Problem
Research questions and friction points this paper is trying to address.
Quantum Error-Correcting Codes
CSS-T Codes
Matrix-Product Codes
Cyclic Codes
Quantum Matrix-Product Codes: CSS-T Characterization and Maximality
🤖 AI Summary
本文通过扩展CSS-T码的代数特征至矩阵积码，特别是对于循环子码使用定义的分圆集进行显式刻画，从而构建新的更长CSS-T码以纠正量子计算中的错误。
📝 Abstract
CSS-T codes are quantum error-correcting codes that play an important role in fault-tolerant quantum computation, as they help mitigate the proliferation of errors. They admit a transversal T-gate and are defined from a pair of nested classical binary linear codes satisfying a specific algebraic condition expressed in terms of their Schur square. We extend this algebraic characterization to the propagation rule known as the $(u \mid u+v)$-construction, that is, the matrix-product code constructed from two constituent codes. Moreover, for cyclic constituent codes, we provide an explicit characterization in terms of the defining cyclotomic sets, which extends existing results for cyclic codes. This framework allows the construction of new and longer CSS-T codes.
Innovation
Methods, ideas, or system contributions that make the work stand out.
CSS-T codes
matrix-product code
(u|u+v)-construction
cyclic codes
cyclotomic sets
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