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。     

An Efficient, Practical Parallelization Methodology for Multicore Architecture Simulation

Multiple core designs have become commonplace in the processor market, and are hence a major focus in modern computer architecture research. Thus, for both product development and research, multiple core processor simulation environments are necessary. A well-known positive feedback property of computer design is that we use today's computers to design tomorrow's. Thus, with the emergence of chip multiprocessors, it is natural to re-examine simulation environments written to exploit parallelism. In this paper we present a programming methodology for directly converting existing uniprocessor simulators into parallelized multiple-core simulators. Our method not only takes significantly less development effort compared to some prior used programming techniques, but also possesses advantages by retaining a modular and comprehensible programming structure. We demonstrate our case with actual developed products after applying this method to two different simulators, one developed from IBM Ibrandot and the other from the SimpleScalar tool set. Our SimpleScalar-based framework achieves a parallel speedup of 2.2times on a dual-CPU dual-core (4-way) Opteron server     

Hybrid Computer Systems

Today's increasing emphasis on simulation of continuous dynamic systems lends a special significance to this issue of Computer. Hybrid computers, with their tremendous computing speed resulting from the all-parallel configuration of their analog subsystem, are particularly suited for dynamic system simulation. Indeed, back in the 1950's analog computers were the only game in town when it came to real-time simulation of flight vehicles. Digital computers of that era were simply too slow in the numerical solution of differential equations.     

A universal quantum circuit scheme for finding complex eigenvalues

We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In addition, we show how the method can be used for the simulation of resonance states for quantum systems.     

Efficient classical simulation of the Deutsch–Jozsa and Simon’s algorithms

A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch–Jozsa and Simon’s problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch–Jozsa problem with probability 1 using only one oracle query, and Simon’s problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch–Jozsa and Simon’s problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.     

用VHDL-AMS进行概念设计

ＶＨＤＬ－ＡＭＳ是ＶＨＤＬ向模拟和混合信号领域的诉展,ＶＨＬＤ－ＡＭＳ为设计者提供了在概念级处理复杂系统的能力,随着ＶＨＤＬ－ＡＭＳ的标准化,将诞生处理复杂的模拟和混合信号模型的有效的模拟器,文中介绍了ＶＨＬＤ－ＡＭＳ模拟扩展的主要内容,展示了一个混合模式模拟环境,并给出了模拟解算器的构成,讨论了连续和离散模拟的同步问题;用４个例子说明ＶＨＤＬ－ＡＭＳ在概念设计中的应用。     

复杂模拟电路定量仿真中的元件建模技术研究

基于电路定量仿真的虚拟测试和故障诊断,对于复杂电路系统可靠性的提高具有重要意义;传统上,模拟电路的定量仿真分析大多采用SPICE模型,这也是目前该领域的主流分析模型;然而由于元件SPICE模型的复杂性,导致PSPICE等电路仿真器的优势难以在大型复杂电路系统的虚拟测试和故障诊断中得到充分发挥。为此,从降低元件模型复杂度,简化电路计算,提高仿真速度和避免收敛问题的角度出发,基于自主研制的DrGraph电路仿真平台,提出非线性二端元件SPICE模型的分段线性化改进技术。仿真实验验证了该技术在大规模复杂模拟电路仿真中具有很强的工程应用价值。     

量子算法模拟系统研究现状

The Quantum Computer has immense power,exceeds the capabilities of a classical computer,but the hardware of such machine is still in research. If we want to develop quantum algorithms,wemust simulate them on classical computer. In this paper ,we first introduce the principle and model usedin quantum computing,and compare the simulators in tile world. At last ,based on the problems in simu-lation,we give a new architecture of quantum algorithm simulator.     

Massively parallel quantum computer simulator

We describe portable software to simulate universal quantum computers on massive parallel computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI Altix 3700 and clusters of PCs running Windows XP. We study the performance of the software by simulating quantum computers containing up to 36 qubits, using up to 4096 processors and up to 1 TB of memory. Our results demonstrate that the simulator exhibits nearly ideal scaling as a function of the number of processors and suggest that the simulation software described in this paper may also serve as benchmark for testing high-end parallel computers.     

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation. Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.      

Algorithms on ensemble quantum computers

In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor’s factorization algorithm, Grover’s search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and s_z^1/4,\sigma_{z}^{1/4}, as these operations cannot be implemented “bitwise”, and their standard fault-tolerant implementations require measurement.     

Simulating Robots Without Conventional Physics: A Neural Network Approach

The construction of physics-based simulators for use in Evolutionary Robotics (ER) can be complex and time-consuming. Alternative simulation schemes construct robotic simulators from empirically-collected data. Such empirical simulators, however, also have associated challenges. This paper therefore investigates the potential use of Artificial Neural Networks, henceforth simply referred to as Neural Networks (NNs), as alternative robotic simulators. In contrast to physics models, NN-based simulators can be constructed without requiring an explicit mathematical model of the system being modeled, which can simplify simulator development. The generalization abilities of NNs, along with NNs’ noise tolerance, suggest that NNs could be well-suited to application in robotics simulation. Investigating whether NNs can be effectively used as robotic simulators in ER is thus the endeavour of this work. Two robot morphologies were selected on which the NN simulators created in this work were based, namely a differentially steered robot and an inverted pendulum robot. Accuracy tests indicated that NN simulators created for these robots generally trained well and could generalize well on data not presented during simulator construction. In order to validate the feasibility of the created NN simulators in the ER process, these simulators were subsequently used to evolve controllers in simulation, similar to controllers developed in related studies. Encouraging results were obtained, with the newly-evolved controllers allowing experimental robots to exhibit obstacle avoidance, light-approaching behaviour and inverted pendulum stabilization. It was thus clearly established that NN-based robotic simulators can be successfully employed as alternative simulation schemes in the ER process.     

