Quantum Annealing with Markov Chain Monte Carlo Simulations and D-Wave Quantum Computers
Quantum Annealing with Markov Chain Monte Carlo Simulations and D-Wave Quantum Computers
复制标题
使用马尔可夫链蒙特卡罗模拟和 D-Wave 量子计算机进行量子退火
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
J. Zou
中科院分区：
文献类型：
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作者：
Yazhen Wang;Shang Wu;J. Zou
量子计算通过使用量子设备而不是遵循经典物理的电子设备来执行计算，并被经典计算机使用。尽管实用规模的通用量子计算机可能还需要很多年的时间，但专用量子计算机的能力正在超过经典计算机。一个突出的例子是所谓的D波量子计算机，它是一种计算硬件设备，用于实施量子退火法来解决组合优化问题。D波计算硬件设备是否表现出量子行为或是否可以用经典模型来描述引起了人们的极大关注，关于量子效应或经典效应在显示D波设备的计算输入输出行为中起关键作用的问题仍存在争议。本文由两部分组成，第一部分回顾了量子退火法及其实现，第二部分提出了分析退火法实验数据的统计方法。具体地说，我们引入量子退火法来解决优化问题，并描述了实现量子退火法的D波计算器件。我们用经典计算机进行的马尔科夫链蒙特卡罗(MCMC)模拟说明了量子退火法的实现。用计算实验产生了数据，并对量子退火法和经典退火法进行了比较。我们提出了统计方法来分析D波装置的计算实验数据和基于MCMC的退火法的模拟数据，并建立了渐近理论并检验了所提出的统计方法的有限样本性能。我们的发现证实了D波装置的输入输出数据中显示的双峰直方图模式，以及基于MCMC的退火法的输入输出数据中显示的U形和单峰直方图模式。进一步的统计探索揭示了U形图案的可能来源。另一方面，我们的统计分析产生了统计证据，表明D波装置的输入输出数据与研究中任何基于MCMC的退火模型的随机行为不一致。我们列出了未来量子退火法和MCMC模拟的统计研究主题。
Quantum computation performs calculations by using quantum devices instead of electronic devices following classical physics and used by classical computers. Although general purpose quantum computers of practical scale may be many years away, special purpose quantum computers are being built with capabilities exceeding classical computers. One prominent case is the so-called D-Wave quantum computer, which is a computing hardware device built to implement quantum annealing for solving combinatorial optimization problems. Whether D-Wave computing hardware devices display a quantum behavior or can be described by a classical model has attracted tremendous attention, and it remains controversial to determine whether quantum or classical effects play a crucial role in exhibiting the computational input–output behaviors of the D-Wave devices. This paper consists of two parts where the first part provides a review of quantum annealing and its implementations, and the second part proposes statistical methodologies to analyze data generated from annealing experiments. Specifically, we introduce quantum annealing to solve optimization problems and describe D-Wave computing devices to implement quantum annealing. We illustrate implementations of quantum annealing using Markov chain Monte Carlo (MCMC) simulations carried out by classical computers. Computing experiments have been conducted to generate data and compare quantum annealing with classical annealing. We propose statistical methodologies to analyze computing experimental data from a D-Wave device and simulated data from the MCMC based annealing methods, and establish asymptotic theory and check finite sample performances for the proposed statistical methodologies. Our findings confirm bimodal histogram patterns displayed in input–output data from the D-Wave device and both U-shape and unimodal histogram patterns exhibited in input–output data from the MCMC based annealing methods. Further statistical explorations reveal possible sources for the U-shape patterns. On the other hand, our statistical analysis produces statistical evidence to indicate that input–output data from the D-Wave device are not consistent with the stochastic behaviors of any MCMC based annealing models under the study. We present a list of statistical research topics for the future study on quantum annealing and MCMC simulations.
物理学和统计遗传学中的伊辛模型。
影响因子：
9.8
作者：
Majewski,J;Li,H;Ott,J
通讯作者：
Ott,J