量子计算机的研究与应用

介绍了量子计算的最新研究方向,简述了量子计算和量子信息技术在保密通信、量子算法、数据库搜索等重要领域的应用。分析了量子计算机与经典计算机相比所具有的优点和目前制约量子计算机应用发展的主要因素,最后展望了其未来发展趋势。     

量子小波变换算法及线路实现

随着小波理论研究的深入,以及小波分析在信号分析和图像处理等领域的广泛应用,小波分析在量子计算领域中也越来越受到重视.应用置换矩阵、W-H变换矩阵和量子傅立叶变换矩阵来对Haar小波及D(4)小波变换矩阵进行分解,给出其算法,然后得出其完整的量子逻辑线路图,最后分析其复杂度.     

Quantum estimation,control and learning: Opportunities and challenges

The development of estimation and control theories for quantum systems is a fundamental task for practical quantum technology. This vision article presents a brief introduction to challenging problems and potential opportunities in the emerging areas of quantum estimation, control and learning. The topics cover quantum state estimation, quantum parameter identification, quantum filtering, quantum open-loop control, quantum feedback control, machine learning for estimation and control of quantum systems, and quantum machine learning.     

A Survey on quantum computing technology

The power of quantum computing technologies is based on the fundamentals of quantum mechanics, such as quantum superposition, quantum entanglement, or the no-cloning theorem. Since these phenomena have no classical analogue, similar results cannot be achieved within the framework of traditional computing. The experimental insights of quantum computing technologies have already been demonstrated, and several studies are in progress. Here we review the most recent results of quantum computation technology and address the open problems of the field.     

Mathematical models of quantum computation

In this paper, we introduce two mathematical models of realistic quantum computation. First, we develop a theory of bulk quantum computation such as NMR (Nuclear Magnetic Resonance) quantum computation. For this purpose, we define bulk quantum Turing machine (BQTM for short) as a model of bulk quantum computation. Then, we define complexity classes EBQP, BBQP and ZBQP as counterparts of the quantum complexity classes EQP, BQP and ZQP, respectively, and show that EBQP=EQP, BBQP=BQP and ZBQP=ZQP. This implies that BQTMs are polynomially related to ordinary QTMs as long as they are used to solve decision problems. We also show that these two types of QTMs are also polynomially related when they solve a function problem which has a unique solution. Furthermore, we show that BQTMs can solve certain instances of NP-complete problems efficiently. On the other hand, in the theory of quantum computation, only feed-forward quantum circuits are investigated, because a quantum circuit represents a sequence of applications of time evolution operators. But, if a quantum computer is a physical device where the gates are interactions controlled by a current computer such as laser pulses on trapped ions, NMR and most implementation proposals, it is natural to describe quantum circuits as ones that have feedback loops if we want to visualize the total amount of the necessary hardware. For this purpose, we introduce a quantum recurrent circuit model, which is a quantum circuit with feedback loops. LetC be a quantum recurrent circuit which solves the satisfiability problem for a blackbox Boolean function includingn variables with probability at least 1/2. And lets be the size ofC (i.e. the number of the gates inC) andt be the number of iterations that is needed forC to solve the satisfiability problem. Then, we show that, for those quantum recurrent circuits, the minimum value ofmax(s, t) isO(n ²2 ^n/3). Tetsuro Nishino, D.Sc.: He is presently an Associate Professor in the Department of Information and Communication Engineering, The University of Electro-Communications. He received the B.S., M.S. and D.Sc degrees in mathematics from Waseda University, in 1982, 1984 and 1991 respectively. From 1984 to 1987, he joined Tokyo Research Laboratory, IBM Japan. From 1987 to 1992, he was a Research Associate of Tokyo Denki University, and from 1992 to 1994, he was an Associate Professor of Japan Advanced Institute of Science and Technology, Hokuriku. His main interests are circuit complexity theory, computational learning theory and quantum complexity theory.     

