Noiseless Subsystems and the Structure of the Commutant in Quantum Error Correction

The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of this set of operators. This led to the discovery of noiseless subsystems. They are described by a set of operators obtained from the commutant of the noise generators. In this paper we derive a general method to compute the structure of this commutant in the case of unital noise. PACS: 03.67.–a, 03.67.Pp     

Quantum Computing and Information Extraction for Dynamical Quantum Systems

We discuss the simulation of complex dynamical systems on a quantum computer. We show that a quantum computer can be used to efficiently extract relevant physical information. It is possible to simulate the dynamical localization of classical chaos and extract the localization length with quadratic speed up with respect to any known classical computation. We can also compute with algebraic speed up the diffusion coefficient and the diffusion exponent, both in the regimes of Brownian and anomalous diffusion. Finally, we show that it is possible to extract the fidelity of the quantum motion, which measures the stability of the system under perturbations, with exponential speed up. The so-called quantum sawtooth map model is used as a test bench to illustrate these results. PACS: 03.67.Lx, 05.45.Mt     

三值量子基本门及其对量子Fourier变换的电路实现

理论上可以把量子基本门组合在一起来实现任何量子电路和构建可伸缩的量子计算机。但由于构建量子线路的量子基本门数量庞大,要正确控制这些量子门十分困难。因此,如何减少构建量子线路的基本门数量是一个非常重要和非常有意义的课题。提出采用三值量子态系统构建量子计算机,并给出了一组三值量子基本门的功能定义、算子矩阵和量子线路图。定义的基本门主要包括三值量子非门、三值控制非门、三值Hadamard门、三值量子交换门和三值控制CR_k门等。通过把量子Fourier变换推广到三值量子态,成功运用部分三值量子基本门构建出能实现量子Fourier变换的量子线路。通过定量分析发现,三值量子Fourier变换的线路复杂度比二值情况降低了至少50%,表明三值量子基本门在降低量子计算线路复杂度方面具有巨大优势。     

Quantum Malware

When quantum communication networks proliferate they will likely be subject to a new type of attack by hackers, virus makers, and other malicious intruders. Here we introduce the concept of “quantum malware” to describe such human-made intrusions. We offer a simple solution for storage of quantum information in a manner, which protects quantum networks from quantum malware. This solution involves swapping the quantum information at random times between the network and isolated, distributed ancillas. It applies to arbitrary attack types, provided the protective operations are themselves not compromised.     

Quantum Information and the PCP Theorem

Our main result is that the membership x∈SAT (for x of length n) can be proved by a logarithmic-size quantum state |Ψ〉, together with a polynomial-size classical proof consisting of blocks of length polylog(n) bits each, such that after measuring the state |Ψ〉 the verifier only needs to read one block of the classical proof. This shows that if a short quantum witness is available then a (classical) PCP with only one query is possible. Our second result is that the class QIP/qpoly contains all languages. That is, for any language L (even non-recursive), the membership x∈L (for x of length n) can be proved by a polynomial-size quantum interactive proof, where the verifier is a polynomial-size quantum circuit with working space initiated with some quantum state |Ψ _L,n 〉 (depending only on L and n). Moreover, the interactive proof that we give is of only one round, and the messages communicated are classical. The advice |Ψ _L,n 〉 given to the verifier can also be replaced by a classical probabilistic advice, as long as this advice is kept as a secret from the prover. Our result can hence be interpreted as: the class IP/rpoly contains all languages. For the proof of the second result, we introduce the quantum low-degree-extension of a string of bits. The main result requires an additional machinery of quantum low-degree-test. R. Raz’s research was supported by Israel Science Foundation (ISF) grant.     

Quantum Communication and Information Processing with Quantum Dots

This paper reviews the single photon sources based on semiconductor quantum dots and their applications to quantum information systems. By optically pumping a system consisting of a semiconductor single quantum dot confined in a monolithic microcavity, it is possible to produce a single photon pulse stream at the Fourier transform limit with a negligible jitter. This single photon source is not only useful for BB84 quantum key distribution (QKD), but also find applications in other quantum information systems such as Ekert91/BBM92 QKD and quantum teleportation gate linear optical quantum computers.     

Visualization of the Quantum Fourier Transform Using a Quantum Computer Simulator

The quantum Fourier transform (QFT) is a key subroutine of quantum algorithms for factoring and simulation and is the heart of the hidden-subgroup problem, the solution of which is expected to lead to the development of new quantum algorithms. The QFT acts on the Hilbert space and alters the quantum mechanical phases and probability amplitudes. Unlike its classical counterpart its schematic representation and visualization are very dif.cult. The aim of this work is to develop a schematic representation and visualization of the QFT by running it on a quantum computer simulator which has been constructed in the framework of this research. Base states, superpositions of base states and entangled states are transformed and the corresponding schematic representations are presented. The visualization of the QFT presented here and the quantum computer simulator developed for this purpose may become a useful tool for introducing the QFT to students and researches without a strong background in quantum mechanics or Fourier analysis. PACS: 03.67.-a, 03.67.Lx     

新量子技术时代下的信息安全

量子技术将在未来深刻影响密码学以及信息安全行业。可以利用上千个量子比特运行量子算法的通用量子计算机将直接威胁信息安全基础算法,导致当前广泛使用的RSA等公钥密码被破解,也会使分组密码算法的密码强度减半。量子通信中量子密钥分发的实施会改变传统保密通信的物理结构。这些重大 应用价值也是发展量子技术的驱动力。结合当前一些关于量子技术的热点新闻,从量子计算和量子通信两个方面分别综述了量子技术对信息安全技术的影响。同时简要介绍了这些技术的最新发展现状,包括通用型和专用型量子计算机的发展、量子密钥分发技术实验室环境的进展以及天地一体化量子通信网络的发展状况等。最后对信息安全技术的未来形态做了思考和总结。未来量子技术将会与现有各种技术深度融合,共同存在。     

Unambiguous State Discrimination in Quantum Key Distribution

The quantum circuit and design are presented for an optimized entangling probe attacking the BB84 Protocol of quantum key distribution (QKD) and yielding maximum information to the probe. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Although standard von-Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key, if instead the probe measurements are performed with a certain positive operator valued measure (POVM), then the measurement results are unambiguous, at least some of the time. It follows that the BB84 (Bennett–Brassard 1984) protocol of quantum key distribution has a vulnerability similar to the well-known vulnerability of the B92 (Bennett 1992) protocol Pacs: 03.67.Dd, 03.67.Hk, 03.65.Ta     

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.     

