文章基本信息
- 标题：Towards Local Testability for Quantum Coding
- 本地全文：下载
- 作者：Anthony Leverrier ; Vivien Londe ; Gilles Z'{e}mor 等
- 期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
- 电子版ISSN：1868-8969
- 出版年度：2021
- 卷号：185
- 页码：65:1-65:11
- DOI：10.4230/LIPIcs.ITCS.2021.65
- 出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
- 摘要：We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the p-faces of the n-cube (for n > p) and stabilizer constraints with faces of dimension (p ± 1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into N = 2^{n-p-1} binom(n,p) physical qubits and displays local testability with a soundness of Ω(1/log(N)) beating the current state-of-the-art of 1/log²(N) due to Hastings. We exploit this local testability to devise an efficient decoding algorithm that corrects arbitrary errors of size less than the minimum distance, up to polylog factors. We then extend this code family by considering the quotient of the n-cube by arbitrary linear classical codes of length n. We establish the parameters of these generalized hemicubic codes. Interestingly, if the soundness of the hemicubic code could be shown to be constant, similarly to the ordinary n-cube, then the generalized hemicubic codes could yield quantum locally testable codes of length not exceeding an exponential or even polynomial function of the code dimension.
- 关键词：Quantum error correcting code
