Realization of Kraus operators and POVM measurements using a duality quantum computer

In this paper, we discuss the ability of realizing Kraus operators and POVM measurements in a duality quantum computer. We prove that not all the Kraus operators can be realized in a duality quantum computer. We introduce a new type of duality quantum circuit, multiduality circuit, by repeating the previous version of duality quantum circuit as a unit, and we can realize universal Kraus operators and POVM measurements with this new circuit. We also give a measure of the complexity of the Kraus operations in terms of the minimum number the units required to realize the Kraus operations in multiduality circuit.     

基于波粒二相机实现大数因子分解

利用波粒二相机,根据原始的分解算法、量子Shor算法以及经典计算机中的费马算法和莱曼算法,提出了能够进行大数因子分解的几种算法.通过对原始分解算法的改进,使得用原始大数因子分解的问题由N次变为1次完成.通过对费马算法和莱曼算法改进,减少了大数质因子分解过程的计算复杂度.与量子计算机相比,波粒二相机使得在经典上需要指数步完成的算法,在多项式时间内就可以解决,减少了计算复杂度.     

Existence and construction of a quantum channel with given inputs and outputs

We derive that sufficient and necessary conditions for existence of a quantum channel φ and a generalized unitary operation ε sending Ai to Bi(1≤ i≤ k) for two given families {Ai}i=1k,{Bi}i=1k of matrices,respectively.As an application,a sufficient and necessary condition for existence of a unitary duality quantum computer with given input-output states is obtained.     

Experimental one-way quantum computing

Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward of their outcomes. Because of the essential role of measurement, a one-way quantum computer is irreversible. In the one-way quantum computer, the order and choices of measurements determine the algorithm computed. We have experimentally realized four-qubit cluster states encoded into the polarization state of four photons. We characterize the quantum state fully by implementing experimental four-qubit quantum state tomography. Using this cluster state, we demonstrate the feasibility of one-way quantum computing through a universal set of one- and two-qubit operations. Finally, our implementation of Grover's search algorithm demonstrates that one-way quantum computation is ideally suited for such tasks.     

Quantum Metropolis sampling

The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.     

Q2Chemistry: A quantum computation platform for quantum chemistry

Quantum computers provide new opportunities for quantum chemistry. In this article,we present a versatile, extensible, and efficient software package, named Q2Chemistry, for developing quantum algorithms and quantum inspired classical algorithms in the field of quantum chemistry. In Q2Chemistry, the wave function and Hamiltonian can be conveniently mapped into the qubit space, then quantum circuits can be generated corresponding to a specific quantum algorithm already implemented in the package or newly developed by the users. The generated circuits can be dispatched to either a physical quantum computer, if available, or to the internal virtual quantum computer realized by simulating quantum circuits on classical computers. As demonstrated by our benchmark simulations, Q2Chemistry achieves excellent performance in simulating medium scale quantum circuits using the matrix product state algorithm. Applications of Q2Chemistry to simulate molecules and periodic systems are given with performance analysis.     

A scheme to implement the Deutsch-Josza algorithm on a superconducting charge-qubit quantum computer

We have studied the implementation of the Deutsch-Josza quantum algorithm in a superconducting charge-qubit quantum computer. Different from previous studies, we have used the inductance coupled system of You et al. The detailed pulse sequences have been designed for the four possible functions in a 2-qubit system. The result is generalized to an arbitrary n-qubit system. This scheme will be useful for practical implementation of the algorithm.     

Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance.

The number of steps any classical computer requires in order to find the prime factors of an l-digit integer N increases exponentially with l, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of N = 15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquid-state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system.     

PID在轴承模拟试验加载系统中的应用

将小二元回归数学模型与PID控制算法相结合，对轴承模拟试验加载系统的智能控制进行了试验研究。由于微机控制系统的计算机程序具有很高的灵活性，可以方便地修改PID控制算式，使得这种控制方式有很高的控制精度。实践也表明PID参数的调整使力加载过程更加准确，经实际运行得到了理想的控制效果。     

AdS黑洞中量子复杂度的晚期增长率与自由能关系

量子复杂度与自由能的关系研究为复杂度-作用量猜想和复杂度-体积猜想之间搭起了一座桥梁.首先,通过无奇点的Bardeen-AdS黑洞、f(R)引力下的带电黑洞和Born-Infeld AdS黑洞检验量子复杂度晚期增长率与自由能关系的普适性;然后,讨论了将量子复杂度晚期增长率作为探针研究相变的可能性;最后,研究了量子复杂度晚期增长率是否违反Lloyd上限的问题.     

