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.
翻译:量子错误校正( QEC) 是实现大型量子计算机的重要研究领域。 在理论方面, 大量的努力被投入到设计错误校正代码以保护量子数据免遭错误的错误, 这不可避免地发生于量子硬件和量子位( Qbits) 的吵闹性质。 使用错误校正代码保护数据需要手段来恢复原始数据, 这是因为存在潜在的腐败数据组任务, 被称为解码。 关键在于解码算法能够有效地恢复实际的无误状态。 虽然对最近QEC方法的理论性质进行了广泛研究, 分析其运行在实际更相关的环境中的运行的运行状态的良好技术仍然是一个广泛未探索的领域。 在这项工作中, 我们提出一套软件工具, 允许对所谓的Qantum Lent- Dentity Patity Check 代码( QLDPC 代码) 进行数字化实验。 这些代码中有些最近被显示为实用的搜索工具良好。 基于这一点, 我们提出一个通用的解算法值应用工具, 最终在运行QLDPC 的运行过程中, 将使用一个普通解算工具。