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

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.

arXiv commentpublished version

References in corpus (7)

• Balanced Product Quantum Codes
• Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
• Quantum "hyperbicycle" low-density parity check codes with finite rate
• Fiber Bundle Codes: Breaking the $N^{1/2}\mathrm{polylog}(N)$ Barrier for Quantum LDPC Codes
• Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds
• Higher-dimensional quantum hypergraph-product codes
• Minimal distances for certain quantum product codes and tensor products of chain complexes

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• Lift-Connected Surface Codes
• Adaptive Syndrome Extraction
• High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory
• Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• qSIEVE: Efficient qLDPC Memory via Systolic Movement in Atom Arrays
• Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes