Quantum variational learning for quantum error-correcting codes

Chenfeng Cao1, Chao Zhang1, Zipeng Wu1, Markus Grassl2, and Bei Zeng1

1Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
2International Centre for Theory of Quantum Technologies, University of Gdansk, 80-309 Gdansk, Poland

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Abstract

Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good code families. However, the majority of these codes are not suitable for near-term quantum devices. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. The cost functions are inspired by the most general and fundamental requirements of a QECC, the Knill-Laflamme conditions. Given the target noise channel (or the target code parameters) and the hardware connectivity graph, we optimize a shallow variational quantum circuit to prepare the basis states of an eligible code. In principle, VarQEC can find quantum codes for any error model, whether additive or non-additive, degenerate or non-degenerate, pure or impure. We have verified its effectiveness by (re)discovering some symmetric and asymmetric codes, e.g., $((n,2^{n-6},3))_2$ for $n$ from 7 to 14. We also found new $((6,2,3))_2$ and $((7,2,3))_2$ codes that are not equivalent to any stabilizer code, and extensive numerical evidence with VarQEC suggests that a $((7,3,3))_2$ code does not exist. Furthermore, we found many new channel-adaptive codes for error models involving nearest-neighbor correlated errors. Our work sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes.

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[1] David F. Locher, Lorenzo Cardarelli, and Markus Müller, "Quantum Error Correction with Quantum Autoencoders", Quantum 7, 942 (2023).

[2] Akshaya Jayashankar and Prabha Mandayam, "Quantum Error Correction: Noise-Adapted Techniques and Applications", Journal of the Indian Institute of Science 103 2, 497 (2023).

[3] Chenfeng Cao, Hiroshi Yano, and Yuya O. Nakagawa, "Accelerated variational quantum eigensolver with joint Bell measurement", Physical Review Research 6 1, 013205 (2024).

[4] Yuan Li and Jin-Yang Li, "Quantum Coding via Quasi-Cyclic Block Matrix", Entropy 25 3, 537 (2023).

[5] Yunlong Yu, Chenfeng Cao, Xiang-Bin Wang, Nic Shannon, and Robert Joynt, "Solution of SAT problems with the adaptive-bias quantum approximate optimization algorithm", Physical Review Research 5 2, 023147 (2023).

[6] Emanuel Dallas, Faidon Andreadakis, and Daniel Lidar, "No $((n,K,d< 127))$ Code Can Violate the Quantum Hamming Bound", IEEE BITS the Information Theory Magazine 2 3, 33 (2022).

[7] Valeria Cimini, Mauro Valeri, Simone Piacentini, Francesco Ceccarelli, Giacomo Corrielli, Roberto Osellame, Nicolò Spagnolo, and Fabio Sciarrino, "Variational quantum algorithm for experimental photonic multiparameter estimation", npj Quantum Information 10 1, 26 (2024).

[8] Chenfeng Cao, Yunlong Yu, Zipeng Wu, Nic Shannon, Bei Zeng, and Robert Joynt, "Mitigating algorithmic errors in quantum optimization through energy extrapolation", Quantum Science and Technology 8 1, 015004 (2023).

[9] Lakshika Rathi, Stephen DiAdamo, and Alireza Shabani, 2024 16th International Conference on COMmunication Systems & NETworkS (COMSNETS) 988 (2024) ISBN:979-8-3503-8311-9.

[10] He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long, "Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation", Science China Physics, Mechanics, and Astronomy 66 5, 250302 (2023).

[11] Vincent Paul Su, ChunJun Cao, Hong-Ye Hu, Yariv Yanay, Charles Tahan, and Brian Swingle, "Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning", arXiv:2305.06378, (2023).

[12] Jan Olle, Remmy Zen, Matteo Puviani, and Florian Marquardt, "Simultaneous Discovery of Quantum Error Correction Codes and Encoders with a Noise-Aware Reinforcement Learning Agent", arXiv:2311.04750, (2023).

[13] Chenfeng Cao, Yunlong Yu, Zipeng Wu, Nic Shannon, Bei Zeng, and Robert Joynt, "Mitigating algorithmic errors in quantum optimization through energy extrapolation", arXiv:2109.08132, (2021).

[14] Akshaya Jayashankar and Prabha Mandayam, "Quantum Error Correction: Noise-adapted Techniques and Applications", arXiv:2208.00365, (2022).

[15] Shi-Yao Hou, Zipeng Wu, Jinfeng Zeng, Ningping Cao, Chenfeng Cao, Youning Li, and Bei Zeng, "Maximum entropy methods for quantum state compatibility problems", arXiv:2207.11645, (2022).

[16] Xiaokai Hou, Qingyu Li, Man-Hong Yung, Xusheng Xu, Zizhu Wang, Chu Guo, and Xiaoting Wang, "A sequentially generated variational quantum circuit with polynomial complexity", arXiv:2305.12856, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-03-28 15:09:48) and SAO/NASA ADS (last updated successfully 2024-03-28 15:09:49). The list may be incomplete as not all publishers provide suitable and complete citation data.