Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtaining probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph is obtained by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determining probability of walk on compficated graphs. Using this method, we calculate the probability of Continuous-time classical and quantum random walks on many of finite direct product Cayley graphs （complete cycle, complete Kn, charter and n-cube）. Also, we inquire that the classical state the stationary uniform distribution is reached as t→∞ but for quantum state is not always satisfied.

Optimized quantum random-walk search algorithm for multi-solution search

This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.

Decoherence in optimized quantum random-walk search algorithm

This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Shenvi et al.have proposed a quantum algorithm based on quantum walking called Shenvi-Kempe-Whaley(SKW)algorithm,but this search algorithm can only search one target state and use a specific search target state vector.Therefore,when there are more than two target nodes in the search space,the algorithm has certain limitations.Even though a multiobjective SKW search algorithm was proposed later,when the number of target nodes is more than two,the SKW search algorithm cannot be mapped to the same quotient graph.In addition,the calculation of the optimal target state depends on the number of target states m.In previous studies,quantum computing and testing algorithms were used to solve this problem.But these solutions require more Oracle calls and cannot get a high accuracy rate.Therefore,to solve the above problems,we improve the multi-target quantum walk search algorithm,and construct a controllable quantum walk search algorithm under the condition of unknown number of target states.By dividing the Hilbert space into multiple subspaces,the accuracy of the search algorithm is improved from p_(c)=(1/2)-O(1/n)to p_(c)=1-O(1/n).And by adding detection gate phase,the algorithm can stop when the amplitude of the target state becomes the maximum for the first time,and the algorithm can always maintain the optimal number of iterations,so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach t_(f)=(π/2)(?).

Effects of systematic phase errors on optimized quantum random-walk search algorithm

This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover＇s algorithm.

连续时间量子行走算法在截断单形晶格上的搜索研究

为证明连续时间量子行走算法在结构型数据库上的搜索可以实现二次加速的效果,对结构型数据库中的截断单形晶格类型,进行了连续时间量子行走算法的应用研究。首先对截断单形晶格进行对称性分析,确定系统演化所处的希尔伯特空间,然后用哈密顿量本征态与基础态的平方叠加、和简并微扰理论两种方法来求解系统演化需要的临界跳跃率。最后通过对图中的边进行加权的方法,合并了量子搜索的步骤,缩短了系统演化的时间,从而实现了平方加速的效果,并表明了边的权重对量子搜索过程的影响。

量子计算机:量子算法与物理实现

量子算法与物理实现是量子计算机研究中的两个基本问题。本文首先总结了相关领域的主要进展,并讨论了有代表性的量子算法,特别介绍了用于求解线性方程组的量子算法,分析了影响新量子算法提出的因素。然后,探讨了物理实现的迪文森佐判据,并介绍了典型的实现方案及性能比较。同时,也关注了对量子计算机研究持有异议的观点。最后,对量子计算机的新研究方向作了探讨。

基于相位匹配的量子行走搜索算法及电路实现

量子行走是经典随机行走在量子力学框架下的对应,理论上可以用来解决一类无序数据库的搜索问题.因为携带信息的量子态的扩散速度与经典相比有二次方式的增长,所以量子行走优于经典随机行走,量子行走的特性值得加以利用.量子行走作为一种新发现的物理现象的数学描述,引发了一种新的思维方式,孕育了一种新的理论计算模型.最新研究表明,量子行走本身也是一种通用计算模型,可被视为设计量子算法的高级工具,因此受到部分计算机理论科学领域学者的关注和研究.对于多数问题求解方案的量子算法的设计,理论上可以只在量子行走模型下进行考虑.基于Grover算法的相位匹配条件,本文提出了一个新的基于量子行走的搜索算法.理论演算表明:一般情况下本算法的时间复杂度与Grover算法相同,但是当搜索的目标数目多于总数的1/3时,本算法搜索成功的概率要大于Grover算法.本文不但利用Grover算法中相位匹配条件构造了一个新的量子行走搜索算法,而且在本研究室原有的量子电路设计研究成果的基础上给出了该算法的量子电路表述.

