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<p class="sd-text-right" id="qat-fermion"><a class="sd-sphinx-override sd-btn sd-text-wrap sd-btn-outline-primary reference external" href="https://github.com/myQLM/myqlm-fermion"><span><svg version="1.1" width="2.812em" height="1.0em" class="sd-octicon sd-octicon-logo-github" viewBox="0 0 45 16" aria-hidden="true"><path d="M8.81 7.35v5.74c0 .04-.01.11-.06.13 0 0-1.25.89-3.31.89-2.49 0-5.44-.78-5.44-5.92S2.58 1.99 5.1 2c2.18 0 3.06.49 3.2.58.04.05.06.09.06.14L7.94 4.5c0 .09-.09.2-.2.17-.36-.11-.9-.33-2.17-.33-1.47 0-3.05.42-3.05 3.73s1.5 3.7 2.58 3.7c.92 0 1.25-.11 1.25-.11v-2.3H4.88c-.11 0-.19-.08-.19-.17V7.35c0-.09.08-.17.19-.17h3.74c.11 0 .19.08.19.17Zm35.85 2.33c0 3.43-1.11 4.41-3.05 4.41-1.64 0-2.52-.83-2.52-.83s-.04.46-.09.52c-.03.06-.08.08-.14.08h-1.48c-.1 0-.19-.08-.19-.17l.02-11.11c0-.09.08-.17.17-.17h2.13c.09 0 .17.08.17.17v3.77s.82-.53 2.02-.53l-.01-.02c1.2 0 2.97.45 2.97 3.88ZM27.68 2.43c.09 0 .17.08.17.17v11.11c0 .09-.08.17-.17.17h-2.13c-.09 0-.17-.08-.17-.17l.02-4.75h-3.31v4.75c0 .09-.08.17-.17.17h-2.13c-.08 0-.17-.08-.17-.17V2.6c0-.09.08-.17.17-.17h2.13c.09 0 .17.08.17.17v4.09h3.31V2.6c0-.09.08-.17.17-.17Zm8.26 3.64c.11 0 .19.08.19.17l-.02 7.47c0 .09-.06.17-.17.17H34.6c-.07 0-.14-.04-.16-.09-.03-.06-.08-.45-.08-.45s-1.13.77-2.52.77c-1.69 0-2.92-.55-2.92-2.75V6.25c0-.09.08-.17.17-.17h2.14c.09 0 .17.08.17.17V11c0 .75.22 1.09.97 1.09s1.3-.39 1.3-.39V6.26c0-.11.06-.19.17-.19Zm-17.406 5.971h.005a.177.177 0 0 1 .141.179v1.5c0 .07-.03.14-.09.16-.1.05-.74.22-1.27.22-1.16 0-2.86-.25-2.86-2.69V8.13h-1.11c-.09 0-.17-.08-.17-.19V6.58c0-.08.05-.15.13-.17.07-.01 1.16-.28 1.16-.28V3.96c0-.08.05-.13.14-.13h2.16c.09 0 .14.05.14.13v2.11h1.59c.08 0 .16.08.16.17v1.7c0 .11-.07.19-.16.19h-1.59v3.131c0 .47.27.83 1.05.83.247 0 .481-.049.574-.05ZM12.24 6.06c.09 0 .17.08.17.17v7.37c0 .18-.05.27-.25.27h-1.92c-.17 0-.3-.07-.3-.27V6.26c0-.11.08-.2.17-.2Zm29.99 3.78c0-1.81-.73-2.05-1.5-1.97-.6.04-1.08.34-1.08.34v3.52s.49.34 1.22.36c1.03.03 1.36-.34 1.36-2.25ZM11.19 2.68c.75 0 1.36.61 1.36 1.38 0 .77-.61 1.38-1.36 1.38-.77 0-1.38-.61-1.38-1.38 0-.77.61-1.38 1.38-1.38Zm7.34 9.35v.001l.01.01h-.001l-.005-.001v.001c-.009-.001-.015-.011-.024-.011Z"></path></svg></span></a></p>
<section id="spin-and-fermionic-systems">
<h1>Spin and fermionic systems<a class="headerlink" href="#spin-and-fermionic-systems" title="Link to this heading"></a></h1>
<p>Qaptiva provides tools to describe and solve spin and fermionic problems. These tools
are packages in the <a class="reference internal" href="04_api_reference/module_qat/module_fermion.html#module-qat.fermion" title="qat.fermion"><code class="xref py py-mod docutils literal notranslate"><span class="pre">qat.fermion</span></code></a> module. This module is open source and part of both
myQLM and the Qaptiva appliance. The source code can be found
<a class="reference external" href="https://github.com/myQLM/myqlm-fermion">on GitHub</a>.</p>
<p>This <a class="reference internal" href="04_api_reference/module_qat/module_fermion.html#module-qat.fermion" title="qat.fermion"><code class="xref py py-mod docutils literal notranslate"><span class="pre">qat.fermion</span></code></a> module includes, among others:</p>
<blockquote>
<div><ul class="simple">
<li><p>objects to help you define <strong>fermionic and spin Hamiltonians</strong>,</p></li>
<li><p>spin-to-fermion transformations, such as Jordan-Wigner, Bravyi-Kitaev or parity basis transformations,</p></li>
<li><p><strong>variational quantum eigensolver</strong> (VQE) tools, including a module to construct a <strong>UCC ansatz</strong>,</p></li>
<li><p>tools aimed at atomic and molecule studies (active space selection, basis transformations,…etc),</p></li>
<li><p>a <strong>trotterization</strong> module,</p></li>
