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            <ol class="chapter"><li><a href="qcgpu.html"><strong aria-hidden="true">1.</strong> QCGPU</a></li><li><ol class="section"><li><a href="getting-started.html"><strong aria-hidden="true">1.1.</strong> Getting Started</a></li></ol></li><li><a href="user-guide/user-guide.html"><strong aria-hidden="true">2.</strong> User Guide</a></li><li><ol class="section"><li><a href="user-guide/registers.html"><strong aria-hidden="true">2.1.</strong> Quantum Registers</a></li><li><a href="user-guide/gates.html" class="active"><strong aria-hidden="true">2.2.</strong> Quantum Gates</a></li><li><a href="user-guide/operations.html"><strong aria-hidden="true">2.3.</strong> Quantum Operations</a></li><li><a href="user-guide/examples.html"><strong aria-hidden="true">2.4.</strong> Examples</a></li><li><a href="user-guide/decoherence.html"><strong aria-hidden="true">2.5.</strong> Decoherence</a></li></ol></li><li><a href="algorithms/algorithms.html"><strong aria-hidden="true">3.</strong> Algorithms</a></li><li><ol class="section"><li><a href="algorithms/bernstein-vazirani.html"><strong aria-hidden="true">3.1.</strong> Bernstein-Vazirani</a></li><li><a href="algorithms/deutsch-jozsa.html"><strong aria-hidden="true">3.2.</strong> Deutsch-Jozsa</a></li><li><a href="algorithms/grover.html"><strong aria-hidden="true">3.3.</strong> Grovers</a></li><li><a href="algorithms/shor.html"><strong aria-hidden="true">3.4.</strong> Shors</a></li><li><a href="algorithms/super-dense.html"><strong aria-hidden="true">3.5.</strong> Super Dense Coding</a></li></ol></li></ol>
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                        <h1 class="menu-title">QCGPU User Guide</h1> 

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                        <a class="header" href="user-guide/gates.html#quantum-gates" id="quantum-gates"><h1>Quantum Gates</h1></a>
<p>Gates are used to manipulate quantum registers and to implement quantum algorithms.</p>
<a class="header" href="user-guide/gates.html#built-in-gates" id="built-in-gates"><h2>Built In Gates</h2></a>
<p>There are a number of gates built in to QCGPU. They can all be applied the same way:</p>
<pre><pre class="playpen"><code class="language-rust">
# #![allow(unused_variables)]
#fn main() {
use qcgpu::State;

let mut state = State::new(5, 0);

state.h(0); // Applies the hadamard (`h`) gate to the 0th qubit
#}</code></pre></pre>
<p><code>h</code> can be replaced with any of the following:</p>
<ul>
<li>The hadmard gate: <strong>h</strong> - <code>state.h(0);</code></li>
<li>The S gate: <strong>s</strong> - <code>state.s(0);</code></li>
<li>The T gate: <strong>t</strong> - <code>state.t(0);</code></li>
<li>The Pauli-X / NOT gate: <strong>x</strong> - <code>state.x(0);</code></li>
<li>The Pauli-Y gate: <strong>y</strong> - <code>state.y(0);</code></li>
<li>The Pauli-Z gate: <strong>z</strong> - <code>state.z(0);</code></li>
<li>The CNOT gate: <strong>cx</strong> - <code>state.cx(0, 1); // CNOT with control = 0, target = 1</code></li>
<li>The SWAP gate: <strong>swap</strong> - <code>state.swap(0,1); // Swaps the 0th and 1st qubit</code></li>
<li>The Toffoli gate: <strong>toffoli</strong> - <code>state.toffoli(0, 1, 2); // Toffoli with control1 = 0, control1 = 1, target = 2</code></li>
</ul>
<p>These are all shorthand methods for the application of arbitrary gates. For example, the application of a hadamard gate above is shorthand for</p>
<pre><pre class="playpen"><code class="language-rust">
# #![allow(unused_variables)]
#fn main() {
use qcgpu::gates::{h};
use qcgpu::State;

let mut state = State::new(5, 0);
state.apply_gate(h(), 0);
#}</code></pre></pre>
<p>You can also use any of the gates as controlled gates. For example, the application of the CNOT gate above is shorthand for</p>
<pre><pre class="playpen"><code class="language-rust">
# #![allow(unused_variables)]
#fn main() {
use qcgpu::gates::{x};
use qcgpu::State;

let mut state = State::new(5, 0);
state.apply_controlled_gate(x(), 0, 1);
#}</code></pre></pre>
<a class="header" href="user-guide/gates.html#user-defined-gates" id="user-defined-gates"><h2>User Defined Gates</h2></a>
<p>Gates in QCGPU are represented by the <code>Gate</code> struct, available through <code>qcgpu::Gate</code>.</p>
<p>It is defined as follows:</p>
<pre><pre class="playpen"><code class="language-rust">
# #![allow(unused_variables)]
#fn main() {
extern crate num_complex;
use num_complex::Complex32;

struct Gate {
    a: Complex32,
    b: Complex32,
    c: Complex32,
    d: Complex32,
}
#}</code></pre></pre>
<p>To create your own gate, you will need to add the <code>num_complex</code> crate to your dependencies.</p>
<p>A gate is created as follows:</p>
<pre><pre class="playpen"><code class="language-rust">
# #![allow(unused_variables)]
#fn main() {
let x = Gate {
    Gate {
        a: Complex32::new(0.0, 0.0),
        b: Complex32::new(1.0, 0.0),
        c: Complex32::new(1.0, 0.0),
        d: Complex32::new(0.0, 0.0),
    }
}
#}</code></pre></pre>
<p>This corresponds to the matrix</p>
<p>\[x = \begin{bmatrix} 0 &amp; 1 \\ 1 &amp; 0 \end{bmatrix}\]</p>
<p>This can be applied using the same long hand method as above:</p>
<pre><pre class="playpen"><code class="language-rust">
# #![allow(unused_variables)]
#fn main() {
let mut state = State::new(1, 0);
state.apply_gate(x, 0);
#}</code></pre></pre>

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