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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<h1>QDistRnd</h1>


<h2>Calculate the distance of a q-ary quantum stabilizer code</h2>

<p>
    0.9.5</p>

<p>
    20 November 2024
  </p>

</div>
<p><b>
    Leonid P. Pryadko




  </b>
<br />Email: <span class="URL"><a href="mailto:leonid.pryadko@gmail.com">leonid.pryadko@gmail.com</a></span>
<br />Homepage: <span class="URL"><a href="http://faculty.ucr.edu/~leonid">http://faculty.ucr.edu/~leonid</a></span>
<br />Address: <br />Department of Physics & Astronomy<br /> University of California<br /> Riverside, CA 92521<br /> USA<br />
</p><p><b>
    V. A. Shabashov



  </b>
<br />Email: <span class="URL"><a href="mailto:vadim.art.shabashov@gmail.com">vadim.art.shabashov@gmail.com</a></span>
<br />Homepage: <span class="URL"><a href="https://sites.google.com/view/vadim-shabashov/">https://sites.google.com/view/vadim-shabashov/</a></span>
</p><p><b>
    V. K. Kozin



  </b>
<br />Email: <span class="URL"><a href="mailto:kozin.valera@gmail.com">kozin.valera@gmail.com</a></span>
<br />Address: <br />Department of Physics, University of Basel<br /> Klingelbergstrasse 82, CH-4056 Basel,<br /> Switzerland<br />
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<h3>Copyright</h3>
<p>© 2021--2024 by L. P. Pryadko, V. K. Kozin, and V. A. Shabashov</p>

<p><strong class="pkg">QDistRnd</strong> package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by <strong class="pkg">GAP</strong> users and developers.</p>

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<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
</div>
<div class="ContChap"><a href="chap2.html#X7A489A5D79DA9E5C">2 <span class="Heading">Examples</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7B229D2B7E58ED2E">2.1 <span class="Heading">The 5-qubit code</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X87244D1D7FAA03A1">2.2 <span class="Heading">Hyperbolic codes from a file</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7A1DF21D8626DA84">2.3 <span class="Heading">Randomly generated cyclic codes</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap3.html#X7E421FAB7D974939">3 <span class="Heading">Description of the algorithm</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7DDF42DF7D7F87EF">3.1 <span class="Heading">Elementary version</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7AE39C5583A02936">3.1-1 <span class="Heading">What it does?</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C198D417DA58DFD">3.1-2 <span class="Heading">The algorithm</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C37FBD078DDC0D5">3.1-3 <span class="Heading">Intuition</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A291E1E7CD313AB">3.1-4 <span class="Heading">CSS version of the algorithm</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D97C75283D26EE5">3.1-5 <span class="Heading">Generic version of the algorithm</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7DA7BD6F7A61E553">3.2 <span class="Heading">Some more details</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X78810FD98017EB84">3.2-1 <span class="Heading">Quantum stabilizer codes</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C198D417DA58DFD">3.2-2 <span class="Heading">The algorithm</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7CCA4B9B834960EE">3.3 <span class="Heading">Empirical estimate of the success probability</span></a>
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</div>
<div class="ContChap"><a href="chap4.html#X7C6522597D7E72FE">4 <span class="Heading">All Functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X826856C47F9890F3">4.1 <span class="Heading">Functions for computing the distance</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X83CF58308216037F">4.1-1 DistRandCSS</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7894F0027B144AB8">4.1-2 DistRandStab</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7A489A5D79DA9E5C">4.1-3 <span class="Heading">Examples</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7E4EA2B38128F66B">4.2 <span class="Heading">Input/Output Functions</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X86210A658573655F">4.2-1 ReadMTXE</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X82F72B6082EEDDF9">4.2-2 WriteMTXE</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7BD4785D8488BAD5">4.3 <span class="Heading">Helper Functions</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80975EC07BDC757B">4.3-1 QDR_AverageCalc</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8615F38C79B4684C">4.3-2 QDR_SymplVecWeight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80BB67727F7F99C3">4.3-3 QDR_WeightMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8441E8807AE9C477">4.3-4 QDR_DoProbOut</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7B6713FC7A5124A8">4.3-5 QDR_ParseFieldStr</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X810D9FD7796AD286">4.3-6 QDR_ParsePolyStr</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8638277B86B97B56">4.3-7 QDR_FieldHeaderStr</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8388DFBC816EF47D">4.3-8 QDR_ProcessFieldHeader</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X82A75836794421A8">4.3-9 QDR_ProcEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7A489A5D79DA9E5C">4.3-10 <span class="Heading">Examples</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8020FCA787C830FE">4.3-11 QDR_MakeH</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X819DC3247F3F7B4F">4.3-12 QDR_DoCirc</a></span>
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<div class="ContChap"><a href="chap5.html#X7D0187B5831B764D">5 <span class="Heading">Extended MTX (MTXE) File Format</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7E294E8678035D23">5.1 <span class="Heading">General information</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8269F2367856BB1E">5.1-1 <span class="Heading">Representation of field elements via integers</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X86FBB72C7BC3B8D2">5.1-2 <span class="Heading">Matrix storage format</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X80B886F0796AF0D5">5.1-3 <span class="Heading">Explicit format of each line</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X80F0F8AB7FD73B0E">5.1-4 <span class="Heading">Matrix Storage Implementation Details</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7F2C657F869D90AD">5.2 <span class="Heading">Example MTXE files</span></a>
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<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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