Quantum theory of nonlinear processes

Principles of development of the quantum theory of nonlinear processes on the basis of Lagrangian formulation are discussed. It is shown that in the framework of this formulation it is possible to preserve succession from the classical theory and, in particular, use these methods for studies of quantum systems. The quantum dispersion of a nonlinear oscillator excited by an external source and of a parametric generator is calculated. Its role is established in the solution of the problem of stability of oscillations.     

Quantum nonlinear resonance in a strong electromagnetic field

The motion of a one-dimensional quantum weakly anharmonic system under the influence of harmonic external field is treated in the range where the transition frequency between the neighboring levels is close to the frequency of the harmonic field (quantum nonlinear resonance). The case of the strong external field, in which the Rabi frequency for the transitions is large in comparison with the field frequency, is studied. The expression for compact wavepackets of quasienergy states that change their content and width periodically (and, possibly, strongly), is obtained.     

Markov Quantum Feedback Control Based on Homodyne Measurement of a Two-Qubit System

We consider the system consisting of two qubits collectively damped,with the output being unit-efficiency measured and subsequently fedback to control the system state. Our primary goal in this paper is (i) to solve the feedback-modified master equation, (ii) to demonstrate the ability of feedback control based on the solutions, and (iii) to pick out different steady states by choosing different driving strengths and feedback strengths tocounteract the effects of both damping and the measurement back-action on the system. We further investigate some properties of the equilibrium steady state, its distribution probability and entanglement vs. the driving and feedback amplitudes. We find that in our feedback model feedback plays a negative role in producing entanglement.     

非线性相互作用下三qubit系统中的量子关联

通过对系统施加不同的非线性作用,利用量子关联的几何度量,研究了三个qubit体系中的两体量子关联.不同的非线性相互作用模型都能使系统产生最大值为0.1752的量子关联.z方向的横场对量子关联的优化有控制作用,对于三个模型,通过调节z方向的横场,系统能产生最大值为0.09645的平均量子关联.最佳组合的三个横场,不仅能够大幅度提高量子关联的振荡周期,使得两qubit长时间处于量子关联态,而且还能够提高两qubit的平均量子关联.     

两量子比特非线性相互作用模型中的量子关联

运用量子态变换的方法论证了两个qubit纯态中量子关联与纠缠的等价性.并利用三种带有横场的非线性相互作用模型研究了两个qubit体系中的量子关联.发现合适的横场对于最大量子关联态的获得、平均量子关联的提高都有着积极的作用.两个qubit体系获得最大量子关联时,不同模型,不同的横场,对应的量子态却各不相同.     

量子过程神经网络模型算法及应用

为提高过程神经网络的逼近和泛化能力, 从研究过程神经元信息处理的量子计算实现机理入手, 提出基于量子旋转门及多位受控非门的物理意义构造量子过程神经元的新思想. 将离散化后的过程式输入信息作为受控非门的控制位, 经过量子旋转门作用后控制目标量子位的状态, 以目标量子位处于状态|1>概率幅作为量子过程神经元的输出. 以量子过程神经元为隐层, 普通神经元为输出层, 可构成量子过程神经网络. 基于量子计算机理推导了该模型的学习算法. 将该模型用于太阳黑子数年均值预测, 应用结果表明, 所提方法与普通过程神经网络相比, 预测精度有所提高, 对于复杂预测问题具有一定理论意义和实用价值.     

Quantum mechanics as a classical diffusion process

A direct construction is provided showing that the classical expectation value for the energy of a particle executing a classical diffusion process is equivalent to the quantum mechanical form with a Hamiltonian structured like that for a charged particle in an electromagnetic field.     

Accelerating an adiabatic process by nonlinear sweeping

We investigate the acceleration of an adiabatic process with the same survival probability of the ground state by sweeping a parameter nonlinearly, fast in the wide gap region and slowly in the narrow gap region, in contrast to the usual linear sweeping. We find the expected acceleration both in the Landau-Zener tunneling model and in the adiabatic quantum computing model for factorizing the number N - 21.     

On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms

In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.     

用两耦合非线性振子模型研究量子纠缠和相干性

我们研究两耦合非线性振子模型的量子纠缠和量子相干动力学,结果表明在适当条件下,纠缠熵与相干度是正相关的.我们也讨论纠缠熵和相干度与两振子相互作用能的联系.     

用两耦合非线性振子模型研究量子纠缠和相干性

我们研究两耦合非线性振子模型的量子纠缠和量子相干动力学, 结果表明在适当条件下, 纠缠熵与相干度是正相关的. 我们也讨论纠缠熵和相干度与两振子子相互作用能的联系.     

