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# QDistRnd

## Calculate the distance of a q-ary quantum stabilizer code

0.9.4

23 February 2024

Leonid P. Pryadko
Email: leonid.pryadko@gmail.com
Homepage: http://faculty.ucr.edu/~leonid
Address:
Department of Physics & Astronomy
University of California
Riverside, CA 92521
USA

V. A. Shabashov
Email: vadim.art.shabashov@gmail.com
Homepage: https://sites.google.com/view/vadim-shabashov/

V. K. Kozin
Email: kozin.valera@gmail.com
Address:
Department of Physics, University of Basel
Klingelbergstrasse 82, CH-4056 Basel,
Switzerland

### Copyright

© 2021--2024 by L. P. Pryadko, V. K. Kozin, and V. A. Shabashov

QDistRnd package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

### Acknowledgements

We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by GAP users and developers.

### Contents

1 Introduction
2 Examples
2.1 The 5-qubit code
2.2 Hyperbolic codes from a file
2.3 Randomly generated cyclic codes
3 Description of the algorithm
3.1 Elementary version
3.1-1 What it does?
3.1-2 The algorithm
3.1-3 Intuition
3.1-4 CSS version of the algorithm
3.1-5 Generic version of the algorithm
3.2 Some more details
3.2-1 Quantum stabilizer codes
3.2-2 The algorithm
3.3 Empirical estimate of the success probability
4 All Functions
4.1 Functions for computing the distance
4.1-1 DistRandCSS
4.1-2 DistRandStab
4.1-3 Examples
4.2 Input/Output Functions
4.2-1 ReadMTXE
4.2-2 WriteMTXE
4.3 Helper Functions
4.3-1 QDR_AverageCalc
4.3-2 QDR_SymplVecWeight
4.3-3 QDR_WeightMat
4.3-4 QDR_DoProbOut
4.3-5 QDR_ParseFieldStr
4.3-6 QDR_ParsePolyStr
4.3-7 QDR_FieldHeaderStr
4.3-8 QDR_ProcessFieldHeader
4.3-9 QDR_ProcEntry
4.3-10 Examples
4.3-11 QDR_MakeH
4.3-12 QDR_DoCirc
5 Extended MTX (MTXE) File Format
5.1 General information
5.1-1 Representation of field elements via integers
5.1-2 Matrix storage format
5.1-3 Explicit format of each line
5.1-4 Matrix Storage Implementation Details
5.2 Example MTXE files
References
Index
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