两硬币量子游走模型中的相干动力学

量子游走是量子计算的重要模型,而多硬币量子游走模型由于在量子通讯协议中表现突出也越来越受到人们的关注.量子相干不仅可以刻画量子态的特点,也可以反映量子演化过程的性质.主要对一维圆上两硬币量子游走模型的量子相干性进行了分析.一方面,讨论了初始量子态和硬币算子的选取对量子相干的影响.当硬币算子为Hadamard算子且初态只要在位置子空间上是均衡叠加态,整个量子游走演化过程是具有周期性的,且量子相干仅依赖于步数和圆上顶点的个数;当初始态是均衡叠加态而对硬币算子没有任何限制时,量子相干的演化也极具规律性.另一方面,发现在利用量子游走实现完美状态转移(perfect state transfer)的过程中,硬币算子的选取直接影响量子相干的值.最后,探讨了2种量子游走模型之间的等价性,并基于此指出了其在量子隐形传输(quantum teleportation)中的应用和改进的可能性.     

基于量子自编码器的量子混合态压缩

量子数据的大小会影响量子计算机的处理速度,量子数据压缩可以减小量子计算机的存储和运行时间,提高量子设备利用率,并减少对容错能力的要求。量子数据压缩技术推动了量子信息和量子计算的发展。量子自编码器是一种提取输入态中最相关特征的前馈型神经网络,后被用作压缩量子数据,来对纯态进行压缩。论文研究了量子自编码器对混合量子态的压缩效果。基于量桨平台（Paddle Quantum）,对量子混合态压缩进行了模拟仿真,结果显示量子自编码器对量子混合态有很好的压缩效果。     

基于状态距离的量子控制策略

基于Bures距离，选择一个表征量子系统期望态和实际态间距离的Lyapunov函数.考虑到初始态与期望态分别正交和不正交的情况，提出一类带有状态反馈的控制策略，它可以保证闭环控制系统的稳定性.特别详细地分析、推导和证明了系统的渐进稳定性.最后，在一个自旋1/2粒子系统上进行了仿真实验，分析了不同参数情况下系统的状态演化时间和控制值间的关系.研究结果对于量子系统的控制具有一般理论意义.     

石墨烯量子点和量子比特

本文主要回顾了石墨烯量子点的制备以及基于石墨烯量子点自旋和电荷量子比特操作的研究进展,由于石墨烯材料相对较轻的原子重量使其具有较小的自旋轨道相互作用,另外含有核自旋的碳同位素13C在自然界中的含量大约只占1%,这使得超精细相互作用(即核自旋和电子自旋相互作用)较弱,所以石墨烯比其他材料具有较长的自旋退相干时间,在量子计算和量子信息中有非常好的应用前景.本文计算了5种静电约束制备的石墨烯量子点:1)扶手型单层石墨烯纳米条带,2)单层石墨烯圆盘,3)双层石墨烯圆盘,4)ABC堆积型三层石墨烯圆盘,5)ABA堆积型三层石墨烯圆盘.石墨烯量子点中自旋比特应用的关键是破坏谷简并,在1)中,主要是利用边界条件破坏谷简并,而2)–5)中是利用外磁场破坏谷简并.文章进一步介绍了自旋轨道相互作用和超精细相互作用对石墨烯量子点中自旋操作的影响.     

量子计算模拟及优化方法综述

在处理某些大规模并行问题时,量子计算因量子位独特的叠加态和纠缠态特性,相比经典计算机在并行处理方面具有更明显的优势。现阶段,物理量子比特计算机受限于可扩展性、相干时间和量子门操作精度,在经典计算机上开展量子计算模拟成为研究量子优越性和量子算法的有效途径。然而,随着量子比特数的增加,模拟所需的计算机资源呈指数增长。因此,研究大规模量子计算模拟在保证计算准确度、精度及效率的情况下减少模拟所需资源具有重要意义。从量子比特、量子门、量子线路、量子操作系统等方面展开,阐述量子计算的基本原理和背景知识。同时总结基于经典计算机的量子计算模拟基本方法,分析不同方法的设计思路和优缺点,列举目前常见的量子计算模拟器。在此基础上,针对量子计算模拟的通信开销问题,从节点拆分和通信优化2个方面出发,讨论基于超级计算机集群的量子计算模拟优化方法。     

广义量子Loop程序初探

在经典计算中,Loop程序是非常重要的程序。对量子计算中Loop程序进行研究非常必要。定义了体为量子运算的广义量子Loop程序,给出了量子Loop程序在输入态上终止,几乎终止以及不终止的定义基于任意的初始态。并证明了量子Loop程序在给定输入态上终止的充要条件以及程序终止的充要条件。作为应用,验证了体为酉运算的量子Loop程序嵌套是一个广义的量子Loop程序。     

