vector of the party whose quantumness is investigated as well as the correlation matrix of this part with the remainder of the system. Being able to detect the quantumness of multipartite systems, such as detecting the quantum critical points in spin chains, alongside with the computability characteristic of the measure, makes it a useful indicator to be exploited in the cases which are out of the scope of the other known measures.     

Global dynamics of two coupled parametrically excited van der Pol oscillators

Using a combination of analytical and numerical methods, the global bifurcations and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators are investigated in detail. With the aid of the method of multiple scales, the slow flow equations are obtained. Based on the slow flow equations, normal form theory and the techniques of choosing complementary space are applied to find the explicit expressions of the simpler normal form associated with a double zero and a pair of pure imaginary eigenvalues. By the simpler normal form, using the global perturbation method developed by Kovacic and Wiggins, the analysis of global bifurcation and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators is given. The results indicate that there exists a Silnikov type single-pulse homoclinic orbit for this class of system which implies the chaotic motions can occur. Numerical simulations are also given and verify the analytical predictions.     

Controllability of quantum harmonic oscillators

It is proven in a previous paper that any modal approximation of the one-dimensional quantum harmonic oscillator is controllable. We prove here that, contrary to such finite-dimensional approximations, the original infinite-dimensional system is not controllable: Its controllable part is of dimension 2 and corresponds to the dynamics of the average position. More generally, we prove that, for the quantum harmonic oscillator of any dimension, similar lacks of controllability occur whatever the number of control is: the controllable part still corresponds to the average position dynamics. We show, with the quantum particle in a moving quadratic potential, that some physically interesting motion planning questions can be however solved.     

Emulation of complex open quantum systems using superconducting qubits

With quantum computers being out of reach for now, quantum simulators are alternative devices for efficient and accurate simulation of problems that are challenging to tackle using conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing “hybrid” simulators by combining both techniques. Here we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bacteria with over 250 phonon modes coupled to each electronic state. Furthermore, we propose physical setups that can be used to reproduce the quantum dynamics of a standard and multiple-mode Holstein model. The proposed scheme is based on currently available technology of superconducting circuits consist of flux qubits and quantum oscillators.     

两个耦合Van der Pol振子系统的一阶近似守恒量

用直接积分法计算两个耦合Van der Pol振子系统的一阶近似守恒量,将两个耦合Van der Pol振子系统看成是未受微扰系统与微扰项的迭加,先通过坐标变换将未受微扰系统解耦,并对解耦系统的3种可能状态进行讨论,得到未受微扰系统的13个精确守恒量,再考虑微扰项对精确守恒量的影响,运用一阶近似守恒量的性质,得到1个稳定的一阶近似守恒量.另外,由13个精确守恒量直接得到13个平凡的一阶近似守恒量.     

A note on quantum correlations in Werner states under two collective noises

Influences of two collective noises, i.e., the dephasing noise and the rotating noise, on quantum correlations in Werner states are considered in this note. It is found that the collective noises do not alter the correlations as far as quantum discord and geometry discord as quantifiers are concerned. Alternatively, quantum correlations in Werner states are robust against the noises.     

Emergent synchrony in locally coupled neural oscillators

The discovery of long range synchronous oscillations in the visual cortex has triggered much interest in understanding the underlying neural mechanisms and in exploring possible applications of neural oscillations. Many neural models thus proposed end up relying on global connections, leading to the question of whether lateral connections alone can produce remote synchronization. With a formulation different from frequently used phase models, we find that locally coupled neural oscillators can yield global synchrony. The model employs a previously suggested mechanism that the efficacy of the connections is allowed to change on a fast time scale. Based on the known connectivity of the visual cortex, the model outputs closely resemble the experimental findings. Furthermore, we illustrate the potential of locally connected oscillator networks in perceptual grouping and pattern segmentation, which seems missing in globally connected ones.     

Entanglement and quantum state transfer between two atoms trapped in two indirectly coupled cavities

Quantum Information Processing - We propose a one-step scheme for implementing entanglement generation and the quantum state transfer between two atomic qubits trapped in two different cavities...     

给定环境下稳定开放量子系统的哈密顿量方法

针对耗散已知情况下Lindblad主方程描述的开放量子系统,本文通过哈密顿量的设计实现了系统对于目标平衡态的稳定化.借助相干矢量体系,将矩阵形式下的原始系统模型转换为了一个矢量形式的线性系统,并证明了变换前后系统稳定属性的等价性.通过保证矢量化线性系统模型的稳定性,并使系统的唯一平衡态等于期望的目标态,得到了系统哈密顿量的设计框架.特别地,本文讨论了这两类条件下系统哈密顿量各元素的范围,并指出根据它们的交集即可构成所设计的系统哈密顿量.最后,在一个两能级系统上进行了数值仿真实验,验证了本文哈密顿量稳定化方案的有效性.     

随机开放量子系统的纯态开关反馈控制EI北大核心CSCD

针对目标态为纯态的情况,本文对有限维随机开放量子系统,提出一种同时适用于本征态和叠加态的开关控制,它是由常量控制和基于李雅普诺夫方法设计的控制律组成,实现随机开放量子系统的状态转移和收敛控制,其中,李雅普诺夫函数为系统的状态距离,常量控制用来驱动系统状态从初始状态进入含有目标态的收敛域中,李雅普诺夫控制用来使进入收敛域中的状态继续收敛到期望的目标态.将所提出的控制方法,应用于2比特随机开放量子系统进行了数值仿真实验,并与本征态开关控制律方法进行了性能对比,实验结果表明了所提出的控制律的优越性.     

Controlling the loss of quantum correlations via quantum memory channels

Quantum Information Processing - We consider the support of the limit distribution of the Grover walk on crystal lattices with the linear scaling. The orbit of the Grover walk is denoted by the...     

QuTiP: An open-source Python framework for the dynamics of open quantum systems

We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.Program summaryProgram title: QuTiP: The Quantum Toolbox in PythonCatalogue identifier: AEMB_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 16 482No. of bytes in distributed program, including test data, etc.: 213 438Distribution format: tar.gzProgramming language: PythonComputer: i386, x86-64Operating system: Linux, Mac OSX, WindowsRAM: 2+ GigabytesClassification: 7External routines: NumPy (http://numpy.scipy.org/), SciPy (http://www.scipy.org/), Matplotlib (http://matplotlib.sourceforge.net/)Nature of problem: Dynamics of open quantum systems.Solution method: Numerical solutions to Lindblad master equation or Monte Carlo wave function method.Restrictions: Problems must meet the criteria for using the master equation in Lindblad form.Running time: A few seconds up to several tens of minutes, depending on size of underlying Hilbert space.     

Geometry of quantum state space and quantum correlations

Quantum state space is endowed with a metric structure, and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by \(2\times 2\) density matrices, we determine a particular Riemannian metric for a state \(\rho \) and show that if \(\rho \) gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equal to square root of that particular Riemannian metric . Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.     

量子谐振子蚁群算法

通过分析目前蚁群算法存在的问题和改进算法的优点,发现量子谐振子系统物理特性能够保证算法最终的收敛性.通过量子谐振子高能态到低能态的转变过程和信息素的增加过程相对应,从而更新信息素,在物理上给算法提供了理论依据.通过量子旋转门改变城市转移规则,通过泡利矩阵变异使蚂蚁有更广阔的空间.综合量子谐振子以上的优点,提出了量子谐振子蚁群算法,并在旅行商问题(TSP)上取得了较好的寻优路径.