Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms

Ming Wang and Frank Mueller · 2024 · Quantum

| 编号 QE121 | 主题 qLDPC 码 | 链接 arXiv:2408.10001 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which surface codes provide regular mappings onto 2D planes suitable for contemporary quantum devices together with known transversal logical gates. Recently, qLDPC codes have been proposed as a means to provide denser encoding with the class of bivariate bicycle (BB) codes promising feasible design for devices.This work contributes a novel subclass of BB codes suitable for quantum error correction. This subclass employs c o p r i m e s and the product x y of the two generating variables x and y to construct polynomials, rather than using x and y separately as in vanilla BB codes. In contrast to vanilla BB codes, where parameters remain unknown prior to code discovery, the rate of the proposed code can be determined beforehand by specifying a factor polynomial as an input to the numerical search algorithm. Using this coprime-BB construction, we found a number of surprisingly short to medium-length codes that were previously unknown. We also propose a l

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