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<h1 id='quantum-circuit-simulator-in-swift' class='heading'>Quantum circuit simulator in Swift</h1>
<p><a href="https://github.com/indisoluble/SwiftQuantumComputing/actions?query=branch%3Amaster"><img src="https://github.com/indisoluble/SwiftQuantumComputing/workflows/build/badge.svg?branch=master" alt="CI Status"></a>
<a href="https://codecov.io/gh/indisoluble/SwiftQuantumComputing"><img src="https://codecov.io/gh/indisoluble/SwiftQuantumComputing/branch/master/graph/badge.svg" alt="codecov"></a>
<img src="https://img.shields.io/badge/platform-iOS%20%7C%20macOS%20%7C%20Linux-lightgrey.svg" alt="platforms">
<a href="https://indisoluble.github.io/SwiftQuantumComputing"><img src="https://indisoluble.github.io/SwiftQuantumComputing/badge.svg" alt="Documentation"></a></p>
<h2 id='usage' class='heading'>Usage</h2>
<h3 id='circuit' class='heading'>Circuit</h3>
<p><img src="https://raw.githubusercontent.com/indisoluble/SwiftQuantumComputing/master/Images/Usage.jpg" alt="Usage"></p>
<p>Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Usage/Circuit.playground/Contents.swift">Circuit.playground</a>.</p>
<h3 id='circuit-with-noise' class='heading'>Circuit with noise</h3>
<pre class="highlight swift"><code><span class="kd">import</span> <span class="kt">SwiftQuantumComputing</span> <span class="c1">// for macOS</span>
<span class="c1">//: 1. Compose a list of quantum gates & noises</span>
<span class="k">let</span> <span class="nv">quantumOperators</span><span class="p">:</span> <span class="p">[</span><span class="kt">QuantumOperatorConvertible</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span>
<span class="kt">Gate</span><span class="o">.</span><span class="nf">hadamard</span><span class="p">(</span><span class="nv">target</span><span class="p">:</span> <span class="mi">0</span><span class="p">),</span>
<span class="kt">Noise</span><span class="o">.</span><span class="nf">bitFlip</span><span class="p">(</span><span class="nv">probability</span><span class="p">:</span> <span class="mf">0.35</span><span class="p">,</span> <span class="nv">target</span><span class="p">:</span> <span class="mi">0</span><span class="p">),</span>
<span class="kt">Gate</span><span class="o">.</span><span class="nf">phaseShift</span><span class="p">(</span><span class="nv">radians</span><span class="p">:</span> <span class="mf">0.25</span><span class="p">,</span> <span class="nv">target</span><span class="p">:</span> <span class="mi">2</span><span class="p">),</span>
<span class="kt">Noise</span><span class="o">.</span><span class="nf">phaseDamping</span><span class="p">(</span><span class="nv">probability</span><span class="p">:</span> <span class="mf">0.75</span><span class="p">,</span> <span class="nv">target</span><span class="p">:</span> <span class="mi">2</span><span class="p">),</span>
<span class="kt">Gate</span><span class="o">.</span><span class="nf">controlled</span><span class="p">(</span><span class="nv">gate</span><span class="p">:</span> <span class="o">.</span><span class="nf">hadamard</span><span class="p">(</span><span class="nv">target</span><span class="p">:</span> <span class="mi">1</span><span class="p">),</span> <span class="nv">controls</span><span class="p">:</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span>
<span class="kt">Noise</span><span class="o">.</span><span class="nf">bitFlip</span><span class="p">(</span><span class="nv">probability</span><span class="p">:</span> <span class="mf">0.8</span><span class="p">,</span> <span class="nv">target</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span>
<span class="p">]</span>
<span class="c1">//: 2. Build a quantum circuit with noise using the list</span>
<span class="k">let</span> <span class="nv">circuit</span> <span class="o">=</span> <span class="kt">MainNoiseCircuitFactory</span><span class="p">()</span><span class="o">.</span><span class="nf">makeNoiseCircuit</span><span class="p">(</span><span class="nv">quantumOperators</span><span class="p">:</span> <span class="n">quantumOperators</span><span class="p">)</span>
<span class="c1">//: 3. Use the quantum circuit with noise</span>
<span class="k">let</span> <span class="nv">result</span> <span class="o">=</span> <span class="k">try</span> <span class="n">circuit</span><span class="o">.</span><span class="nf">densityMatrix</span><span class="p">()</span><span class="o">.</span><span class="nf">get</span><span class="p">()</span>
<span class="nf">print</span><span class="p">(</span><span class="s">"Density matrix: </span><span class="se">\(</span><span class="n">result</span><span class="se">)\n</span><span class="s">"</span><span class="p">)</span>
<span class="nf">print</span><span class="p">(</span><span class="s">"Probabilities: </span><span class="se">\(</span><span class="n">result</span><span class="o">.</span><span class="nf">probabilities</span><span class="p">()</span><span class="se">)\n</span><span class="s">"</span><span class="p">)</span>
</code></pre>
<p>Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Usage/NoiseCircuit.playground/Contents.swift">NoiseCircuit.playground</a>.</p>
<h2 id='performance' class='heading'>Performance</h2>
<pre class="highlight shell"><code>~/SwiftQuantumComputing % swift run sqc-measure-performance
</code></pre>
<p>Run this application to check the performance of this simulator in your computer. Execute <code>swift run sqc-measure-performance -h</code> to see all available options.</p>
