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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>API · QuantumGradientGenerators.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://juliaquantumcontrol.github.io/QuantumGradientGenerators.jl/api/"/><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/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/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="../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="../">QuantumGradientGenerators.jl</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>API</a><ul class="internal"><li><a class="tocitem" href="#Index"><span>Index</span></a></li><li><a class="tocitem" href="#Reference"><span>Reference</span></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"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>API</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>API</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaQuantumControl/QuantumGradientGenerators.jl/blob/master/docs/src/api.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="QuantumGradientGenerators-API"><a class="docs-heading-anchor" href="#QuantumGradientGenerators-API"><code>QuantumGradientGenerators</code> API</a><a id="QuantumGradientGenerators-API-1"></a><a class="docs-heading-anchor-permalink" href="#QuantumGradientGenerators-API" title="Permalink"></a></h1><h2 id="Index"><a class="docs-heading-anchor" href="#Index">Index</a><a id="Index-1"></a><a class="docs-heading-anchor-permalink" href="#Index" title="Permalink"></a></h2><ul><li><a href="#QuantumGradientGenerators.GradGenerator"><code>QuantumGradientGenerators.GradGenerator</code></a></li><li><a href="#QuantumGradientGenerators.GradVector"><code>QuantumGradientGenerators.GradVector</code></a></li><li><a href="#QuantumGradientGenerators.GradgenOperator"><code>QuantumGradientGenerators.GradgenOperator</code></a></li><li><a href="#QuantumGradientGenerators.resetgradvec!-Tuple{GradVector}"><code>QuantumGradientGenerators.resetgradvec!</code></a></li></ul><h2 id="Reference"><a class="docs-heading-anchor" href="#Reference">Reference</a><a id="Reference-1"></a><a class="docs-heading-anchor-permalink" href="#Reference" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="QuantumGradientGenerators.GradGenerator" href="#QuantumGradientGenerators.GradGenerator"><code>QuantumGradientGenerators.GradGenerator</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Extended generator for the standard dynamic gradient.</p><pre><code class="language-julia hljs">G̃ = GradGenerator(G)</code></pre><p>contains the original time-dependent generator <code>G</code> (a Hamiltonian or Liouvillian) in <code>G̃.G</code>, a vector of control derivatives <span>$∂G/∂ϵₗ(t)$</span> in <code>G̃.control_derivs</code>, and the controls in <code>G̃.controls</code>.</p><p>For a generator <span>$G = Ĥ(t) = Ĥ₀ + ϵ₁(t) Ĥ₁ + … +  ϵₙ(t) Ĥₙ$</span>, this extended generator encodes the block-matrix</p><p class="math-container">\[G̃ = \begin{pmatrix}
+         Ĥ(t)  &amp;  0    &amp;  \dots   &amp;  0     &amp;  Ĥ₁     \\
+         0     &amp;  Ĥ(t) &amp;  \dots   &amp;  0     &amp;  Ĥ₂     \\
+    \vdots     &amp;       &amp;  \ddots  &amp;        &amp;  \vdots \\
+         0     &amp;  0    &amp;  \dots   &amp;  Ĥ(t)  &amp;  Ĥₙ     \\
+         0     &amp;  0    &amp;  \dots   &amp;  0     &amp;  Ĥ(t)
