机器学习辅助绝热量子算法设计

林键; 叶梦; 朱家纬; 李晓鹏

doi:10.7498/aps.70.20210831

摘要

量子计算在近十年取得了长足的进展. 随着量子调控技术达到前所未有的高度, 包括超导量子比特、光量子器件、原子系综等在内的量子实验平台都进入到了崭新的时代. 目前在特定计算任务上超越经典的量子计算优势也已经被报道. 其中一种可以有效运用可控量子器件的计算方案是采用绝热量子计算. 绝热量子计算中算法的选择与研究至关重要, 其将直接决定量子计算优势是否能够最大限度地被挖掘. 本综述主要介绍近期机器学习在绝热量子算法设计方面的应用, 并讲述该计算架构在3-SAT和Grover搜索等问题上的应用. 通过与未经机器学习优化设计的绝热量子算法对比, 研究表明机器学习方法的应用可以极大提高绝热量子算法的计算效率.

关键词:

Abstract

Quantum computing has made dramatic progress in the last decade. The quantum platforms including superconducting qubits, photonic devices, and atomic ensembles, have all reached a new era, with unprecedented quantum control capability developed. Quantum computation advantage over classical computers has been reported on certain computation tasks. A promising computing protocol of using the computation power in these controllable quantum devices is implemented through quantum adiabatic computing, where quantum algorithm design plays an essential role in fully using the quantum advantage. Here in this paper, we review recent developments in using machine learning approach to design the quantum adiabatic algorithm. Its applications to 3-SAT problems, and also the Grover search problems are discussed.

Keywords:

作者及机构信息

复旦大学物理学系, 上海　200433

通信作者: 李晓鹏, xiaopeng_li@fudan.edu.cn

基金项目: 国家自然科学基金(批准号: 11934002)、国家重点基础研究发展计划(973计划)(批准号: 2017YFA0304204)和上海量子信息技术市级科技重大专项(批准号: 2019SHZDZX01)资助的课题

Authors and contacts

Department of Physics, Fudan University, Shanghai 200433, China

Corresponding author: Li Xiao-Peng, xiaopeng_li@fudan.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11934002), the National Basic Research Program of China (Grant No. 2017YFA0304204), and the Shanghai Municipal Science and Technology Major Project, China (Grant No. 2019SHZDZX01)

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施引文献

图 1 强化学习辅助绝热量子算法设计的示意图^[173]. 其中强化学习中的智能体(agent)根据绝热量子计算(AQC)输出的结果来获取奖励, 并根据深度神经网络近似表示的Q值表格来选择动作更新绝热量子算法

Fig. 1. Schematic diagram of the reinforcement learning approach for quantum adiabatic algorithm design^[173]. The learning agent collects the reward according to the result obtained from adiabatic quantum computing (AQC) and produces an action to update the quantum adiabatic algorithm based on its Q table represented by a deep neural network.

下载: 全尺寸图片幻灯片

图 2 强化学习辅助设计的绝热量子算法在Grover搜索问题上的表现^[173]. 其中成功概率(success probability)是演化终态与目标态交叠的平方, 总的演化时间T与系统规模n的关系为$ T = \sqrt{2^n}$. 图中蓝色虚线表示的线性演化路径成功概率会随着系统尺寸增大不断降低. 红色实线和黑色虚线分别表示强化学习设计得到的演化路径和解析获得的非线性路径^[66]的表现. 在选择的演化时间下, 两者的成功概率都能接近于1, 说明两者都具有平方的量子加速

Fig. 2. Performance of reinforcement learning designed quantum adiabatic algorithm in success probability for Grover search problem^[173]. The success probability is obtained by taking the square of wave-function overlap of the final evolved quantum state with the target state. The total adiabatic evolution time is chosen as $ T = \sqrt{2^n}$ where n is the system size. The blue dashed line denotes the success probability of linear path which decreases as increasing the system size. The red solid line and black dashed line denote the performance of the reinforcement learning designed path and the nonlinear path^[66], respectively. Given the choice of total evolution time, the success probability close to 1 by both implies that they both exhibit quadratic quantum speed up.

下载: 全尺寸图片幻灯片

图 3 强化学习在Grover搜索问题的绝热量子算法设计中的拓展性^[173]. 其中绿线是线性路径的表现, 蓝线是将10 qubits系统中强化学习学到的路径推广到更大系统, 橘线是将在n qubits系统强化学习获得的路径推广到$ n+1$qubits系统

Fig. 3. Transferability of reinforcement learning based quantum adiabatic algorithm design for Grover search problem^[173]. The green line denotes the infidelity of linear path. The blue line denotes the infidelity of the path obtained by training the 10 qubits system. The orange line denotes the performance of applying the path learned from the n qubits system to the $ n+1$ qubits system.

下载: 全尺寸图片幻灯片

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