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{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-12T13:45:44","documenter_version":"1.7.0"}}
{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-17T01:41:05","documenter_version":"1.7.0"}}
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Bibliography · QuantumSymbolics.jl</title><meta name="title" content="Bibliography · QuantumSymbolics.jl"/><meta property="og:title" content="Bibliography · QuantumSymbolics.jl"/><meta property="twitter:title" content="Bibliography · QuantumSymbolics.jl"/><meta name="description" content="Documentation for QuantumSymbolics.jl."/><meta property="og:description" content="Documentation for QuantumSymbolics.jl."/><meta property="twitter:description" content="Documentation for QuantumSymbolics.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script data-outdated-warner src="../assets/warner.js"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 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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="../">QuantumSymbolics.jl</a></li><li><a class="tocitem" href="../introduction/">Getting Started with QuantumSymbolics.jl</a></li><li><a class="tocitem" href="../express/">Express Functionality</a></li><li><a class="tocitem" href="../qubit_basis/">Qubit Basis Choice</a></li><li><a class="tocitem" href="../QHO/">Quantum Harmonic Oscillators</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 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docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Bibliography"><a class="docs-heading-anchor" href="#Bibliography">Bibliography</a><a id="Bibliography-1"></a><a class="docs-heading-anchor-permalink" href="#Bibliography" title="Permalink"></a></h1><div class="citation canonical"><ul></ul></div></article><nav class="docs-footer"><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 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Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Bibliography · QuantumSymbolics.jl</title><meta name="title" content="Bibliography · QuantumSymbolics.jl"/><meta property="og:title" content="Bibliography · QuantumSymbolics.jl"/><meta property="twitter:title" content="Bibliography · QuantumSymbolics.jl"/><meta name="description" content="Documentation for QuantumSymbolics.jl."/><meta property="og:description" content="Documentation for QuantumSymbolics.jl."/><meta property="twitter:description" content="Documentation for QuantumSymbolics.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 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href="../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><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><script src="../assets/init.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">QuantumSymbolics.jl</a></span></div><button class="docs-search-query 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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>Bibliography</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Bibliography</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/QuantumSavory/QuantumSymbolics.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/QuantumSymbolics.jl/blob/main/docs/src/bibliography.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="Bibliography"><a class="docs-heading-anchor" href="#Bibliography">Bibliography</a><a id="Bibliography-1"></a><a class="docs-heading-anchor-permalink" href="#Bibliography" title="Permalink"></a></h1><div class="citation canonical"><ul></ul></div></article><nav class="docs-footer"><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 17 September 2024 01:41">Tuesday 17 September 2024</span>. 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0.0 + 0.0im))</code></pre><p>The caching feature of <a href="../API/#QuantumSymbolics.express"><code>express</code></a> prevents a specific representation for a symbolic quantum object from being computed more than once. This becomes handy for translations of more complex operations, which can become computationally expensive. We also have the ability to express <span>$|Z_1\rangle$</span> in the Clifford formalism with <a href="https://github.com/QuantumSavory/QuantumClifford.jl"><code>QuantumClifford.jl</code></a>:</p><pre><code class="language-julia hljs">express(ψ, CliffordRepr())</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">𝒟ℯ𝓈𝓉𝒶𝒷
+ X
𝒮𝓉𝒶𝒷
+ Z</code></pre><p>Here, we specified an instance of <code>CliffordRepr</code> in the second argument to convert <code>ψ</code> into a tableau of Pauli operators containing its stabilizer and destabilizer states. Now, both the state vector and Clifford representation of <code>ψ</code> have been cached:</p><pre><code class="language-julia hljs">ψ.metadata</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">QuantumSymbolics.Metadata(Dict{Tuple{AbstractRepresentation, AbstractUse}, Any}((CliffordRepr(), UseAsState()) =&gt; MixedDestablizer 1×1, (QuantumOpticsRepr(2), UseAsState()) =&gt; Ket(dim=2)
+ Z</code></pre><p>Here, we specified an instance of <code>CliffordRepr</code> in the second argument to convert <code>ψ</code> into a tableau of Pauli operators containing its stabilizer and destabilizer states. Now, both the state vector and Clifford representation of <code>ψ</code> have been cached:</p><pre><code class="language-julia hljs">ψ.metadata</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">QuantumSymbolics.Metadata(Dict{Tuple{AbstractRepresentation, AbstractUse}, Any}((QuantumOpticsRepr(2), UseAsState()) =&gt; Ket(dim=2)
basis: Spin(1/2)
1.0 + 0.0im
0.0 + 0.0im))</code></pre><p>More involved examples can be explored. For instance, say we want to apply the tensor product <span>$X\otimes Y$</span> of the Pauli operators <span>$X$</span> and <span>$Y$</span> to the Bell state <span>$|\Phi^{+}\rangle = \dfrac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right)$</span>, and numerically express the result in the quantum optics formalism. This would be done as follows:</p><pre><code class="language-julia hljs">bellstate = (Z1⊗Z1+Z2⊗Z2)/√2
0.0 + 0.0im, (CliffordRepr(), UseAsState()) =&gt; MixedDestablizer 1×1))</code></pre><p>More involved examples can be explored. For instance, say we want to apply the tensor product <span>$X\otimes Y$</span> of the Pauli operators <span>$X$</span> and <span>$Y$</span> to the Bell state <span>$|\Phi^{+}\rangle = \dfrac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right)$</span>, and numerically express the result in the quantum optics formalism. This would be done as follows:</p><pre><code class="language-julia hljs">bellstate = (Z1⊗Z1+Z2⊗Z2)/√2
tp = σˣ⊗σʸ
express(tp*bellstate)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Ket(dim=4)
basis: [Spin(1/2) ⊗ Spin(1/2)]
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0.0+0.0im 1.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im
0.0+0.0im 0.0+0.0im 2.0+0.0im 0.0+0.0im 0.0+0.0im
0.0+0.0im 0.0+0.0im 0.0+0.0im 3.0+0.0im 0.0+0.0im
0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 4.0+0.0im</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../introduction/">« Getting Started with QuantumSymbolics.jl</a><a class="docs-footer-nextpage" href="../qubit_basis/">Qubit Basis Choice »</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="Thursday 12 September 2024 13:45">Thursday 12 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
0.0+0.0im 0.0+0.0im 0.0+0.0im 0.0+0.0im 4.0+0.0im</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../introduction/">« Getting Started with QuantumSymbolics.jl</a><a class="docs-footer-nextpage" href="../qubit_basis/">Qubit Basis Choice »</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 17 September 2024 01:41">Tuesday 17 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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