Self-protected quantum algorithms based on quantum state tomography

Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new quantum algorithms are given which are based on quantum state tomography. These include an algorithm for the calculation of several quantum mechanical expectation values and an algorithm for the determination of polynomial factors. These quantum algorithms are important in their own right. However, it is remarkable that these quantum algorithms are immune to a large class of errors. We describe these algorithms and provide conditions for immunity.      

量子力学和量子计算机

In this paper,the relationship between computation and physics and the application of the principle of Quantum mechanics to Quantum Computing and Quantum Computers was reviewed     

Optimal computation with non-unitary quantum walks

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times, respectively. Non-unitary quantum walks can provide a useful optimisation of these properties, producing a more uniform distribution on the line, and faster mixing times on the cycle. We investigate the interplay between quantum and random dynamics by comparing the resources required, and examining numerically how the level of quantum correlations varies during the walk. We show numerically that the optimal non-unitary quantum walk proceeds such that the quantum correlations are nearly all removed at the point of the final measurement. This requires only O(logT)$O(logT)$ random bits for a quantum walk of T$T$ steps.     

Combating Quantum Burst-errors with Quantum Interleaving Technique

Based on the interleaving technique, a kn-qubit code is constructed in this paper with more error-correcting ability than one n-qubit quantum error-correcting code without introducing the redundant qubits. By converting quantum bursts of errors into quantum random errors with the help of the quantum interleaving of the several states of the same quantum code, the proposed technique becomes an effective means to combat quantum bursts of errors. It is much simple and applicable for the quantum interleaving techniques to be used in the optical-fiber communications.     

Quantum covariance and filtering

We give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum covariances and conditional expectations on von Neumann algebras play an essential part in the presentation.     

Analysis and synthesis of attractive quantum Markovian dynamics

We propose a general framework for investigating a large class of stabilization problems in Markovian quantum systems. Building on the notions of invariant and attractive quantum subsystem, we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics. Our general analysis results are exploited to assess the ability of open-loop Hamiltonian and output-feedback control strategies to synthesize Markovian generators which stabilize a target subsystem, subspace, or pure state. In particular, we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite-dimensional Markovian systems, that leads to a constructive strategy for designing the relevant controllers. Implications for stabilization of entangled pure states are addressed by example.     

量子查找算法的发展与前瞻

量子查找算法是一种利用波的特性进行查找的新方法，它以量子位作为描述问题 的基本信息单位，为 NP-完全问题的解决提供了一种有效的途径。量子查找算法的主要特 点 是查找的高度并行性、非结构化查找和巨大的信息存储容量。该文介绍了量子查找的基 本思 想；综述了量子查找的典型实例及其广泛应用；分析了量子查找算法的特点及其与传 统算法 的关系；指出了量子计算目前存在的问题；最后对量子计算的发展前景进行展望。     

Message Authentication Scheme Based on Quantum Error-correction Codes

With the use of the theory of Quantum Error-correction Code （QECC）, a quantum message authentication scheme is proposed to defend several different kinds of attacks in this paper. The scheme can simultaneously distribute the sharing key and verify the identities of the communicators. Security analysis shows that the scheme is unconditional security.     

OptQC: An optimized parallel quantum compiler

The software package Qcompiler (Chen and Wang 2013) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software OptQC  , which finds permutation matrices P$P$ and Q$Q$ for a given unitary matrix U$U$ such that the number of gates in the quantum circuit of U=Q^TP^TU^′PQ$U=Q^T{P}^T{U}^{\prime }PQ$ is significantly reduced, where U^′$U^{\prime }$ is equivalent to U$U$ up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators.     

