Determining the Upper-Bound on the Code Distance of Quantum Stabilizer Codes Through the Monte Carlo Method Based on Fully Decoupled Belief Propagation.

Zhipeng Liang, Zicheng Wang, Zhengzhong Yi, Fusheng Yang, Xuan Wang

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Article in Entropy (Basel, Switzerland), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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5 authors.

Zhipeng LiangSchool of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China.

Zicheng WangSchool of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China.

Zhengzhong YiHefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.

Fusheng YangSchool of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China.

Xuan WangSchool of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China.

Funding

Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies 2022B1212010005Harbin Institute of Technology, Shenzhen- SpinQ quantum information Joint Research Center Project HITSZ20230111Shenzhen Science and Technology Program, China JCYJ20241202123906009the Colleges and Universities Stable Support Project of Shenzhen, China GXWD20220811170225001the Colleges and Universities Stable Support Project of Shenzhen, China GXWD20220817164856008

6 · The paper itself

Abstract

The code distance is a critical parameter of quantum stabilizer codes (QSCs), and determining it-whether exactly or approximately-is known to be an NP-complete problem. However, its upper bound can be determined efficiently by some methods such as the Monte Carlo method. Leveraging the Monte Carlo method, we propose an algorithm to compute the upper bound on the code distance of a given QSC using fully decoupled belief propagation combined with ordered statistics decoding (FDBP-OSD). Our algorithm demonstrates high precision: for various QSCs with known distances, the computed upper bounds match the actual values. Additionally, we explore upper bounds for the minimum weight of logical

Indexed as

Chamon codecode distancequantum stabilizer codequantum XYZ product codeZ-type Tanner-graph-recursive-expansion code

Identifiers

PMID41008066

DOI10.3390/e27090940

PMCPMC12468434

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