QDistRnd: A GAP package for computing the distance ofquantum error-correcting codes
Leonid P. Pryadko, Vadim A. Shabashov, Valerii K. Kozin
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.