Quantum computing in molecular magnets

Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.     

“Which Way”实验,波粒二象性的可能破缺和新的二象性

最近的某些实验显示出量子物理的许多新特性.WhichWay(WW)实验暗示波粒二象性可能破缺.由此应该继续检验量子波动性对单个粒子、极小的时空范围、短程强弱相互作用及高能过程等方面的有效性.这些实验为粒子物理的发展方向提出了多种可能性.基于对量子力学的统计基础和粒子物理的总体特征进行的讨论,可以得到理论的一种发展方向:对称性-统计性的新的二象性.由于统计性和量子场论一一对应,它又联系于一般的泛量子理论.       

光量子与光的波粒二象性的历史评述——物理学方法案例分析

本文通过对光量子假说及波粒二象性提出过程的历史分析,指出光量子假说不是爱因斯坦对普朗克能量子假说的推广,并对现有教科书对光量子及光的波粒二象性的处理提出了自己的看法.     

量子计算原理及研究进展

 量子计算机是量子力学与计算问题相结合的产物,是近几年的研究热点,引起了广泛的社会关注。本文回顾量子计算机的发展,介绍了量子算法和量子计算模型,并以离子阱和超导线路为例阐述了量子计算机的物理实现,然后介绍了为了克服消相干而发展出的量子编码,以玻色取样为例讨论了量子霸权。展望未来,近期内可以展示量子霸权,进而实现解决特定问题的量子模拟器,但是普适的量子计算机的研制仍然需要很长的时间。     

八粒子量子态对彩色图像的存储方案

经典彩色图像的存储方法存在着数据量很大且很费内存等缺点,针对这些缺点,提出了一种在量子比特阵列中采用八粒子量子态存储彩色图像的方法,借助于量子态的巨大存储能力,通过采用量子并行计算特性的Grover量子搜索算法,起到平方根加速的理想效果.在图像存储和图像重构的过程中,对量子比特阵列进行搜索找到相应的彩色图像,证明所采用的方法有很好的效果.     

波粒二象性的信息熵解释

微观粒子具有波粒二象性,因而微观粒子的行为并不象经典系统那样确定,其物理量的取值具有随机性.这便产生了物理解释上的困难,甚至导致了逻辑上和哲学上的困惑而无法得到一个满意的解释.若从信息论的角度出发对这种不确定性进行描述,将有可能揭示量子规律的新的一面.本文试图从信息论的角度,阐明微观量子系统间不但存在能量、动量、质量的传递,同时还存在着信息的传递,并可用信息熵表示波粒二象性的统计特性.     

A quantum algorithm that deletes marked states from an arbitrary database

We present a general quantum deletion algorithm that deletes M marked states from an N-item quantum database with arbitrary initial distribution. The general behavior of this algorithm is analyzed, and analytic result is given. When the number of marked states is no more than 3N/4 , this algorithm requires just a single query, and this achieves exponential speedup over classical algorithm.     

一类绝对值规划的算法

针对一类绝对值规划问题,提出对偶规划,给出其弱对偶性及对偶问题的最优性充分条件,并证明对偶间隙也是该类绝对值规划问题的解。同时,引入变量代换,基于线性规划的单纯形法,提出该类绝对值规划问题的全局优化求解算法。算例表明该算法是有效的。     

Driven coherent oscillations of a single electron spin in a quantum dot

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.     

一种基于量子遗传算法的多播路由算法

提出了一种基于量子遗传算法QGA（quantum genetic algorithm）解决多播QoS（quality of service）路由问题的算法．介绍了量子遗传算法的基本原理，给出了算法实现的方法和具体流程，并进行了量子遗传算法在多播路由选择优化方面的仿真实验，证明了量子遗传算法优于常规遗传算法．