开放量子行走的击中时分析

作为量子搜索算法研究的一个基本工具,量子行走是一个重要研究课题。同时,击中时是衡量量子行走到达某一目标顶点速度的标准,对量子算法研究具有广泛的应用。在开放量子环境下,给出开放量子行走的四种击中时定义:单次击中时、并行击中时、平均击中时和极限击中时。区分四种击中时,说明前两种用于刻画开放量子行走局部到达目标顶点,而后两种从全局和极限角度分析目标顶点到达情况。针对同质开放量子行走、异质开放量子行走和嵌套开放量子行走,分别给出四种击中时具体计算。

集成光量子计算的研究进展

基于量子力学的叠加和纠缠等性质,量子计算具备超越经典计算机的强大计算能力.光子作为一种高效信息载体,具有传输速度快、操控性高及相干时间长的优点,是实现量子计算的一个理想物理平台.集成光量子技术,使得我们在微型结构上便能够稳定地实现光量子态的产生、处理和探测.近年来,随着新兴的集成光量子技术的快速发展,集成光量子计算的实验复杂度和规模在不断提高,并成功模拟和解决了复杂的物理和计算问题.为此,本综述总结了近年来集成光量子计算的技术进展,包括各类集成光量子实验平台,并讨论了基于集成光量子平台实现的量子行走实验范例.最后,我们亦简述了基于光量子行走而实现的量子算法和量子模拟的方案.

基于IBM Q平台的量子算法研究

为探究多比特量子算法在量子芯片和模拟器中的实现现状,分别在IBM量子芯片和模拟器上运行Grover搜索算法、量子随机行走算法以及量子傅里叶变换算法。针对2 bit Grover搜索算法和2 bit量子随机行走算法,分析测量次数对运行结果的影响并选用最高可模拟次数对量子芯片和模拟器的运算结果进行比对。设计并运行5 bit量子傅里叶变换算法和3 bit Grover搜索算法,分别采用IBM Q模拟器进行最高次数的模拟。实验结果表明,量子芯片测试结果并没有随测量次数的增加而优化,模拟器计算结果的准确度明显优于量子芯片。

基于置换群的多粒子环上量子行走的反馈搜索算法

在量子计算科学中,如何更好地构建量子搜索算法一直以来受到学者们的广泛关注,并且基于量子行走寻找新的搜索算法也仍吸引着学者们不断深入研究与探索.本文从减少搜索过程中的时间消耗、增加算法搜索的准确性和可控性等多方面进行考虑,提出了一种基于置换群的多粒子量子行走搜索算法.首先分析得到置换群在空间中可看成一个闭环,定义了置换集合,并且通过同构映射将数据点所在数据集映射到定义的置换集,使得置换集合中元素数据点形成一一对应的关系.其次,根据给定初始态和硬币算符,在数据点集与置换集合张成的搜索空间中利用多粒子的量子行走在环上进行目标数据搜索.最后,根据函数Φ(w)=1找到目标数据,并用量子态存储数值,用于形成搜索算法的反馈控制;同时通过控制硬币算符从而控制量子行走在环上的行走方向,增加搜索的可操作性与准确性.本文利用多粒子的量子行走进行搜索,分析得到粒子数量参数j与时间复杂度呈非线性负相关;提出的量子行走搜索算法符合零点条件与下确界条件,且不受变量数j的影响;通过数值分析得到量子行走搜索算法的时间复杂度等价于O(3√N),相比于Grover搜索算法提高了搜索效率.

Quantum Algorithm Design:Techniques and Applications

In recent years, rapid developments of quantum computer are witnessed in both the hardware and the algorithm domains, making it necessary to have an updated review of some major techniques and applications in quantum algorithm design.In this survey as well as tutorial article, the authors ?rst present an overview of the development of quantum algorithms, then investigate ?ve important techniques: Quantum phase estimation, linear combination of unitaries, quantum linear solver, Grover search, and quantum walk, together with their applications in quantum state preparation, quantum machine learning, and quantum search. In the end, the authors collect some open problems in?uencing the development of future quantum algorithms.

基于量子漫步算法的地震震前异常挖掘

地震特别是大震前会产生一些异常,但这些异常信息难以识别,导致无法充分利用这些异常信息预测地震的发生时间,减少地震带来的灾害影响.针对这个问题,提出一种基于量子漫步算法的震前异常挖掘方法,提取汶川地震和芦山地震的震前射出长波辐射(Outgoing Long-wave Radiation, OLR)异常,进而计算地震前后的P值,异常值CD等数据,通过统计分析方法,探索OLR异常与地震的关系.并且通过实验将该算法扩展到最近十年左右全球发生的8.0级及以上地震,验证该算法的有效性.实验结果表明,该算法能够有效的反映在地震前后会出现OLR异常,而且越大的地震异常越明显.因此,该算法适用于震前异常挖掘.