构造最小生成树的量子算法

图的最小生成树问题是网络优化中的一类基本问题。目前构造最小生成树的算法都是基于传统计算机的算法如Prim算法和Kruskal算法。该文提出了一个用于构造图的最小生成树的量子算法,它结合量子搜索的方法和经典Kruskal算法的思想,对于n个节点m条边的图,依次搜索出n-1条边使它们构成一棵最小生成树。这一算法的时间复杂性为O(nm√)。与经典Kruskal算法相比,在同等条件下,该文的算法有较快的加速。     

基于量子层析的量子态测量方案及其仿真

为解决量子态信息获取问题,基于量子层析理论,深入分析了单量子比特和多量子比特的层析理论,设计了利用量子态层析进行量子态测量的实验方案,并通过计算机仿真技术对单量子比特层析实验进行了模拟．在理论分析和仿真实验的基础上得到如下结论：通过适当选取测量次数,量子层析技术可以较为精确地重构量子态密度矩阵,获取量子态信息,同时可以兼顾实验效率．     

QKD网络量子信道管理关键技术研究

随着网络的发展,网络传播的信息日益增多,其中某些信息需要较高的安全性,因此信息加密手段的研究具有重大意义。量子密钥分发(Quantum Key Distribution,QKD)技术基于量子力学中的不可克隆定理,即不可能复制一个未知的量子态而不对其造成扰动,保证了其无条件的安全性,能够实现安全的密钥分发。但目前QKD网络规模较小,不能满足大规模组网的需求。同时,经典网络的路由技术已经不能适应QKD网络,量子信道寻径成为了一个需要解决的问题。鉴于以上问题,提出了一种能够满足较大规模QKD通信的基于光开关切换的QKD网络模型,并重点设计了其网络结构和信令体系,在此基础上设计了一个用于量子信道寻径的先导信号协议,并提出了量子信道管理机制。经实验验证,该模型的性能良好。     

QSATS: MPI-driven quantum simulations of atomic solids at zero temperature

We describe QSATS, a parallel code for performing variational path integral simulations of the quantum mechanical ground state of monatomic solids. QSATS is designed to treat Boltzmann quantum solids, in which individual atoms are permanently associated with distinguishable crystal lattice sites and undergo large-amplitude zero-point motions around these sites. We demonstrate the capabilities of QSATS by using it to compute the total energy and potential energy of hexagonal close packed solid ⁴He at the density .

Program summary

Program title:QSATSCatalogue identifier: AEJE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 7329No. of bytes in distributed program, including test data, etc.: 61 685Distribution format: tar.gzProgramming language: Fortran 77.Computer: QSATS should execute on any distributed parallel computing system that has the Message Passing Interface (MPI) [1] libraries installed.Operating system: Unix or Linux.Has the code been vectorized or parallelized?: Yes, parallelized using MPI [1].RAM: The memory requirements of QSATS depend on both the number of atoms in the crystal and the number of replicas in the variational path integral chain. For parameter sets A and C (described in the long write-up), approximately 4.5 Mbytes and 12 Mbytes, respectively, are required for data storage by QSATS (exclusive of the executable code).Classification: 7.7, 16.13.External routines: Message Passing Interface (MPI) [1]Nature of problem: QSATS simulates the quantum mechanical ground state for a monatomic crystal characterized by large-amplitude zero-point motions of individual (distinguishable) atoms around their nominal lattice sites.Solution method: QSATS employs variational path integral quantum Monte Carlo techniques to project the system?s ground state wave function out of a suitably-chosen trial wave function.Restrictions: QSATS neglects quantum statistical effects associated with the exchange of identical particles. As distributed, QSATS assumes that the potential energy function for the crystal is a pairwise additive sum of atom–atom interactions.Additional comments: An auxiliary program, ELOC, is provided that uses the output generated by QSATS to compute both the crystal?s ground state energy and the expectation value of the crystal?s potential energy. End users can modify ELOC as needed to compute the expectation value of other coordinate-space observables.Running time: QSATS requires roughly 3 hours to run a simulation using parameter set A on a cluster of 12 Xeon processors with clock speed 2.8 GHz. Roughly 15 hours are needed to run a simulation using parameter set C on the same cluster.References:

• [1] 

  For information about MPI, visit http://www.mcs.anl.gov/mpi/.