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  <div class="section" id="quantum-registers">
<h1>Quantum Registers<a class="headerlink" href="#quantum-registers" title="Permalink to this headline">¶</a></h1>
<p>QCGPU provides a class to represent the register, <code class="docutils literal notranslate"><span class="pre">qcgpu.State</span></code>. The
register class stores (on the OpenCL device) a state vector. This state
vector is a chunk of memory, the size of which is:</p>
<div class="math notranslate nohighlight">
\[64 \cdot 2^n \text{ bits}.\]</div>
<p>This means you would need just 2kb of memory to have a 5 qubit register,
a 30 qubit register would take up 9gb of memory.</p>
<p>This is something to be aware of, as the state vector must fit in the
memory of the device you wish to use.</p>
<div class="section" id="using-the-state-class">
<h2>Using the <code class="docutils literal notranslate"><span class="pre">State</span></code> class<a class="headerlink" href="#using-the-state-class" title="Permalink to this headline">¶</a></h2>
<p>To create a new register, you can use</p>
<div class="code python highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">qcgpu</span>

<span class="n">register</span> <span class="o">=</span> <span class="n">qcgpu</span><span class="o">.</span><span class="n">State</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<p>This will create a 5 qubit register.</p>
<p>When you run this, you may be prompted to choose a device. This is
normal, as you can have more than 1 device that supports OpenCL in your
computer. Just choose the one you want.</p>
</div>
<div class="section" id="mathematical-description">
<h2>Mathematical Description<a class="headerlink" href="#mathematical-description" title="Permalink to this headline">¶</a></h2>
<p>This class represents a state vector <span class="math notranslate nohighlight">\(\lvert \psi \rangle\)</span> with</p>
<div class="math notranslate nohighlight">
\[\lvert \psi \rangle = \sum_{j = 0}^{2^n - 1} \alpha_j \lvert j \rangle\]</div>
<p>where <span class="math notranslate nohighlight">\(n\)</span> is the number of qubits, <span class="math notranslate nohighlight">\(\alpha_j\)</span> is the
amplitude and the state is <span class="math notranslate nohighlight">\(j\)</span> runs overall <span class="math notranslate nohighlight">\(2^n\)</span> basis
states.</p>
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