量子游走相关算法研究进展

量子游走是经典随机游走在量子世界的对应,已经被证明是一种通用的量子计算模型,也是设计高效量子算法和量子信息处理方案的基础工具之一。简要介绍了量子游走的概念和基本原理,阐述了量子游走在搜索问题及其他方面的一些重要应用,并总结和展望了量子游走的未来发展前景。

基于随机梯度下降算法实现对环上量子游走的动态完全控制

寻找如何实现幺正量子操作是量子计算领域的基本问题,主要研究通过环上的离散时间量子游走实现任意幺正量子操作的可能.首先推广引入了特殊的环上的离散时间量子游走模型,并对模型实现任意量子操作的有效性进行了探讨.对于两量子比特的量子系统,给出了通用量子门集合与量子傅里叶变换的构造解.由于高维情况构造解较难精确给出,引入机器学习中常用的随机梯度下降算法,得以在高维系统近似实现所需要的幺正量子操作.此外,如对算法进行进一步微调,可以在位置空间上的实现任意的幺正量子操作以及两结果半正定算子测量.在高维情况下,这意味着通过控制两能级的硬币系统即可控制位置空间上大型系统,从而实现小系统对大系统的间接完全控制.这些任务的完成表明,基于随机梯度下降算法可以实现对整个环上量子游走过程的动态完全控制.

一种加速量子网络信息分布的研究方法

Gossip算法是描述自然网络中不可靠信息传播协议的常用术语,但并不是网络实体间通信的最佳设计。经典的Gossip算法主要针对数据比较稳定的场景,如果数据变化比较频繁,会对网络带宽、CPU资源造成很大的负载。该算法无法保证在某个时刻所有节点状态一致,比较适合小数据量的同步。由此考虑把Gossip算法应用在量子网络中,不考虑量子网络的初始配置,通过结构更新来加速量子网络信息分布,更新允许通过量子隐形传态来异化信息,这种处理方式是兼容量子网络游走的,可证明任何量子网络都可以更新到与本地操作和经典通信的最佳配置。Gossip算法具有多方面的应用,该研究方法可以作为量子网络计算中的一种参考模型。

Dynamical learning of a photonics quantum-state engineering process

Experimental engineering of high-dimensional quantum states is a crucial task for several quantum information protocols.However,a high degree of precision in the characterization of the noisy experimental apparatus is required to apply existing quantum-state engineering protocols.This is often lacking in practical scenarios,affecting the quality of the engineered states.We implement,experimentally,an automated adaptive optimization protocol to engineer photonic orbital angular momentum(OAM)states.The protocol,given a target output state,performs an online estimation of the quality of the currently produced states,relying on output measurement statistics,and determines how to tune the experimental parameters to optimize the state generation.To achieve this,the algorithm does not need to be imbued with a description of the generation apparatus itself.Rather,it operates in a fully black-box scenario,making the scheme applicable in a wide variety of circumstances.The handles controlled by the algorithm are the rotation angles of a series of waveplates and can be used to probabilistically generate arbitrary four-dimensional OAM states.We showcase our scheme on different target states both in classical and quantum regimes and prove its robustness to external perturbations on the control parameters.This approach represents a powerful tool for automated optimizations of noisy experimental tasks for quantum information protocols and technologies.

Fast quantum search driven by environmental engineering

Studies have demonstrated that a joined complete graph is a typical mathematical model that can support a fast quantum search. In this paper, we study the implementation of joined complete graphs in atomic systems and realize a quantum search of runtime ■ based on this implementation with a success probability of 50%. Even though the practical systems inevitably interact with the surrounding environment, we reveal that a successful quantum search can be realized through delicately engineering the environment itself. We consider that our study will bring about a feasible way to realize quantum information processing including quantum algorithms in reality.

星图上的散射量子行走搜索算法

量子行走是一种典型的量子计算模型,近年来开始受到量子计算理论研究者们的广泛关注.本文首先证明了在星图上硬币量子行走与散射量子行走的酉等价关系,之后提出了一个在星图上的散射量子行走搜索算法.该算法的时间复杂度与Grover算法相同,但是当搜索的目标数目多于总数的1/3时搜索成功概率大于Grover算法.