<!DOCTYPE HTML>
<html lang="en" class="sidebar-visible no-js">
<head>
<!-- Book generated using mdBook -->
<meta charset="UTF-8">
<title>Quantum Gates - QCGPU User Guide</title>
<meta content="text/html; charset=utf-8" http-equiv="Content-Type">
<meta name="description" content="The user guide / prose documentation for QCGPU">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="theme-color" content="#ffffff" />
<base href="../">
<link rel="stylesheet" href="book.css">
<link href="https://fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,600italic,700italic,800italic,400,300,600,700,800" rel="stylesheet" type="text/css">
<link href="https://fonts.googleapis.com/css?family=Source+Code+Pro:500" rel="stylesheet" type="text/css">
<link rel="shortcut icon" href="favicon.png">
<!-- Font Awesome -->
<link rel="stylesheet" href="_FontAwesome/css/font-awesome.css">
<link rel="stylesheet" href="highlight.css">
<link rel="stylesheet" href="tomorrow-night.css">
<link rel="stylesheet" href="ayu-highlight.css">
<!-- Custom theme stylesheets -->
<!-- MathJax -->
<script async type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
</head>
<body class="light">
<!-- Work around some values being stored in localStorage wrapped in quotes -->
<script type="text/javascript">
try {
var theme = localStorage.getItem('mdbook-theme');
var sidebar = localStorage.getItem('mdbook-sidebar');
if (theme.startsWith('"') && theme.endsWith('"')) {
localStorage.setItem('mdbook-theme', theme.slice(1, theme.length - 1));
}
if (sidebar.startsWith('"') && sidebar.endsWith('"')) {
localStorage.setItem('mdbook-sidebar', sidebar.slice(1, sidebar.length - 1));
}
} catch (e) { }
</script>
<!-- Set the theme before any content is loaded, prevents flash -->
<script type="text/javascript">
var theme;
try { theme = localStorage.getItem('mdbook-theme'); } catch(e) { }
if (theme === null || theme === undefined) { theme = 'light'; }
document.body.className = theme;
document.querySelector('html').className = theme + ' js';
</script>
<!-- Hide / unhide sidebar before it is displayed -->
<script type="text/javascript">
var html = document.querySelector('html');
var sidebar = 'hidden';
if (document.body.clientWidth >= 1080) {
try { sidebar = localStorage.getItem('mdbook-sidebar'); } catch(e) { }
sidebar = sidebar || 'visible';
}
html.classList.remove('sidebar-visible');
html.classList.add("sidebar-" + sidebar);
</script>
<nav id="sidebar" class="sidebar" aria-label="Table of contents">
<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>
</nav>
<div id="page-wrapper" class="page-wrapper">
<div class="page">
<div id="menu-bar" class="menu-bar">
<div id="menu-bar-sticky-container">
<div class="left-buttons">
<button id="sidebar-toggle" class="icon-button" type="button" title="Toggle Table of Contents" aria-label="Toggle Table of Contents" aria-controls="sidebar">
<i class="fa fa-bars"></i>
</button>
<button id="theme-toggle" class="icon-button" type="button" title="Change theme" aria-label="Change theme" aria-haspopup="true" aria-expanded="false" aria-controls="theme-list">
<i class="fa fa-paint-brush"></i>
</button>
<ul id="theme-list" class="theme-popup" aria-label="Themes" role="menu">
<li role="none"><button role="menuitem" class="theme" id="light">Light <span class="default">(default)</span></button></li>
<li role="none"><button role="menuitem" class="theme" id="rust">Rust</button></li>
<li role="none"><button role="menuitem" class="theme" id="coal">Coal</button></li>
<li role="none"><button role="menuitem" class="theme" id="navy">Navy</button></li>
<li role="none"><button role="menuitem" class="theme" id="ayu">Ayu</button></li>
</ul>
<button id="search-toggle" class="icon-button" type="button" title="Search. (Shortkey: s)" aria-label="Toggle Searchbar" aria-expanded="false" aria-keyshortcuts="S" aria-controls="searchbar">
<i class="fa fa-search"></i>
</button>
</div>
<h1 class="menu-title">QCGPU User Guide</h1>
<div class="right-buttons">
<a href="print.html" title="Print this book" aria-label="Print this book">
<i id="print-button" class="fa fa-print"></i>
</a>
</div>
</div>
</div>
<div id="search-wrapper" class="hidden">
<form id="searchbar-outer" class="searchbar-outer">
<input type="search" name="search" id="searchbar" name="searchbar" placeholder="Search this book ..." aria-controls="searchresults-outer" aria-describedby="searchresults-header">
</form>
<div id="searchresults-outer" class="searchresults-outer hidden">
<div id="searchresults-header" class="searchresults-header"></div>
<ul id="searchresults">
</ul>
</div>
</div>
<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
<script type="text/javascript">
document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
document.getElementById('sidebar').setAttribute('aria-hidden', sidebar !== 'visible');
Array.from(document.querySelectorAll('#sidebar a')).forEach(function(link) {
link.setAttribute('tabIndex', sidebar === 'visible' ? 0 : -1);
});
</script>
<div id="content" class="content">
<main>
<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>\[x = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\]</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>
</main>
<nav class="nav-wrapper" aria-label="Page navigation">
<!-- Mobile navigation buttons -->
<a rel="prev" href="user-guide/registers.html" class="mobile-nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
<i class="fa fa-angle-left"></i>
</a>
<a rel="next" href="user-guide/operations.html" class="mobile-nav-chapters next" title="Next chapter" aria-label="Next chapter" aria-keyshortcuts="Right">
<i class="fa fa-angle-right"></i>
</a>
<div style="clear: both"></div>
</nav>
</div>
</div>
<nav class="nav-wide-wrapper" aria-label="Page navigation">
<a href="user-guide/registers.html" class="nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
<i class="fa fa-angle-left"></i>
</a>
<a href="user-guide/operations.html" class="nav-chapters next" title="Next chapter" aria-label="Next chapter" aria-keyshortcuts="Right">
<i class="fa fa-angle-right"></i>
</a>
</nav>
</div>
<script src="searchindex.js" type="text/javascript" charset="utf-8"></script>
<script src="elasticlunr.min.js" type="text/javascript" charset="utf-8"></script>
<script src="mark.min.js" type="text/javascript" charset="utf-8"></script>
<script src="searcher.js" type="text/javascript" charset="utf-8"></script>
<script src="clipboard.min.js" type="text/javascript" charset="utf-8"></script>
<script src="highlight.js" type="text/javascript" charset="utf-8"></script>
<script src="book.js" type="text/javascript" charset="utf-8"></script>
<!-- Custom JS scripts -->
</body>
</html>