Quantum Coin Method for Numerical Integration

Light transport simulation in rendering is formulated as a numerical integration problem in each pixel, which is commonly estimated by Monte Carlo integration. Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e. samples) of the function (integrand). For N queries of the integrand, Monte Carlo integration achieves the estimation error of . Recently, Johnston [Joh16] introduced quantum super-sampling (QSS) into rendering as a numerical integration method that can run on quantum computers. QSS breaks the fundamental limitation of the convergence rate of Monte Carlo integration and achieves the faster convergence rate of approximately which is the best possible bound of any quantum algorithms we know today [NW99]. We introduce yet another quantum numerical integration algorithm, quantum coin (QCoin) [AW99], and provide numerical experiments that are unprecedented in the fields of both quantum computing and rendering. We show that QCoin's convergence rate is equivalent to QSS's. We additionally show that QCoin is fundamentally more robust under the presence of noise in actual quantum computers due to its simpler quantum circuit and the use of fewer qubits. Considering various aspects of quantum computers, we discuss how QCoin can be a more practical alternative to QSS if we were to run light transport simulation in quantum computers in the future.     

Simulating fermions on a quantum computer

The real-time probabilistic simulation of quantum systems in classical computers is known to be limited by the so-called dynamical sign problem, a problem leading to exponential complexity. In 1981 Richard Feynman raised some provocative questions in connection to the “exact imitation” of such systems using a special device named a “quantum computer”. Feynman hesitated about the possibility of imitating fermion systems using such a device. Here we address some of his concerns and, in particular, investigate the simulation of fermionic systems. We show how quantum computers avoid the sign problem in some cases by reducing the complexity from exponential to polynomial. Our demonstration is based upon the use of isomorphisms of algebras. We present specific quantum algorithms that illustrate the main points of our algebraic approach.     

An Adventure with a Sad Ending: The SEA

The Société d'Electronique et d'Automatisme (SEA) was created in 1948 by the electronics engineer F. H. Raymond. At first it produced analog computers (OME and NADAC series) and developed process control devices and flight simulators. In 1955, the SEA installed the first stored-program computer in France, CAB 1011, at a military deciphering service. Other computers followed (CUBA, CAB 2000 series) for scientific and business uses. In 1960, the SEA introduced its small CAB 500 computer, based on novel magnetic circuits with a programming language, PAF; a series of transistorized machines was then produced (CAB 3900 and 4000, DOROTHEE). In 1966, the SEA (800 employees) was absorbed in the merger which created the Compagnie Internationale pour l'Informatique (CII) in the context of the Plan Calcul.     

Deductive Synthesis of Numerical Simulation Programs from Networks of Algebraic and Ordinary Differential Equations

Scientists and engineers face recurring problems of constructing, testing and modifying numerical simulation programs. The process of coding and revising such simulators is extremely time-consuming, because they are almost always written in conventional programming languages. Scientists and engineers can therefore benefit from software that facilitates construction of programs for simulating physical systems. Our research adapts the methodology of deductive program synthesis to the problem of constructing numerical simulation codes. We have focused on simulators that can be represented as second order functional programs composed of numerical integration and root extraction routines. We have developed a system that uses first order Horn logic to synthesize numerical simulators built from these components. Our approach is based on two ideas: first, we axiomatize only the relationship between integration and differentiation. We neither attempt nor require a complete axiomatization of mathematical analysis. Second, our system uses a representation in which functions are reified as objects. Function objects are encoded as lambda expressions. Our knowledge base includes an axiomatization of term equality in the lambda calculus. It also includes axioms defining the semantics of numerical integration and root extraction routines. We use depth bounded SLD resolution to construct proofs and synthesize programs. Our system has successfully constructed numerical simulators for computational design of jet engine nozzles and sailing yachts, among others. Our results demonstrate that deductive synthesis techniques can be used to construct numerical simulation programs for realistic applications.     

The promise of analog computation

Future computing paradigms and technologies will have to be more like the physical processes by which they are realized, and because these processes are primarily continuous, post-Moore’s law computing will involve an increased use of analog computation. Traditionally analog computers have computed ordinary differential equations of time, but analog field computation permits massively parallel temporal integration of partial differential equations. In principle many different physical media – not just electronics – can be exploited to implement the basic operations of analog computing, a small number of which are sufficient to approximate a wide variety of analog computations, thus providing a basis for universal analog computation and general-purpose analog computers. The contentious issue of the computational power of analog computers is addressed best on its own terms, rather by asking it within the context of Church-Turing computation, which distorts the relevant questions and their answers.     

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。