混合量子-经典算法: 基础、设计与应用

陈然一鎏; 赵犇池; 宋旨欣; 赵炫强; 王琨; 王鑫

doi:10.7498/aps.70.20210985

摘要

量子计算作为一种新兴的计算范式, 有望解决在组合优化、量子化学、信息安全、人工智能领域中经典计算机难以解决的技术难题. 目前量子计算硬件与软件都在持续高速发展, 不过未来几年预计仍无法达到通用量子计算的标准. 因此短期内如何利用量子硬件解决实际问题成为了当前量子计算领域的一个研究热点, 探索近期量子硬件的应用对理解量子硬件的能力与推进量子计算的实用化进程有着重要意义. 针对近期量子硬件, 混合量子-经典算法(也称变分量子算法)是一个较为合理的模型. 混合量子-经典算法借助经典计算机尽可能发挥量子设备的计算能力, 结合量子计算与机器学习技术, 有望实现量子计算的首批实际应用, 在近期量子计算设备的算法研究中具有重要地位. 本文综述了混合量子-经典算法的设计框架以及在量子信息、组合优化、量子机器学习、量子纠错等领域的研究进展, 并对混合量子-经典算法的挑战以及未来研究方向进行了展望.

关键词:

Abstract

Quantum computing, as an emerging computing paradigm, is expected to tackle problems such as quantum chemistry, optimization, quantum chemistry, information security, and artificial intelligence, which are intractable with using classical computing. Quantum computing hardware and software continue to develop rapidly, but they are not expected to realize universal quantum computation in the next few years. Therefore, the use of quantum hardware to solve practical problems in the near term has become a hot topic in the field of quantum computing. Exploration of the applications of near-term quantum hardware is of great significance in understanding the capability of quantum hardware and promoting the practical process of quantum computing. Hybrid quantum-classical algorithm (also known as variational quantum algorithm) is an appropriate model for near-term quantum hardware. In the hybrid quantum-classical algorithm, classical computers are used to maximize the power of quantum devices. By combining quantum computing with machine learning, the hybrid quantum-classical algorithm is expected to achieve the first practical application of quantum computation and play an important role in the studying of quantum computing. In this review, we introduce the framework of hybrid quantum-classical algorithm and its applications in quantum chemistry, quantum information, combinatorial optimization, quantum machine learning, and other fields. We further discuss the challenges and future research directions of the hybrid quantum-classical algorithm.

Keywords:

作者及机构信息

百度研究院量子计算研究所, 北京　100193

通信作者: 王鑫, wangxin73@baidu.com

Authors and contacts

Institute for Quantum Computing, Baidu Research, Beijing 100193, China

Corresponding author: Wang Xin, wangxin73@baidu.com

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 混合量子-经典算法流程

Fig. 1. Diagram for hybrid quantum-classical algorithms.

下载: 全尺寸图片幻灯片

图 2 (a) 交换测试电路; (b)破坏性交换测试电路; (c) 哈达玛测试电路

Fig. 2. (a) Swap test circuit; (b) destructive swap test circuit; (c) Hadamard test circuit.

下载: 全尺寸图片幻灯片

图 3 (a) 量子感知机; (b)量子卷积神经网络; (c)影子电路

Fig. 3. (a) Quantum perceptron; (b) quantum convolutional neural network; (c) shadow circuit.

下载: 全尺寸图片幻灯片

图 4 量子纠错基本框架: 量子态$\left| \varPsi \right\rangle $使用编码信道${\cal{U}}$编码, 经过噪声信道${\cal{N}}$后使用纠错信道${\cal{W}}$纠正错误, 最后使用解码信道${\cal{U}}^\dagger$解码, 还原输入量子态

Fig. 4. Framework of quantum error correction. The quantum state $\left| \varPsi \right\rangle $ first is encoded by the encoding channel ${\cal{U}}$, then passes the noise channel ${\cal{N}}$, and then is corrected by the correction channel ${\cal{W}}$, finally is recovered by the decoding channel ${\cal{U}}^\dagger$.

下载: 全尺寸图片幻灯片

图 5 无噪(左)与有噪(右)条件下损失函数景观对比

Fig. 5. Comparison between noise-free (left) and noisy (right) cost function landscape.

下载: 全尺寸图片幻灯片

表 1 主要符号表

Table 1. Notations

定义	符号
厄米特算符	H
含参数酉算符	${\boldsymbol U}({\boldsymbol{\theta} }), {\boldsymbol V}({\boldsymbol{\theta} })$
不含参数酉算符	W
可调参数	θ
量子态	${\boldsymbol \rho}, {\boldsymbol \sigma}$
量子比特数	n
电路层数	L
损失函数	$ C, C({\boldsymbol{\theta}})$
能量	E
泡利算符	P
迹	Tr

下载: 导出CSV

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