Software Tools for Decoding Quantum Low-Density Parity-Check Codes

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 certain 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 facilitate numerical experiments 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 a highly efficient heuristic decoder that eliminates the runtime bottlenecks of the general QLDPC decoder while still maintaining comparable decoding performance. These tools eventually make it possible 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/cda-tum/qecc as part of the Munich Quantum Toolkit (MQT), is meant to provide a playground for the search for "practically good" quantum codes.