Cylindrical and Möbius Quantum Codes for Asymmetric Pauli Errors

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2025-02-28 DOI:10.1109/TIT.2025.3546769

Lorenzo Valentini;Diego Forlivesi;Marco Chiani

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引用次数: 0

Abstract

In the implementation of quantum information systems, one type of Pauli error, such as phase-flip errors, may occur more frequently than others, like bit-flip errors. For this reason, quantum error-correcting codes that handle asymmetric errors are critical to mitigating the impact of such impairments. To this aim, several asymmetric quantum codes have been proposed. These include variants of surface codes like the XZZX and ZZZY surface codes, tailored to preserve quantum information in the presence of error asymmetries. In this work, we propose two classes of Calderbank, Shor and Steane (CSS) topological codes, referred to as cylindrical and Möbius codes, particular cases of the fiber bundle family. Cylindrical codes maintain a fully planar structure, while Möbius codes are quasi-planar, with minimal non-local qubit interactions. We construct these codes employing the algebraic chain complexes formalism, providing theoretical upper bounds for the logical error rate. Our results demonstrate that cylindrical and Möbius codes outperform standard surface codes when using the minimum weight perfect matching (MWPM) decoder.

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非对称泡利错误的圆柱形和Möbius量子码

在量子信息系统的实现中，一种类型的泡利错误（如相位翻转错误）可能比其他类型的泡利错误（如位翻转错误）发生得更频繁。因此，处理非对称错误的量子纠错码对于减轻这种损害的影响至关重要。为此，提出了几种非对称量子码。这些包括表面代码的变体，如XZZX和ZZZY表面代码，专门用于在存在错误不对称的情况下保存量子信息。在这项工作中，我们提出了两类Calderbank， Shor和Steane （CSS）拓扑码，即圆柱码和Möbius码，这是光纤束族的特殊情况。圆柱码保持一个完全平面的结构，而Möbius码是准平面的，具有最小的非局部量子比特相互作用。我们采用代数链复合体的形式构造了这些码，给出了逻辑错误率的理论上界。我们的研究结果表明，当使用最小权重完美匹配（MWPM）解码器时，圆柱形和Möbius代码优于标准表面代码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.