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pr-2683/applications/python/adapt_qaoa.html

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@@ -783,7 +783,7 @@ <h1>ADAPT-QAOA algorithm<a class="headerlink" href="#ADAPT-QAOA-algorithm" title
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parameter</p>
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<p>3- Optimize all parameters currently in the Ansatz <span class="math notranslate nohighlight">\(\beta_m, \gamma_m = 1, 2, ...k\)</span> such that <span class="math notranslate nohighlight">\(\braket{\psi (k)|H_C|\psi(k)}\)</span> is minimized, and return to the second step.</p>
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<p>Below is a schematic representation of the ADAPT-QAOA algorithm explained above.</p>
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<div><p><img alt="284b8ea11af24078bd88ebd8f434c692" class="no-scaled-link" src="../../_images/adapt-qaoa.png" style="width: 600px;" /></p>
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<div><p><img alt="d5fdcd0deab84de899e98d98cb265d42" class="no-scaled-link" src="../../_images/adapt-qaoa.png" style="width: 600px;" /></p>
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</div><div class="nbinput nblast docutils container">
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<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[ ]:
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</pre></div>

pr-2683/applications/python/deutschs_algorithm.html

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@@ -840,7 +840,7 @@ <h2>XOR <span class="math notranslate nohighlight">\(\oplus\)</span><a class="he
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</section>
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<section id="Quantum-oracles">
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<h2>Quantum oracles<a class="headerlink" href="#Quantum-oracles" title="Permalink to this heading"></a></h2>
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<p><img alt="2dc1c2e423a742288c8d84d6533a3238" class="no-scaled-link" src="../../_images/oracle.png" style="width: 300px; height: 150px;" /></p>
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<p><img alt="b1142592f5bd4a7ab6ebd64eff50aee7" class="no-scaled-link" src="../../_images/oracle.png" style="width: 300px; height: 150px;" /></p>
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<p>Suppose we have <span class="math notranslate nohighlight">\(f(x): \{0,1\} \longrightarrow \{0,1\}\)</span>. We can compute this function on a quantum computer using oracles which we treat as black box functions that yield the output with an appropriate sequence of logical gates.</p>
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<p>Above you see an oracle represented as <span class="math notranslate nohighlight">\(U_f\)</span> which allows us to transform the state <span class="math notranslate nohighlight">\(\ket{x}\ket{y}\)</span> into:</p>
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<div class="math notranslate nohighlight">
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<h2>Deutsch’s Algorithm:<a class="headerlink" href="#Deutsch's-Algorithm:" title="Permalink to this heading"></a></h2>
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<p>Our aim is to find out if <span class="math notranslate nohighlight">\(f: \{0,1\} \longrightarrow \{0,1\}\)</span> is a constant or a balanced function? If constant, <span class="math notranslate nohighlight">\(f(0) = f(1)\)</span>, and if balanced, <span class="math notranslate nohighlight">\(f(0) \neq f(1)\)</span>.</p>
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<p>We step through the circuit diagram below and follow the math after the application of each gate.</p>
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<p><img alt="2874a5fcd49249528e4819f63ce970a1" class="no-scaled-link" src="../../_images/deutsch.png" style="width: 500px; height: 210px;" /></p>
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<p><img alt="ca929ad3b98c4bfcb9349686b478cccf" class="no-scaled-link" src="../../_images/deutsch.png" style="width: 500px; height: 210px;" /></p>
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<div class="math notranslate nohighlight">
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\[\ket{\psi_0} = \ket{01}
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\tag{1}\]</div>

pr-2683/applications/python/quantum_transformer.html

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pr-2683/examples/python/performance_optimizations.html

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@@ -768,9 +768,9 @@ <h1>Optimizing Performance<a class="headerlink" href="#Optimizing-Performance" t
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<section id="Gate-Fusion">
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<h2>Gate Fusion<a class="headerlink" href="#Gate-Fusion" title="Permalink to this heading"></a></h2>
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<p>Gate fusion is an optimization technique where consecutive gates are combined into a single gate operation to improve the efficiency of the simulation (See figure below). By targeting the <code class="docutils literal notranslate"><span class="pre">nvidia-mgpu</span></code> backend and setting the <code class="docutils literal notranslate"><span class="pre">CUDAQ_MGPU_FUSE</span></code> environment variable, you can select the degree of fusion that takes place. A full command line example would look like <code class="docutils literal notranslate"><span class="pre">CUDAQ_MGPU_FUSE=4</span> <span class="pre">python</span> <span class="pre">c2h2VQE.py</span> <span class="pre">--target</span> <span class="pre">nvidia</span> <span class="pre">--target-option</span> <span class="pre">fp64,mgpu</span></code></p>
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<p><img alt="fdac1fbc679940468f2560de79cef046" src="../../_images/gate-fuse.png" /></p>
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<p><img alt="29a3a19ed9c34b8b9830f62a8480fa7e" src="../../_images/gate-fuse.png" /></p>
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<p>The importance of gate fusion is system dependent, but can have a large influence on the performance of the simulation. See the example below for a 24 qubit VQE experiment where changing the fusion level resulted in significant performance boosts.</p>
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<p><img alt="fe69aaddb9ba4ca5b663adb72f14df32" src="../../_images/gatefusion.png" /></p>
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<p><img alt="4eb02042f75f4af5b3054bb753ea00a6" src="../../_images/gatefusion.png" /></p>
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</section>
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</section>
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pr-2683/searchindex.js

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pr-2683/sphinx/examples/cpp/dynamics/cavity_qed.cpp

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// Here we choose a Runge-`Kutta` method for time evolution.
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// `dt` defines the time step for the numerical integration, and order 4
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// indicates a 4`th` order method.
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cudaq::RungeKuttaIntegrator integrator;
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cudaq::integrators::runge_kutta integrator;
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integrator.dt = 0.01;
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integrator.order = 4;
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pr-2683/sphinx/examples/cpp/dynamics/cross_resonance.cpp

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// Use Runge-`Kutta` integrator (4`th` order) to solve the time-dependent
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// evolution. `dt` is the integration time step, and `order` sets the accuracy
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// of the integrator method.
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cudaq::RungeKuttaIntegrator integrator;
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cudaq::integrators::runge_kutta integrator;
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integrator.dt = 0.0001;
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integrator.order = 4;
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pr-2683/sphinx/examples/cpp/dynamics/heisenberg_model.cpp

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// Use a Runge-`Kutta` integrator (4`th` order) with a small time step `dt`
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// = 0.001.
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cudaq::RungeKuttaIntegrator integrator;
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cudaq::integrators::runge_kutta integrator;
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integrator.dt = 0.001;
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integrator.order = 4;
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pr-2683/sphinx/examples/cpp/dynamics/qubit_control.cpp

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cudaq::Schedule schedule(steps, {"t"});
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// A Runge-`Kutta` integrator (4`th` order) with a small time step `dt`.
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cudaq::RungeKuttaIntegrator integrator;
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cudaq::integrators::runge_kutta integrator;
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integrator.dt = dt;
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integrator.order = 4;
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pr-2683/sphinx/examples/cpp/dynamics/qubit_dynamics.cpp

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cudaq::Schedule schedule(steps);
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// Runge-`Kutta` integrator with a time step of 0.001 and order 4
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cudaq::RungeKuttaIntegrator integrator;
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cudaq::integrators::runge_kutta integrator;
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integrator.dt = 0.01;
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integrator.order = 4;
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