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{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-09-25T22:24:20","documenter_version":"1.7.0"}}
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-10-02T06:30:47","documenter_version":"1.7.0"}}
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version = {v0.1.0},
doi = {10.5281/zenodo.6390515},
url = {https://doi.org/10.5281/zenodo.6390515}
}</code></pre><p>–&gt;</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="manual/1-intro/">Introduction »</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="Wednesday 25 September 2024 22:24">Wednesday 25 September 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
}</code></pre><p>–&gt;</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="manual/1-intro/">Introduction »</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="Wednesday 2 October 2024 06:30">Wednesday 2 October 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Introduction · QUBODrivers.jl</title><meta name="title" content="Introduction · QUBODrivers.jl"/><meta property="og:title" content="Introduction · QUBODrivers.jl"/><meta property="twitter:title" content="Introduction · QUBODrivers.jl"/><meta name="description" content="Documentation for QUBODrivers.jl."/><meta property="og:description" content="Documentation for QUBODrivers.jl."/><meta property="twitter:description" content="Documentation for QUBODrivers.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/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" 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><link href="../../assets/extra_styles.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.svg" alt="QUBODrivers.jl logo"/></a><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="../../">Home</a></li><li><span class="tocitem">Manual</span><ul><li class="is-active"><a class="tocitem" href>Introduction</a><ul class="internal"><li><a class="tocitem" href="#QUBO"><span>QUBO</span></a></li><li><a class="tocitem" href="#Table-of-Contents"><span>Table of Contents</span></a></li></ul></li><li><a class="tocitem" href="../2-solve/">Solving QUBO</a></li><li><a class="tocitem" href="../3-samplers/">Samplers</a></li><li><a class="tocitem" href="../4-setup/">Sampler Setup</a></li><li><a class="tocitem" href="../5-tests/">Test Suite</a></li><li><a class="tocitem" href="../6-benchmarks/">Benchmarking</a></li></ul></li><li><span class="tocitem">Booklet</span><ul><li><a class="tocitem" href="../../booklet/1-intro/">Itroduction</a></li><li><a class="tocitem" href="../../booklet/2-interface/">Sampler Interface</a></li><li><a class="tocitem" href="../../booklet/3-attributes/">Attribute System</a></li></ul></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><a class="is-disabled">Manual</a></li><li class="is-active"><a href>Introduction</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Introduction</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaQUBO/QUBODrivers.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/JuliaQUBO/QUBODrivers.jl/blob/master/docs/src/manual/1-intro.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="Introduction"><a class="docs-heading-anchor" href="#Introduction">Introduction</a><a id="Introduction-1"></a><a class="docs-heading-anchor-permalink" href="#Introduction" title="Permalink"></a></h1><h2 id="QUBO"><a class="docs-heading-anchor" href="#QUBO">QUBO</a><a id="QUBO-1"></a><a class="docs-heading-anchor-permalink" href="#QUBO" title="Permalink"></a></h2><p>An optimization problem is in its QUBO form if it is written as</p><p class="math-container">\[\begin{array}{rl}
\min &amp; \alpha \left[ \mathbf{x}&#39;\mathbf{Q}\,\mathbf{x} + \mathbf{\ell}&#39;\mathbf{x} + \beta \right] \\
\text{s.t.} &amp; \mathbf{x} \in S \cong \mathbb{B}^{n}
\end{array}\]</p><p>with linear terms <span>$\mathbf{\ell} \in \mathbb{R}^{n}$</span> and quadratic <span>$\mathbf{Q} \in \mathbb{R}^{n \times n}$</span>. <span>$\alpha, \beta \in \mathbb{R}$</span> are, respectively, the scaling and offset factors.</p><p>The MOI-JuMP optimizers defined using the <code>QUBODrivers.AbstractSampler{T} &lt;: MOI.AbstractOptimizer</code> interface only support models given in the QUBO form. <code>QUBODrivers.jl</code> employs <a href="https://github.com/psrenergy/QUBOTools.jl">QUBOTools</a> on many tasks involving data management and querying. It is worth taking a look at <a href="https://psrenergy.github.io/QUBOTools.jl">QUBOTool&#39;s docs</a>.