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-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Most Common Gates · BPGates.jl</title><meta name="title" content="Most Common Gates · BPGates.jl"/><meta property="og:title" content="Most Common Gates · BPGates.jl"/><meta property="twitter:title" content="Most Common Gates · BPGates.jl"/><meta name="description" content="Documentation for BPGates.jl."/><meta property="og:description" content="Documentation for BPGates.jl."/><meta property="twitter:description" content="Documentation for BPGates.jl."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">BPGates.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">BPGates.jl</a></li><li class="is-active"><a class="tocitem" href>Most Common Gates</a></li><li><a class="tocitem" href="../measurements/">Coincidence Measurements</a></li><li><a class="tocitem" href="../noisy/">Noisy Gates</a></li><li><a class="tocitem" href="../API/">API</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Most Common Gates</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Most Common Gates</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/QuantumSavory/BPGates.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/QuantumSavory/BPGates.jl/blob/main/docs/src/most_common.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="cnotlike-gates"><a class="docs-heading-anchor" href="#cnotlike-gates">CNOT-like Purification Gates</a><a id="cnotlike-gates-1"></a><a class="docs-heading-anchor-permalink" href="#cnotlike-gates" title="Permalink"></a></h1><p>As a reminder, we have the following basis states (written in binary, in decimal, and as list of stabilizers):</p><pre><code class="nohighlight hljs">00 = 0 = +XX
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Most Common Gates · BPGates.jl</title><meta name="title" content="Most Common Gates · BPGates.jl"/><meta property="og:title" content="Most Common Gates · BPGates.jl"/><meta property="twitter:title" content="Most Common Gates · BPGates.jl"/><meta name="description" content="Documentation for BPGates.jl."/><meta property="og:description" content="Documentation for BPGates.jl."/><meta property="twitter:description" content="Documentation for BPGates.jl."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" 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href="../">BPGates.jl</a></li><li class="is-active"><a class="tocitem" href>Most Common Gates</a></li><li><a class="tocitem" href="../measurements/">Coincidence Measurements</a></li><li><a class="tocitem" href="../noisy/">Noisy Gates</a></li><li><a class="tocitem" href="../API/">API</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Most Common Gates</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Most Common Gates</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/QuantumSavory/BPGates.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/QuantumSavory/BPGates.jl/blob/main/docs/src/most_common.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="cnotlike-gates"><a class="docs-heading-anchor" href="#cnotlike-gates">CNOT-like Purification Gates</a><a id="cnotlike-gates-1"></a><a class="docs-heading-anchor-permalink" href="#cnotlike-gates" title="Permalink"></a></h1><p>As a reminder, we have the following basis states (written in binary, in decimal, and as list of stabilizers):</p><pre><code class="nohighlight hljs">00 = 0 = +XX
          +ZZ
 
 01 = 1 = +XX
@@ -9,4 +9,4 @@
          +ZZ
 
 11 = 3 = -XX
-         -ZZ</code></pre><p>If we consider purification circuits that preserve the <code>00</code> state, the majority of useful gates in purification circuits can be written in the form:</p><img style="width:50%" src="../a_good_bp_gate.png"><p>Above the entangled pairs are qubit 1&amp;3 and qubits 2&amp;4.</p><p>The main property of this type of circuits is that they always map the &quot;good&quot; state to itself, while they permute the rest of the Bell basis states.</p><p>The <span>$h_a\otimes h_b$</span> (and <span>$f_a\otimes f_b$</span>) can be one of the six permutations of <code>01, 10, 11</code>, implemented by single-qubit Clifford gates. There are 6 possible such operations. The hard-coded CNOT gate provides the necessary entangling.</p><p>These gates are implemented as <a href="../API/#BPGates.CNOTPerm"><code>CNOTPerm</code></a>.</p><p>The 6 permutations (i.e. the gates <span>$h_a\otimes h_b$</span> and <span>$f_a\otimes f_b$</span>) are:</p><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; BPGates.good_perm_tuple</code><code class="nohighlight hljs ansi" style="display:block;">((1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4), (1, 3, 4, 2), (1, 4, 2, 3), (1, 4, 3, 2))</code></pre><p>The gates represented as Clifford operations are:</p><p>TODO finish this listing</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« BPGates.jl</a><a class="docs-footer-nextpage" href="../measurements/">Coincidence Measurements »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Thursday 20 June 2024 00:13">Thursday 20 June 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+         -ZZ</code></pre><p>If we consider purification circuits that preserve the <code>00</code> state, the majority of useful gates in purification circuits can be written in the form:</p><img style="width:50%" src="../a_good_bp_gate.png"><p>Above the entangled pairs are qubit 1&amp;3 and qubits 2&amp;4.</p><p>The main property of this type of circuits is that they always map the &quot;good&quot; state to itself, while they permute the rest of the Bell basis states.</p><p>The <span>$h_a\otimes h_b$</span> (and <span>$f_a\otimes f_b$</span>) can be one of the six permutations of <code>01, 10, 11</code>, implemented by single-qubit Clifford gates. There are 6 possible such operations. The hard-coded CNOT gate provides the necessary entangling.</p><p>These gates are implemented as <a href="../API/#BPGates.CNOTPerm"><code>CNOTPerm</code></a>.</p><p>The 6 permutations (i.e. the gates <span>$h_a\otimes h_b$</span> and <span>$f_a\otimes f_b$</span>) are:</p><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; BPGates.good_perm_tuple</code><code class="nohighlight hljs ansi" style="display:block;">((1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4), (1, 3, 4, 2), (1, 4, 2, 3), (1, 4, 3, 2))</code></pre><p>The gates represented as Clifford operations are:</p><p>TODO finish this listing</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« BPGates.jl</a><a class="docs-footer-nextpage" href="../measurements/">Coincidence Measurements »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Tuesday 5 November 2024 03:17">Tuesday 5 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>