量子线性卷积及其在图像处理中的应用

线性卷积在图像处理中发挥着重要作用, 但是在处理海量高分辨率图像时, 求解线性卷积会消耗许多计算资源. 为此, 本文就量子线性卷积及其在图像处理问题中的应用开展相关研究, 首先提出单通道, 单位步长, 零补充情况下的量子一维和二维线性卷积, 然后实现多通道, 非单位步长, 非零补充的情况, 最后将量子二维线性卷积应用于量子图像平滑, 量子图像锐化和量子图像边缘检测. 通过理论分析证明了量子线性卷积的空间复杂度${\rm{O}}(\mathrm{log}M)$和时间复杂度${\rm{O}}({\mathrm{log}}^{2}M)$较经典线性卷积有指数级下降, 且基于Qiskit的仿真实验成功验证了量子线性卷积和量子图像处理算法的正确性和可行性.     

网格局部性及其优化研究

数据网格已逐步在科学研究领域得到应用.提高数据网格的性能以适应分布式数据管理已经成为研究数据网格的一个热点.提出了网格局部性的概念,分析了网格局部性对数据网格性能的影响,并从增强网格局部性的角度对数据网格的性能进行优化,提出了综合跳一扩散副本替换策略(jump-DRP)和参考生物外激素的任务调度策略(JARIP).实验结果表明,考虑了网格局部性因素的jump-DRP与JARIP的策略组合提高了网格平台的任务处理性能,并对各类应用背景及任务的复杂程度具有鲁棒性.     

Spin-Based Quantum Dot Quantum Computing in Silicon

The spins of localized electrons in silicon are strong candidates for quantum information processing because of their extremely long coherence times and the integrability of Si within the present microelectronics infrastructure. This paper reviews a strategy for fabricating single electron spin qubits in gated quantum dots in Si/SiGe heterostructures. We discuss the pros and cons of using silicon, present recent advances, and outline challenges. PACS: 03.67.Pp, 03.67.Lx, 85.35.Be, 73.21.La     

Probabilities of Failure for Quantum Error Correction

We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect against errors, presenting formulae for the probability of failure when the errors affect more qudits than that specified by the code’s minimum distance. Such formulae provide a means to rank different codes of the same minimum distance. We consider both error detection and error correction, treating explicit examples in the case of stabilizer codes constructed from qubits and encoding a single qubit Pacs: 03.67.Pp     

Some Issues in Quantum Information Theory

Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the principles of quantum mechanics. In this review, we first survey some of the significant advances in quantum information theory in the last twenty years. We then focus mainly on two special subjects： discrimination of quantum objects and transformations between entanglements. More specifically, we first discuss discrimination of quantum states and quantum apparatus in both global and local settings. Secondly, we present systematical characterizations and equivalence relations of several interesting entanglement transformation phenomena, namely entanglement catalysis, multiple-copy entanglement transformation, and partial entanglement recovery.     

An Explicit Universal Gate-Set for Exchange-Only Quantum Computation

A single physical interaction might not be universal for quantum computation in general. It has been shown, however, that in some cases it can achieve universal quantum computation over a subspace. For example, by encoding logical qubits into arrays of multiple physical qubits, a single isotropic or anisotropic exchange interaction can generate a universal logical gate-set. Recently, encoded universality for the exchange interaction was explicitly demonstrated on three-qubit arrays, the smallest nontrivial encoding. We now present the exact specification of a discrete universal logical gate-set on four-qubit arrays. We show how to implement the single qubit operations exactly with at most 3 nearest neighbor exchange operations and how to generate the encoded controlled-NOT with 27 parallel nearest neighbor exchange interactions or 50 serial gates, obtained from extensive numerical optimization using genetic algorithms and Nelder–Mead searches. We also give gate-switching times for the three-qubit encoding to much higher accuracy than previously and provide the full speci.cation for exact CNOT for this encoding. Our gate-sequences are immediately applicable to implementations of quantum circuits with the exchange interaction. PACS: 03.67.Lx, 03.65.Ta, 03.65.Fd, 89.70.+c     

Estimation of Quantum Channels with Finite Resources

We examine the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We discuss simple protocols for the estimation of the parameters of several classes of channels that are studied in the current literature. A quantitative measures of the quality of the estimation schemes can be given on the basis of the standard deviation or of the fidelity. Protocols that employ entangled particles are also discussed. The use of entangled particles as a nonclassical resource enhances the estimation quality of some classes of quantum channel. Further, the methods presented here can be extended to higher dimensional quantum systems. PACS: 03.67.Hk     

量子遗传算法研究现状

Quantum Genetic Algorithm (QGA)is the combination of quantum computation and genetic algorithm. In this paper, actuality of research on QGA is summarized. QGA and Multi-universe Parallel Quantum Genetic Algorithm (MPQGA)are discussed in detail. Application progenies in respective regions are introduced. The subsequent research on QGA is also prospected.