</p><h2 id="Table-of-Contents"><a class="docs-heading-anchor" href="#Table-of-Contents">Table of Contents</a><a id="Table-of-Contents-1"></a><a class="docs-heading-anchor-permalink" href="#Table-of-Contents" title="Permalink"></a></h2><ul><li><a href="../2-solve/#Solving-QUBO">Solving QUBO</a></li><li class="no-marker"><ul><li><a href="../2-solve/#Solving-Simple-QUBO-Model-with-QUBODrivers&#39;-[RandomSampler.Optimizer](@ref)">Solving Simple QUBO Model with QUBODrivers&#39; <code>RandomSampler.Optimizer</code></a></li></ul></li><li><a href="../3-samplers/#Samplers">Samplers</a></li><li class="no-marker"><ul><li><a href="../3-samplers/#Utility-Samplers">Utility Samplers</a></li><li><a href="../3-samplers/#Showcase">Showcase</a></li></ul></li><li><a href="../4-setup/#Sampler-Setup">Sampler Setup</a></li><li class="no-marker"><ul><li><a href="../4-setup/#Imports">Imports</a></li><li><a href="../4-setup/#The-[QUBODrivers.@setup](@ref)-macro">The <code>QUBODrivers.@setup</code> macro</a></li><li><a href="../4-setup/#The-[QUBODrivers.sample](@ref)-method">The <code>QUBODrivers.sample</code> method</a></li><li><a href="../4-setup/#A-complete-example">A complete example</a></li></ul></li><li><a href="../5-tests/#Test-Suite">Test Suite</a></li><li><a href="../6-benchmarks/#Benchmarking">Benchmarking</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../2-solve/">Solving QUBO »</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="Wednesday 25 September 2024 22:24">Wednesday 25 September 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
\end{array}\]</p><p>with linear terms <span>$\mathbf{\ell} \in \mathbb{R}^{n}$</span> and quadratic <span>$\mathbf{Q} \in \mathbb{R}^{n \times n}$</span>. <span>$\alpha, \beta \in \mathbb{R}$</span> are, respectively, the scaling and offset factors.</p><p>The MOI-JuMP optimizers defined using the <code>QUBODrivers.AbstractSampler{T} &lt;: MOI.AbstractOptimizer</code> interface only support models given in the QUBO form. <code>QUBODrivers.jl</code> employs <a href="https://github.com/psrenergy/QUBOTools.jl">QUBOTools</a> on many tasks involving data management and querying. It is worth taking a look at <a href="https://psrenergy.github.io/QUBOTools.jl">QUBOTool&#39;s docs</a>.</p><h2 id="Table-of-Contents"><a class="docs-heading-anchor" href="#Table-of-Contents">Table of Contents</a><a id="Table-of-Contents-1"></a><a class="docs-heading-anchor-permalink" href="#Table-of-Contents" title="Permalink"></a></h2><ul><li><a href="../2-solve/#Solving-QUBO">Solving QUBO</a></li><li class="no-marker"><ul><li><a href="../2-solve/#Solving-Simple-QUBO-Model-with-QUBODrivers&#39;-[RandomSampler.Optimizer](@ref)">Solving Simple QUBO Model with QUBODrivers&#39; <code>RandomSampler.Optimizer</code></a></li></ul></li><li><a href="../3-samplers/#Samplers">Samplers</a></li><li class="no-marker"><ul><li><a href="../3-samplers/#Utility-Samplers">Utility Samplers</a></li><li><a href="../3-samplers/#Showcase">Showcase</a></li></ul></li><li><a href="../4-setup/#Sampler-Setup">Sampler Setup</a></li><li class="no-marker"><ul><li><a href="../4-setup/#Imports">Imports</a></li><li><a href="../4-setup/#The-[QUBODrivers.@setup](@ref)-macro">The <code>QUBODrivers.@setup</code> macro</a></li><li><a href="../4-setup/#The-[QUBODrivers.sample](@ref)-method">The <code>QUBODrivers.sample</code> method</a></li><li><a href="../4-setup/#A-complete-example">A complete example</a></li></ul></li><li><a href="../5-tests/#Test-Suite">Test Suite</a></li><li><a href="../6-benchmarks/#Benchmarking">Benchmarking</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../2-solve/">Solving QUBO »</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="Wednesday 2 October 2024 06:30">Wednesday 2 October 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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yi = objective_value(model; result=i) # Energy

println(&quot;f($xi) = $(yi)&quot;)
end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">f([1.0, 0.0, 0.0]) = -1.0
end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">f([0.0, 0.0, 1.0]) = -1.0
f([1.0, 0.0, 0.0]) = -1.0
f([0.0, 1.0, 0.0]) = -1.0
f([0.0, 0.0, 1.0]) = -1.0
f([0.0, 0.0, 0.0]) = 0.0
f([1.0, 0.0, 1.0]) = 2.0
f([1.0, 1.0, 0.0]) = 2.0
f([0.0, 1.0, 1.0]) = 2.0
f([1.0, 1.0, 1.0]) = 9.0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../1-intro/">« Introduction</a><a class="docs-footer-nextpage" href="../3-samplers/">Samplers »</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="Wednesday 25 September 2024 22:24">Wednesday 25 September 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
f([1.0, 1.0, 1.0]) = 9.0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../1-intro/">« Introduction</a><a class="docs-footer-nextpage" href="../3-samplers/">Samplers »</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="Wednesday 2 October 2024 06:30">Wednesday 2 October 2024</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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