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  <div class="section" id="quantum-operations">
<h1>Quantum Operations<a class="headerlink" href="#quantum-operations" title="Permalink to this headline">¶</a></h1>
<p>There are a number of operations you can perform on quantum registers
with QCGPU.</p>
<div class="section" id="measurement">
<h2>Measurement<a class="headerlink" href="#measurement" title="Permalink to this headline">¶</a></h2>
<p>Measurement of a register in QCGPU doesn’t collapse the state (although
this may be added in the future). When you measure the state, you can
specify the number of times to sample. The output of this <code class="docutils literal notranslate"><span class="pre">measure</span></code>
function is a dictionary with the bitstrings of the outputs, along with
the number of times they were measured.</p>
<p>You can measure a register as follows,</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>

<span class="n">register</span><span class="o">.</span><span class="n">measure</span><span class="p">(</span><span class="n">samples</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="c1"># {&#39;00000&#39;: 1000}</span>
</pre></div>
</div>
<p>There is also a convenience method to measure only a single qubit.
Again, the state is not collapsed</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>

<span class="n">register</span><span class="o">.</span><span class="n">h</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

<span class="n">register</span><span class="o">.</span><span class="n">measure_qubit</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">samples</span><span class="o">=</span><span class="mi">1000</span><span class="p">)</span>
<span class="c1"># {&#39;1&#39;: 523, &#39;0&#39;: 477}</span>
</pre></div>
</div>
</div>
<div class="section" id="probability">
<h2>Probability<a class="headerlink" href="#probability" title="Permalink to this headline">¶</a></h2>
<p>QCGPU provides another method for getting the probability of each
outcome.</p>
<p>The probability of getting an outcome <span class="math notranslate nohighlight">\(j\)</span> from a state
<span class="math notranslate nohighlight">\(\lvert \psi \rangle = \sum_{j = 0}^{2^n - 1} \alpha_j \lvert j \rangle\)</span>
is</p>
<div class="math notranslate nohighlight">
\[P(j) = \lvert \alpha_j \lvert^2\]</div>
<p>The method <code class="docutils literal notranslate"><span class="pre">probabilities</span></code> returns a numpy array with each of the
values corresponding to <span class="math notranslate nohighlight">\(\lvert \alpha_j \lvert ^2\)</span> for each index
<span class="math notranslate nohighlight">\(j\)</span>.</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">1</span><span class="p">)</span>
<span class="n">register</span><span class="o">.</span><span class="n">h</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

<span class="n">register</span><span class="o">.</span><span class="n">probabilities</span><span class="p">()</span> <span class="c1"># [0.5, 0.5]</span>
</pre></div>
</div>
<p>This method is particularly useful to plot the probabilities of each
outcome.</p>
</div>
</div>


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