一种新型量子演化算法及其应用研究

针对传统演化算法难以模拟量子物理特性的难题,提出一种新型量子演化算法模型。采用将进化算法与量子计算相结合的方法,在常规染色体结构上附加随机干涉,从数理角度模拟量子计算的叠态、纠缠等特性。将其应用于解决多维背包问题,实验结果表明,该算法能增加种群的基因多样性,并提高全局优化能力。     

自旋量子系统的可控李代数计算

动态系统可控性同是经典和量子控制中研究的一个基本问题,本文研究了单自旋和双自旋量子系统的可控李代数的计算.首先基于量子系统可控的等价性条件,通过单量子系统Hamiltonian算符的李括号运算,给出了与基系数相关的系统可控的充要条件.然后利用Cartan分解方法构造了李代数su(4)的矩阵基,同时根据可控性基本定理提出了Hamiltonian算符多重李括号的计算方法及系统的可控性判据.     

量子投影滤波

量子滤波器基于贝叶斯原理,利用连续弱测量数据给出当前时刻量子系统状态的最优估计,是量子计算和量子调控技术中极为重要的一环.然而,随着量子系统能级数提高,量子滤波器的实时计算复杂度呈二次型增长.本文介绍了一种量子投影滤波方法,用于减少量子滤波器的实时计算复杂度.基于量子信息几何方法,量子轨迹被限制在了一个由一类非归一化量子密度矩阵组成的子流形中.量子态从而可通过计算子流形的坐标系统来近似获得.仿真实验说明了投影滤波方法的有效性.     

量子信息技术与区块链的融合模式研究

区块链与量子信息技术是近年来兴起的前沿科学技术,受到了业界广泛的关注与研究。其中区块链具有去中心化性质,以区块链为核心技术的应用在金融科技、物联网、民生与政治等诸多领域相继涌现。量子信息技术主要分为量子计算、量子通信、量子测量。其中量子计算的研究主要体现在相较于经典计算的计算优越性,量子计算的运行速度已被证明在解决某些复杂问题上远超经典计算。而在两者迅猛发展的同时,相互之间也存在亟需解决的问题。由于区块链采用的部分经典密码学技术已被证明会被量子计算破解,例如基于非对称密码体制的数字签名,导致区块链的安全受到威胁。针对此问题,已有研究表明,将量子信息技术应用于区块链,可以保护其不受量子攻击。以区块链与量子信息技术相结合为出发点,通过介绍区块链和量子计算的基本结构,以及分析区块链遭受的量子挑战并总结现有的量子解决方案,指出区块链和量子信息技术的融合可以促进区块链在量子时代良好地发展,而这也是不可阻挡的趋势。     

Perfect state transfer via quantum probability theory

The transfer of quantum states plays an important role in quantum information processing. In fact, the transfer of a quantum state from point A to point B with unit fidelity has been the center of attention during the last decades. One of the ways to aim this goal is to transfer a quantum state in a spin chain described by designing a Hamiltonian in which a mirror symmetry with respect to the network center is created. In this paper, we introduce a method based on the spectral distribution of the adjacency matrix and stratifying a spin network, with respect to an arbitrary vertex denoted by o which is called starting vertex (reference vertex), to make perfect quantum state transfer possible between antipodes in the spin network. Then we design the coupling coefficients in a way to create a mirror symmetry in the Hamiltonian with respect to the center of the network. In this method the initial state is encoded on the starting vertex and then it is received at its antipode. There is no need to consider any external control in this approach.     

Quantum computing and quantum simulation with group-II atoms

Recent experimental progress in controlling neutral group-II atoms for optical clocks, and in the production of degenerate gases with group-II atoms has given rise to novel opportunities to address challenges in quantum computing and quantum simulation. In these systems, it is possible to encode qubits in nuclear spin states, which are decoupled from the electronic state in the ¹S₀ ground state and the long-lived ³P₀ metastable state on the clock transition. This leads to quantum computing scenarios where qubits are stored in long lived nuclear spin states, while electronic states can be accessed independently, for cooling of the atoms, as well as manipulation and readout of the qubits. The high nuclear spin in some fermionic isotopes also offers opportunities for the encoding of multiple qubits on a single atom, as well as providing an opportunity for studying many-body physics in systems with a high spin symmetry. Here we review recent experimental and theoretical progress in these areas, and summarise the advantages and challenges for quantum computing and quantum simulation with group-II atoms.     

