论文标题
用于解码量子低密度平价检查代码的软件工具
Software Tools for Decoding Quantum Low-Density Parity Check Codes
论文作者
论文摘要
量子误差校正(QEC)是实现大规模量子计算机的重要研究领域。从理论方面来说,在设计误差校正的代码上,将量子数据免受误差的影响而付出了很大的努力,由于量子硬件和量子位(Qubits)的嘈杂性质,这种量子数据不可避免地发生。使用错误纠正的代码保护数据需要恢复原始数据的方法,鉴于可能损坏的数据集 - 称为解码的任务。解码算法可以有效地恢复无错误状态至关重要。虽然最近对QEC方法的理论特性进行了广泛的研究,但在几乎相关的环境中分析其性能的良好技术仍然是一个广泛尚未开发的领域。在这项工作中,我们提出了一组软件工具,这些工具允许使用所谓的Quantum低密度平价检查代码(QLDPC代码)进行数值实验 - 广泛的代码,其中一些代码最近已被证明是渐近的。基于此,我们为QLDPC代码提供了一般解码器的实现。最重要的是,我们提出了一个有效的启发式解码器,该解码器可以解决一般QLDPC解码器的运行时瓶颈,同时仍保持可比的解码性能。这些工具最终允许在更实用的环境中确认围绕QLDPC代码的理论结果,并展示软件工具的价值(除了理论考虑之外),以调查用于实际应用的代码。在MIT许可下,该工具可在https://github.com/lucasberent/qecc上公开获取,旨在为搜索“实际上好”的量子代码提供操场。
Quantum Error Correction (QEC) is an essential field of research towards the realization of large-scale quantum computers. On the theoretical side, a lot of effort is put into designing error-correcting codes that protect quantum data from errors, which inevitably happen due to the noisy nature of quantum hardware and quantum bits (qubits). Protecting data with an error-correcting code necessitates means to recover the original data, given a potentially corrupted data set-a task referred to as decoding. It is vital that decoding algorithms can recover error-free states in an efficient manner. While theoretical properties of recent QEC methods have been extensively studied, good techniques to analyze their performance in practically more relevant settings is still a widely unexplored area. In this work, we propose a set of software tools that allows to numerically experiment with so-called Quantum Low-Density Parity Check codes (QLDPC codes)-a broad class of codes, some of which have recently been shown to be asymptotically good. Based on that, we provide an implementation of a general decoder for QLDPC codes. On top of that, we propose an efficient heuristic decoder that tackles the runtime bottlenecks of the general QLDPC decoder while still maintaining comparable decoding performance. These tools eventually allow to confirm theoretical results around QLDPC codes in a more practical setting and showcase the value of software tools (in addition to theoretical considerations) for investigating codes for practical applications. The resulting tool, which is publicly available at https://github.com/lucasberent/qecc under the MIT license, is meant to provide a playground for the search for "practically good" quantum codes.