纤维丛码：打破量子LDPC码的N^{1/2} polylog(N)距离壁垒
量子物理
2024-07-08 v2 信息论
组合数学
math.IT
摘要
我们提出了一个量子LDPC码族，其距离为Ω(N^{3/5}/polylog(N))，逻辑量子比特数为\tildeΘ(N^{3/5})。这是首个距离大于N^{1/2} polylog(N)的量子LDPC码构造。该构造基于将码的同调积推广到纤维丛。
引用
@article{arxiv.2009.03921,
title = {Fiber Bundle Codes: Breaking the $N^{1/2} \operatorname{polylog}(N)$ Barrier for Quantum LDPC Codes},
author = {Matthew B. Hastings and Jeongwan Haah and Ryan O'Donnell},
journal= {arXiv preprint arXiv:2009.03921},
year = {2024}
}
备注
39 pages, 2 figures; v2 gives self-contained presentation of weight reduction using weight reduction for classical base code. Also contains explanation of relation between codes in terms of homotopy equivalence of chain complexes