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Non-binary entanglement-assisted quantum stabilizer codes

非二元纠缠辅助量子稳定子码

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Abstract

In this paper, we present the p m-ary entanglement-assisted (EA) stabilizer formalism, where p is a prime and m is a positive integer. Given an arbitrary non-abelian “stabilizer”, the problem of code construction and encoding is settled perfectly in the case of m = 1. The optimal number of required maximally entangled pairs is discussed and an algorithm to determine the encoding and decoding circuits is proposed. We also generalize several bounds on p-ary EA stabilizer codes, such as the BCH bound, the G-V bound and the linear programming bound. However, the issue becomes tricky when it comes to m > 1, in which case, the former construction method applies only when the non-commuting “stabilizer” satisfies a sophisticated limitation.

中文摘要

本文对pm元纠缠辅助量子稳定子码进行了深入研究, 其中p为素数, m为正整数。在m=1, 即p元码的情况下, 给定任意一个非交换的“稳定子”, 纠缠辅助码的构造及编码问题均得到了彻底解决。同时, 本文还计算了p元码构造时所需的最优最大纠缠对数目以及BCH界、G-V界、线性规划界等码界。此外, 本文还提出了确定p元纠缠辅助码编码及译码线路的确切算法。然而需要注意的是, 当m>1时, p元码的构造方法只有当所给的非交换的“稳定子”满足一个苛刻的条件时才能适用。

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Correspondence to Zhi Ma.

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Luo, L., Ma, Z., Wei, Z. et al. Non-binary entanglement-assisted quantum stabilizer codes. Sci. China Inf. Sci. 60, 42501 (2017). https://doi.org/10.1007/s11432-015-0932-y

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Keywords

  • entanglement
  • non-commutativity
  • non-binary stabilizer codes
  • quantum error-correction
  • quantum circuits
  • bounds

关键词

  • 纠缠
  • 非对易
  • 非二元稳定子码
  • 量子纠错
  • 量子线路
  • 码界