通过基于完全脱的信念传播的蒙特卡洛方法确定量子稳定器代码的代码距离的上限
Zhipeng Liang1, Zicheng Wang1, Zhengzhong Yi2,3,4
1School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China.
Entropy (Basel, Switzerland)
|September 27, 2025
概括
我们使用蒙特卡洛方法开发了一个高效的算法来计算量子稳定器代码 (QSC) 距离的上限. 这种方法精确地估计了代码距离,有助于量子错误校正开发.
科学领域:
- 量子信息科学 量子信息科学
- 量子错误纠正方法 量子错误纠正方法
- 计算复杂性 计算复杂性
背景情况:
- 确定量子稳定器代码 (QSC) 的确切代码距离是NP-完整的.
- 有效计算代码距离的上限对于实际的QSC应用至关重要.
- 像蒙特卡洛这样的现有方法为估计上限提供了可行的方法.
研究的目的:
- 提出和验证一种新的算法,用于计算QSCs代码距离的上限.
- 为此计算,利用完全脱的信念传播与有序统计解码 (FDBP-OSD) 相结合.
- 调查特定QSC的代码距离上限,包括Z-TGRE和Chamon代码.
主要方法:
- 使用蒙特卡洛方法与完全脱的信念传播和有序统计解码 (FDBP-OSD) 结合使用.
- 开发一个计算算法来确定任意QSC的代码距离的上限.
- 应用算法来分析Z型坦纳图递归扩展 (Z-TGRE) 代码和查蒙代码.
主要成果:
- 拟议的FDBP-OSD算法准确计算代码距离的上限,匹配各种QSC的已知值.
- 对于Z-TGRE代码,计算的上限与理论预测一致.
- 对Chamon代码的分析表明,潜在的代码距离缩放为O ((N^2/3),支持现有的猜测.
结论:
- FDBP-OSD算法提供了一种精确有效的方法来计算QSC代码距离的上限.
- 这些发现为Z-TGRE和Chamon代码的性能提供了宝贵的见解.
- 结果有助于理解复杂量子代码中的代码距离属性,并支持理论猜测.
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