<li><p>a <strong>quantum phase estimation</strong> module,</p></li>
<li><p>an adaptative ansatz VQE plugin (ADAPT-VQE),</p></li>
<li><p>a natural gradient-based optimizer,</p></li>
<li><p>a sequential hybrid classical-quantum optimizer,</p></li>
<li><p>a zero noise extrapolator plugin for multiqubit noise mitigation,</p></li>
<li><p>…</p></li>
</ul>
</div></blockquote>
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Creating and manipulating Hamiltonians</div>
</div>
<a class="sd-stretched-link sd-hide-link-text reference internal" href="fermion/01_hamiltonians.html"><span class="doc">fermion/01_hamiltonians.rst</span></a></div>
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Quantum application (including Ansätze and state preparation)</div>
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<a class="sd-stretched-link sd-hide-link-text reference internal" href="fermion/02_algorithms.html"><span class="doc">fermion/02_algorithms.rst</span></a></div>
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Plugins</div>
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<a class="sd-stretched-link sd-hide-link-text reference internal" href="fermion/03_plugins.html"><span class="doc">fermion/03_plugins.rst</span></a></div>
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Migrating code based on deprecated library qat.dqs</div>
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<a class="sd-stretched-link sd-hide-link-text reference internal" href="fermion/04_migrating.html"><span class="doc">fermion/04_migrating.rst</span></a></div>
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<section id="demos">
<h2>Demos<a class="headerlink" href="#demos" title="Link to this heading"></a></h2>
<p>We also provide the following Jupyter notebooks:</p>
<blockquote>
<div><ul class="simple">
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_spin_fermion_transforms.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Spin-fermions transforms</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_vqe_hubbard.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Variational Quantum Eigensolver for fermions</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_vqe_ucc_example_1_h2.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">VQE for a H2 molecule using the UCC ansatz</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_vqe_ucc_example_2_lih.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">VQE for a LiH molecule using the UCC ansatz</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_qpe_hubbard_molecule.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Quantum Phase Estimation on the Hubbard molecule</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_quantum_subspace_expansion_h2.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Advanced VQE: Quantum Subspace Expansion</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_natural_gradient_vqe.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Natural gradient-based optimizer</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_sequential_optimization_plugin.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Optimizing circuits with the sequential optimization plugin</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_multiple_launches_analyzer_plugin.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Running several optimizations and keeping the best one with MultipleLaunchesPlugin</a></p></li>
<li><p><a href="https://mybinder.org/v2/gh/myQLM/myqlm-notebooks/HEAD?filepath=tutorials%2Fdigital_quantum_simulations_spin_fermion%2Fqat_fermion_zero_noise_extrapolation_plugin.ipynb" style="color: #ff7823; text-decoration: underline; cursor: pointer">Mitigating multiqubit noise (QLM users only)</a></p></li>
</ul>
</div></blockquote>
</section>
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