<p>Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Sources/SQCMeasurePerformance/main.swift">SQCMeasurePerformance/main.swift</a>.</p>
<h2 id='algorithms' class='heading'>Algorithms</h2>
<ul>
<li>Use a genetic algorithm to automatically generate a quantum circuit - Check example in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Usage/Genetic.playground/Contents.swift">Genetic.playground</a>.</li>
<li>Two-level decomposition: Decompose any gate into an equivalent sequence of not gates and fully controlled phase shifts, z-rotations, y-rotations & not gates - Check example in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Usage/TwoLevelDecomposition.playground/Contents.swift">TwoLevelDecomposition.playground</a>.</li>
</ul>
<h2 id='other-algorithms' class='heading'>Other algorithms</h2>
<ul>
<li>Euclidean Algorithm: Find greatest common divisor of two integers - Check example in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Usage/EuclideanAlgorithm.playground/Contents.swift">EuclideanAlgorithm.playground</a>.</li>
<li>Continued Fractions: Find an approximation to a given rational number - Check example in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Usage/ContinuedFractions.playground/Contents.swift">ContinuedFractions.playground</a>.</li>
<li>Gaussian Elimination: Solve a system of XOR equations - Check example in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Usage/XorGaussianElimination.playground/Contents.swift">XorGaussianElimination.playground</a>.</li>
</ul>
<h2 id='more-examples' class='heading'>More examples</h2>
<ul>
<li>Bernstein–Vazirani algorithm - Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Example/BernsteinVaziraniAlgorithm.playground/Contents.swift">BernsteinVaziraniAlgorithm.playground</a>.</li>
<li>Deutsch’s algorithm - Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Example/DeutschAlgorithm.playground/Contents.swift">DeutschAlgorithm.playground</a>.</li>
<li>Deutsch-Jozsa algorithm - Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Example/DeutschJozsaAlgorithm.playground/Contents.swift">DeutschJozsaAlgorithm.playground</a>.</li>
<li>Grover’s algorithm - Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Example/GroverAlgorithm.playground/Contents.swift">GroverAlgorithm.playground</a>.</li>
<li>Shor’s Algorithm - Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Example/ShorAlgorithm.playground/Contents.swift">ShorAlgorithm.playground</a>.</li>
<li>Simon’s periodicity algorithm - Check code in <a href="https://github.com/indisoluble/SwiftQuantumComputing/tree/master/Playground/Example/SimonPeriodicityAlgorithm.playground/Contents.swift">SimonPeriodicityAlgorithm.playground</a>.</li>
</ul>
<h2 id='documentation' class='heading'>Documentation</h2>
<p>Documentation for the project can be found <a href="https://indisoluble.github.io/SwiftQuantumComputing">here</a>.</p>
<h2 id='references' class='heading'>References</h2>
<ul>
<li><a href="https://github.com/aws/amazon-braket-default-simulator-python">Amazon Braket Default Simulator</a></li>
<li><a href="https://www.amazon.com/Automatic-Quantum-Computer-Programming-Approach/dp/038736496X">Automatic Quantum Computer Programming: A Genetic Programming Approach</a></li>
<li><a href="https://www.math.u-bordeaux.fr/%7Epjaming/M1/exposes/MA2.pdf">Continued Fractions and the Euclidean Algorithm</a></li>
<li><a href="https://arxiv.org/abs/1210.7366">Decomposition of unitary matrices and quantum gates</a></li>
<li><a href="https://github.com/fedimser/quantum_decomp/blob/master/res/Fedoriaka2019Decomposition.pdf">Decomposition of unitary matrix into quantum gates</a></li>
<li><a href="https://github.com/Qiskit/qiskit-terra">IBM Qiskit</a></li>
<li><a href="https://arxiv.org/abs/1601.07195">qHiPSTER: The Quantum High Performance Software Testing Environment</a></li>
<li><a href="https://www.amazon.com/Quantum-Computing-Computer-Scientists-Yanofsky/dp/0521879965">Quantum Computing for Computer Scientists</a></li>
<li><a href="https://arxiv.org/abs/quant-ph/0010034">Shor’s Quantum Factoring Algorithm</a></li>
</ul>
<h2 id='swiftpm-dependencies' class='heading'>SwiftPM dependencies</h2>
<ul>
<li><a href="https://github.com/indisoluble/CBLAS-Linux">CBLAS-Linux</a> (only for Linux)</li>
<li><a href="https://github.com/indisoluble/CLapacke-Linux">CLapacke-Linux</a> (only for Linux)</li>
<li><a href="https://github.com/apple/swift-argument-parser">Swift Argument Parser</a></li>
<li><a href="https://github.com/apple/swift-numerics">Swift Numerics</a></li>
</ul>
<h3 id='linux' class='heading'>Linux</h3>
<p>This package depends on <a href="http://www.netlib.org/blas/">BLAS</a> & <a href="http://www.netlib.org/lapack/">LAPACK</a> if running on Linux, more exactly, <a href="https://www.ubuntu.com">Ubuntu</a>.</p>
<p>These dependencies are reflected in <code>Package.swift</code> with:</p>
<ul>
<li><a href="https://github.com/indisoluble/CBLAS-Linux">CBLAS-Linux</a>, which in turn expects to find: <code>/usr/include/x86_64-linux-gnu/cblas-netlib.h</code></li>
<li><a href="https://github.com/indisoluble/CLapacke-Linux">CLapacke-Linux</a>, which in turn expects to find: <code>/usr/include/lapacke.h</code></li>
</ul>
<p>So, after installing <a href="http://www.netlib.org/blas/">BLAS</a> & <a href="http://www.netlib.org/lapack/">LAPACK</a> (in case they are not already there):</p>
<pre class="highlight plaintext"><code>sudo apt-get install libblas-dev liblapacke-dev
</code></pre>
<p>Check <code>cblas-netlib.h</code> & <code>lapacke.h</code> are in the expected locations.</p>
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