Non-binary entanglement-assisted quantum stabilizer codes非二元纠缠辅助量子稳定子码

被引：0
作者：
Lan Luo
Zhi Ma
Zhengchao Wei
Riguang Leng
机构：
[1] State Key Laboratory of Mathematical Engineering and Advanced Computing,
来源：
Science China Information Sciences | 2017年 / 60卷
关键词：
entanglement; non-commutativity; non-binary stabilizer codes; quantum error-correction; quantum circuits; bounds; 纠缠; 非对易; 非二元稳定子码; 量子纠错; 量子线路; 码界;
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学科分类号：
摘要：
In this paper, we present the pm-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.
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