Hybrid quantum-classical algorithms: Foundation, design and applications

Chen Ran-Yi-Liu; Zhao Ben-Chi; Song Zhi-Xin; Zhao Xuan-Qiang; Wang Kun; Wang Xin

doi:10.7498/aps.70.20210985

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:

Authors and contacts

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

Corresponding author: Wang Xin, wangxin73@baidu.com

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References

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Cited By

图 1 混合量子-经典算法流程

Figure 1. Diagram for hybrid quantum-classical algorithms.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

图 3 (a) 量子感知机; (b)量子卷积神经网络; (c)影子电路

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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 ${\cal{U}}^\dagger$.

DownLoad: Full-Size Img PowerPoint

图 5 无噪(左)与有噪(右)条件下损失函数景观对比

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

DownLoad: Full-Size Img PowerPoint

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

DownLoad: CSV

[1]	Shor P W 1994 FOCS: 35th Annual Symposium on Foundations of Computer Science Santa Fe, New Mexico, USA, November 20–22, 1994 pp124–134
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[53]	Bauer B, Wang L, Pižorn I, Troyer M 2015 arXiv: 1501.06914 [cond-mat.dis-nn]
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