An implicit Lyapunov control for finite‐dimensional closed quantum systems

In this paper, the state convergence problem for closed quantum systems is investigated. We consider two degenerate cases, where the internal Hamiltonian of the system is not strongly regular or the linearized system around the target state is not controllable. Both the cases are closely related to practical systems such as one‐dimensional oscillators and coupled two spin systems. An implicit Lyapunov‐based control strategy is adopted for the convergence analysis. In particular, two kinds of Lyapunov functions are defined by implicit functions and their existences are guaranteed by a fixed point theorem. The convergence analysis is investigated by the LaSalle invariance principle for both cases. Moreover, the two Lyapunov functions are unified in a general form, and the characterization of the largest invariant set is presented. Finally, simulation studies are included to show the effectiveness and advantage of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Universality and programmability of quantum computers

Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum logic circuit model, developed by Feynman and Deutsch, has been more prominent in the research literature than Deutsch’s quantum Turing machines. Quantum Turing machines form a class closely related to deterministic and probabilistic Turing machines and one might hope to find a universal machine in this class. A universal machine is the basis of a notion of programmability. The extent to which universality has in fact been established by the pioneers in the field is examined and this key notion in theoretical computer science is scrutinised in quantum computing by distinguishing various connotations and concomitant results and problems.     

Implicit Lyapunov‐based control strategy for closed quantum systems with dipole and polarizability coupling

In this paper, the state transfer of finite dimensional closed quantum systems with dipole and polarizability coupling in non‐ideal cases is investigated. Two kinds of non‐ideal systems are considered, where the internal Hamiltonian of the system is not strongly regular and not all the eigenvectors of the internal Hamiltonian are directly coupled with the target state. Such systems often exist in practical quantum systems such as the one‐dimensional oscillator and coupled two‐spin system. An implicit Lyapunov‐based control strategy is proposed here with convergence analysis for quantum systems modeled by finite dimensional bilinear Schrödinger equations. Specifically, two kinds of Lyapunov functions are defined via implicit functions, and their existences are guaranteed with the help of a fixed point theorem. Then, the local convergence analysis is investigated with the explicit characterization of the largest invariant set by LaSalle invariance principle. Finally, the performance of the feedback design is illustrated by numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd.     

利用相位的自旋1/2量子系统的相干控制

针对两个自旋1/2粒子组成的封闭量子系统, 建立了具有Ising相互作用的量子系统模型. 在此基础上通过具有特定幅值及相对相位的半反直觉脉冲, 制备了相应的量子相干态. 并通过系统数值仿真实验, 归纳出系统终态与相对相位之间的近似关系式, 分析了控制脉冲的幅值和时间延迟对制备过程的影响. 利用部分绝热通道技术实现了相位相干控制.     

基于四粒子团簇态的量子安全直接通信协议仿真

随着量子通信在近年来的不断发展, 量子安全直接通信成为了量子通信的一大重要分支。但目前的实验设备很难满足量子通信实验, 导致通信协议的正确性和安全性无法得到验证。针对这一问题, 提出了一种协议仿真算法。在Microsoft Visual C++6. 0平台上利用C++语言编写了量子安全直接通信协议的仿真程序, 最终实现了发送方和接收方之间的有效安全通信。仿真结果体现了量子通信的高效性和绝对安全性。实验结果与理论结果相吻合, 进一步验证了协议是安全、正确的, 也证明了用计算机对量子计算进行仿真的可行性。     

磁场控制下的电子自旋量子系统参数辨识

了解量子控制系统的性能参数是设计精确控制器的基础. 为解决这一问题, 本文基于量子过程层析, 提出了辨识量子控制系统参数的方法, 设计了以电子自旋磁场控制系统为对象的具体实验方案, 并利用计算机仿真技术对其进行了模拟. 仿真结果表明, 辨识得到的量子控制系统参数与理论值较为吻合, 达到了预定的准确度指标. 结合理论分析和仿真结果可知, 利用量子过程层析可以有效实现量子控制系统的参数辨识.     

基于恒定磁场的电子自旋量子比特系统任意量子态的最优制备

借助单量子位的Bloch球面表示,结合量子门实现量子态幺正演化的量子态调控机制,以恒定磁场为控制场,引入开关控制思想,提出了一种针对电子自旋量子系统任意量了态的最优制备策略.建立了量子系统及控制场的模型,并借助李群李代数,由经典最优控制的思想,获得任意量子态的最优制备.理论分析与仿真实验说明了该策略的优越性.     

量子计算与量子计算机

量子计算是一种依照量子力学理论进行的新型计算,量子计算的基础和原理以及重要量子算法为在计算速度上超越图灵机模型提供了可能。在发展与完善量子计算理论的同时,量子计算机的物理实现方案也被不断提出。光子量子计算机,基于核磁共振、离子阱或谐振子等技术的量子计算机物理模型已被逐一实现。近年来亦出现了几个典型的基于量子计算机的量子算法。2001年在一台基于核磁共振技术的量子计算设备上成功演示的Shor量子算法,显示出量子计算机处理复杂问题的巨大潜能。文章对当前量子计算机物理实现的研究进展进行了综述。