+\end{pmatrix}\]</p><p>Note that the <span>$∂G/∂ϵₗ(t)$</span> (<span>$Ĥₗ$</span> in the above example) may be time-dependent, to account for the possibility of non-linear control terms.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaQuantumControl/QuantumGradientGenerators.jl/blob/9222839bd33b8f728f8927be5ff5c3ec46b695b9/src/grad_generator.jl#L6-L32">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="QuantumGradientGenerators.GradVector" href="#QuantumGradientGenerators.GradVector"><code>QuantumGradientGenerators.GradVector</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Extended state-vector for the dynamic gradient.</p><pre><code class="language-julia hljs">Ψ̃ = GradVector(Ψ, num_controls)</code></pre><p>for an initial state <code>Ψ</code> and <code>num_controls</code> control fields.</p><p>The <code>GradVector</code> conceptually corresponds to a direct-sum (block) column-vector <span>$Ψ̃ = (|Ψ̃₁⟩, |Ψ̃₂⟩, … |Ψ̃ₙ⟩, |Ψ⟩)^T$</span>, where <span>$n$</span> is <code>num_controls</code>. With a matching <span>$G̃$</span> as in the documentation of <a href="#QuantumGradientGenerators.GradGenerator"><code>GradGenerator</code></a>, we have</p><p class="math-container">\[G̃ Ψ̃ = \begin{pmatrix}
+Ĥ |Ψ̃₁⟩ + Ĥ₁|Ψ⟩ \\
+\vdots \\
+Ĥ |Ψ̃ₙ⟩ + Ĥₙ|Ψ⟩ \\
+Ĥ |Ψ⟩
+\end{pmatrix}\]</p><p>and</p><p class="math-container">\[e^{-i G̃ dt} \begin{pmatrix} 0 \\ \vdots \\ 0 \\ |Ψ⟩ \end{pmatrix}
+= \begin{pmatrix}
+\frac{∂}{∂ϵ₁} e^{-i Ĥ dt} |Ψ⟩ \\
+\vdots \\
+\frac{∂}{∂ϵₙ} e^{-i Ĥ dt} |Ψ⟩ \\
+e^{-i Ĥ dt} |Ψ⟩
+\end{pmatrix}.\]</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaQuantumControl/QuantumGradientGenerators.jl/blob/9222839bd33b8f728f8927be5ff5c3ec46b695b9/src/grad_vector.jl#L4-L38">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="QuantumGradientGenerators.GradgenOperator" href="#QuantumGradientGenerators.GradgenOperator"><code>QuantumGradientGenerators.GradgenOperator</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Static generator for the dynamic gradient.</p><pre><code class="language-julia hljs">using QuantumPropagators.Controls: evaluate
+
+G::GradgenOperator = evaluate(gradgen::GradGenerator; vals_dict)</code></pre><p>is the result of plugging in specific values for all controls in a <a href="#QuantumGradientGenerators.GradGenerator"><code>GradGenerator</code></a>.</p><p>The resulting object can be multiplied directly with a <a href="#QuantumGradientGenerators.GradVector"><code>GradVector</code></a>, e.g., in the process of evaluating a piecewise-constant time propagation.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaQuantumControl/QuantumGradientGenerators.jl/blob/9222839bd33b8f728f8927be5ff5c3ec46b695b9/src/gradgen_operator.jl#L6-L20">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="QuantumGradientGenerators.resetgradvec!-Tuple{GradVector}" href="#QuantumGradientGenerators.resetgradvec!-Tuple{GradVector}"><code>QuantumGradientGenerators.resetgradvec!</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Reset the given gradient vector for a new gradient evaluation.</p><pre><code class="language-julia hljs">resetgradvec!(Ψ̃::GradVector)</code></pre><p>zeroes out <code>Ψ̃.grad_states</code> but leaves <code>Ψ̃.state</code> unaffected.</p><pre><code class="language-julia hljs">resetgradvec!(Ψ̃::GradVector, Ψ)</code></pre><p>additionally sets <code>Ψ̃.state</code> to <code>Ψ</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaQuantumControl/QuantumGradientGenerators.jl/blob/9222839bd33b8f728f8927be5ff5c3ec46b695b9/src/grad_vector.jl#L52-L66">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><div class="flexbox-break"></div><p class="footer-message"><a href="https://github.com/JuliaQuantumControl/QuantumGradientGenerators.jl">QuantumGradientGenerators.jl</a> v0.1.2 docs powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</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="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 0.27.24 on <span class="colophon-date" title="Tuesday 16 May 2023 04:03">Tuesday 16 May 2023</span>. Using Julia version 1.9.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>