-
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.
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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${\cal{U}}^\dagger$ .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 -
[1] [2] [3] Lloyd S 1996 Science 273 1073
[4] Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505
Google Scholar
[5] Allen S, Kim J, Moehring D L, Monroe C R 2017 ICRC: IEEE International Conference on Rebooting Computing Washington DC, USA, November 8–9, 2017 pp1–3
[6] Zhong H S, Wang H, Deng Y H, et al. 2020 Science 370 1460
Google Scholar
[7] Gong M, Wang S, Zha C, et al. 2021 arXiv: 2102.02573 [quant-ph]
[8] Preskill J 2018 Quantum 2 79
Google Scholar
[9] Hadfield S, Wang Z, O’Gorman B, Rieffel E G, Venturelli D, Biswas R 2019 Algorithms 12 34
Google Scholar
[10] Peruzzo A, McClean J, Shadbolt P, Yung M H, Zhou X Q, Love P J, Aspuru-Guzik A, O’brien J L 2014 Nat. Commun. 5 1
Google Scholar
[11] Benedetti M, Lloyd E, Sack S, Fiorentini M 2019 Quantum Sci. Technol. 4 043001
Google Scholar
[12] Zeng J, Wu Y, Liu J G, Wang L, Hu J 2019 Phys. Rev. A 99 052306
Google Scholar
[13] Farhi E, Goldstone J, Gutmann S 2014 arXiv: 1411.4028 [quant-ph]
[14] Liu J G, Zhang Y H, Wan Y, Wang L 2019 Phys. Rev. Res. 1 023025
Google Scholar
[15] 2020 Paddle Quantum URL https://github.com/Paddle Paddle/ Quantum
[16] Bergholm V, Izaac J, Schuld M, et al. 2018 arXiv: 1811.04968 [quant-ph]
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[25] Sim S, Johnson P D, Aspuru-Guzik A 2019 Adv. Quantum Technol. 2 1900070
Google Scholar
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Google Scholar
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[29] Zhang K, Hsieh M H, Liu L, Tao D 2020 arXiv: 2011.06258 [quant-ph]
[30] Pesah A, Cerezo M, Wang S, Volkoff T, Sornborger A T, Coles P J 2020 arXiv: 2011.02966 [quant-ph]
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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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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Google Scholar
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Google Scholar
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Google Scholar
[57] Romero J, Olson J P, Aspuru-Guzik A 2017 Quantum Sci. Technol. 2 045001
Google Scholar
[58] Cao C, Wang X 2021 arXiv: 2012.08331 [quant-ph]
[59] Schuld M 2021 arXiv: 2101.11020 [quant-ph]
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Google Scholar
[61] Schuld M, Killoran N 2019 Phys. Rev. Lett. 122 040504
Google Scholar
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Google Scholar
[63] Schuld M, Fingerhuth M, Petruccione F 2017 EPL 119 60002
Google Scholar
[64] Li T, Chakrabarti S, Wu X 2019 ICML: International Conference on Machine Learning Long Beach, USA, June 9–15, 2019 pp3815–3824
[65] Wang K, Xiao L, Yi W, Ran S J, Xue P 2020 arXiv: 2003.08551 [quant-ph]
[66] Goodfellow I J, Pouget-Abadie J, Mirza M, et al. 2014 arXiv: 1406.2661 [stat.ML]
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Google Scholar
[68] Arjovsky M, Chintala S, Bottou L 2017 ICML: International Conference on Machine Learning Sydney, Australia, August 6–11, 2017 pp214–223
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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