GAP package QDistRnd

The GAP package for calculating the distance of a $q$-ary quantum stabilizer code.

Overview

The GAP package QDistRnd implements a probabilistic algorithm for finding the distance of a $q$-ary quantum low-density parity-check code linear over a finite field GF($q$). An empirical convergence criterion is provided to estimate the probability that a minimum weight codeword has actually been found. Versions of the routines for CSS and regular stabilizer codes are given.

In addition, a format for storing matrices associated with $q$-ary quantum codes is introduced and implemented via provided import/export routines. The format 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, the files are readable by any software package which supports MTX.

Requirements

The package QDistRnd requires the Guava package to run; GAPDoc and AutoDoc are required to generate the documentation (see the file PackageInfo.g for versions required). All of these packages are included with GAP version 4.11; this or later version of GAP is strongly recommended.

Installation

Starting with GAP 4.13.0, the QDistRnd package is distributed with a standard installation of GAP.

To install the package permanently, download the latest released version from releases and unpack it in the pkg directory of one of your GAP root directories. After installation, the package can be loaded at the GAP prompt by typing

gap> LoadPackage("QDistRnd");

Alternatively, if you just want to try it, you can unpack the package anywhere and type at the GAP prompt

gap> SetPackagePath("QDistRnd","absolute_path_to_the_package_QDistRnd" );

After that you can load the package as you would do normally.

Testing

After installation, basic tests of the package (most of the examples listed in the package manual) can by performed by running

gap> TestPackage("qdistrnd");

at the GAP command prompt. Note that the package name must be in lowercase.

The same tests are run as a part of documentation processing script which is also executed as a GitHub Action every time changes are commited.

Documentation

Documentation for the package can be found in the doc subdirectory in HTML form as chap0.html and PDF form as manual.pdf. Documentation can also be accessed on the package website and through the standard GAP help system. Documentation can be recompiled by running

gap makedoc.g

in the package directory.

Plans for the future

1. The package only deals with Galois-qubit q-ary codes. It would be nice to develop and implement similar methods for quantum codes over a finite ring, e.g., Z(q) with q not necessarily a power of a prime. This could be done with the help of Smith normal form decomposition. The required complexity may be higher, however.

2. Write sample read/write routines for MTXE files in Mathematica and/or C.

3. If there is need (or interest), add routines for the alternate integer format to represent elements from extension fields, where polynomials over a prime field GF(p) will be encoded as p-ary integers. The only apparent advantage would be a unification with the currently used format for prime field elements using the equivalence with Z(p). On the other hand, it would not improve readability: the corresponding decimal integers would be as difficult to interpret as the currently used integer powers of a primitive field element.