QDistRnd: A GAP package for computing the distance of quantum error-correcting codes

TL;DR

The paper introduces QDistRnd, a GAP package that uses a probabilistic algorithm to estimate the minimum distance of quantum error-correcting codes, with an emphasis on practical implementation and data format compatibility.

Contribution

It presents a new GAP package with a probabilistic method for minimum distance estimation and a compatible matrix storage format for q-ary quantum codes.

Findings

Empirical convergence criterion for minimum distance estimation

Implementation of a compatible matrix format (MTXE)

Practical tool for quantum code analysis

Abstract

The GAP package QDistRnd implements a probabilistic algorithm for finding the minimum distance of a quantum low-density parity-check code linear over a finite field GF(q). At each step several codewords are randomly drawn from a distribution biased toward smaller weights. The corresponding weights are used to update the upper bound on the distance, which eventually converges to the minimum distance of the code. While there is no performance guarantee, an empirical convergence criterion is given to estimate the probability that a minimum weight codeword has been found. In addition, a format for storing matrices associated with q-ary quantum codes is introduced and implemented via the provided import/export functions. The format, MTXE, is based on the well established MaTrix market eXchange (MTX) Coordinate format developed at NIST, and is designed for full backward compatibility with this format. Thus, MTXE files are readable by any software package which supports MTX.