Quantum Zeno effect in two coupled nonlinear optical processes

Consecutive nonlinear optical interactions consisting of two coupled parametric processes, namely, the nondegenerate spontaneous parametric down-conversion and up-conversion, are analyzed. The vacuum state of the input light is considered to be an unstable state decaying into a reservoir of down-converted modes, with one of the modes generated being continuously measured using the up-conversion process. Mean photon numbers at interacting frequencies are studied. Special attention is paid to the case where the nonlinear coupling coefficient for the up-conversion process is much larger than that for the nondegenerate spontaneous parametric down-conversion. It is shown that in this case the result of such consecutive interactions can be interpreted from the viewpoint of the quantum Zeno effect.     

Variational Beta Process Hidden Markov Models with Shared Hidden States for Trajectory Recognition

Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.     

基于灰色马尔科夫模型的团簇数量演变预测方法

本文以分子动力学方法模拟液态Si的凝固过程为基础,首次建立基于马尔科夫修正的灰色预测模型对不同团簇的演变过程进行分析,利用该模型对液态Si降温过程中团簇数量的变化进行预测.结果证实应用灰色马尔科夫模型在对团簇结构的演变预测是可行的,采用马尔科夫链预测方法能提高预测结果的准确性,该方法能有效描述凝固过程中团簇的形成和演变的整体变化规律,为研究材料微观结构演变提供了一种新的思路和方法 .     

基于灰色马尔科夫模型的团簇数量演变预测方法

本文以分子动力学方法模拟液态Si的凝固过程为基础,首次建立基于马尔科夫修正的灰色预测模型对不同团簇的演变过程进行分析,利用该模型对液态Si降温过程中团簇数量的变化进行预测。结果证实应用灰色马尔科夫模型在对团簇结构的演变预测是可行的,采用马尔科夫链预测方法能提高预测结果的准确性,该方法能有效描述凝固过程中团簇的形成和演变的整体变化规律,为研究材料微观结构演变提供了一种新的思路和方法。     

Dynamical Entropy of Generalized Quantum Markov Chains on Gauge-invariant C *-algebras

We prove that the mean entropy and the dynamical entropy are equal for generalized quantum Markov chains on gauge-invariant C ^*-algebras.     

The Wronskian technique for nonlinear evolution equations

The investigation of the exact traveling wave solutions to the nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena. To understand the mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. The Wronskian technique is a powerful tool to construct multi-soliton solutions for many nonlinear evolution equations possessing Hirota bilinear forms. In the process of utilizing the Wronskian technique,the main difficulty lies in the construction of a system of linear differential conditions, which is not unique. In this paper,we give a universal method to construct a system of linear differential conditions.     

Quantum routing of few photons using a nonlinear cavity coupled to two chiral waveguides

We investigate few-photon scattering properties in two one-dimensional waveguides chirally coupled to a nonlinear cavity. The quantum states of scattered few photons are solved analytically via a real-space approach, and the solution indicates the few-photon reflection and transmission properties. When inputting two photons of equal energy to resonate with the cavity, the propagation characteristics of the two photons will be interesting, which is different from the previous anti-bunching effects with a quantum emitter. More importantly, when the total energy of the two incident photons equals the energy of a nonlinear cavity accommodating two photons, influence of the bound state will become larger to result in disappearance of antibunching effect. However, the bound state has no effect on probability of routing to another waveguide.     

一类强非线性发展方程孤波变分迭代解法

研究了一类强非线性发展方程. 利用变分迭代方法,首先构造了相应的变分;其次选取了适当的初始近似;再用迭代方法得到了孤波的任意次精度的近似解. 关键词： 发展方程 非线性 孤波 近似方法.     

囚禁离子非线性Rabi模型量子场熵演化特性

本文研究了基于单个囚禁离子与两束激光场相互作用的非线性Rabi模型中的纠缠动力学.利用Von-Neumann熵来表征纠缠度.通过数值模拟,详细讨论了Lamb-Dicke参数对量子场熵的影响.在单光子非线性Rabi模型中,随着Lamb-Dicke参数和初始平均光子数的增加,场熵的平均值并不单调增加.在双光子非线性Rabi模型中,场熵的时间演化是周期性振荡的.随着Lamb-Dicke参数的增加,场熵的周期振荡逐渐消失.对于较小的Lamb-Dicke参数,纠缠和退纠缠周期性地出现.