Planar: A software for exact decoding quantum error correction codes with planar structure
Dongyang Feng(冯东阳)1,2,3,†, Hanyan Cao(曹涵彦)2,3,†, and Pan Zhang(张潘)1,2,‡
1 School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China; 2 CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China; 3 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Abstract Quantum error correction is essential for realizing fault-tolerant quantum computing, where both the efficiency and accuracy of the decoding algorithms play critical roles. In this work, we introduce the implementation of the Planar algorithm, a software framework designed for fast and exact decoding of quantum codes with a planar structure. The algorithm first converts the optimal decoding of quantum codes into a partition function computation problem of an Ising spin glass model. Then it utilizes the exact Kac-Ward formula to solve it. In this way, Planar offers the exact maximum likelihood decoding in polynomial complexity for quantum codes with a planar structure, including the surface code with independent code-capacity noise and the quantum repetition code with circuit-level noise. Unlike traditional minimum-weight decoders such as minimum-weight perfect matching (MWPM), Planar achieves theoretically optimal performance while maintaining polynomial-time efficiency. In addition, to demonstrate its capabilities, we exemplify the implementation using the rotated surface code, a commonly used quantum error correction code with a planar structure, and show that Planar achieves a threshold of approximately under the depolarizing error model, with a time complexity scaling of , where is the number of spins in the Ising model.
Fund: This work is supported by the National Natural Science Foundation of China (Grant Nos. 12325501, 12047503, and 12247104) and the Chinese Academy of Sciences (Grant No. ZDRW-XX-2022-3-02). P. Z. is partially supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0301900).
Corresponding Authors:
Pan Zhang
E-mail: panzhang@itp.ac.cn
Cite this article:
Dongyang Feng(冯东阳), Hanyan Cao(曹涵彦), and Pan Zhang(张潘) Planar: A software for exact decoding quantum error correction codes with planar structure 2025 Chin. Phys. B 34 050311
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