<!DOCTYPE HTML>
<html lang="en" class="sidebar-visible">
<head>
<!-- Book generated using mdBook -->
<meta charset="UTF-8">
<title>Quantum Operations - 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="https://maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css">
<link rel="stylesheet" href="highlight.css">
<link rel="stylesheet" href="tomorrow-night.css">
<link rel="stylesheet" href="ayu-highlight.css">
<!-- Custom theme -->
<!-- MathJax -->
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<!-- Fetch Clipboard.js from CDN but have a local fallback -->
<script src="https://cdn.jsdelivr.net/clipboard.js/1.6.1/clipboard.min.js"></script>
<script>
if (typeof Clipboard == 'undefined') {
document.write(unescape("%3Cscript src='clipboard.min.js'%3E%3C/script%3E"));
}
</script>
<noscript>
<style type="text/css">
.javascript-only {
display: none;
}
</style>
</noscript>
</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;
</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"><strong aria-hidden="true">2.2.</strong> Quantum Gates</a></li><li><a href="user-guide/operations.html" class="active"><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 javascript-only">
<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="searchbar-outer" class="searchbar-outer">
<input type="search" id="searchbar" name="searchbar" placeholder="Search this book ..." aria-controls="searchresults-outer" aria-describedby="searchresults-header">
</div>
<div id="searchresults-outer" class="searchresults-outer">
<div class="searchresults-header" id="searchresults-header"></div>
<ul id="searchresults">
</ul>
</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/operations.html#quantum-operations" id="quantum-operations"><h1>Quantum Operations</h1></a>
<p>There are a number of operations you can preform on quantum registers with QCGPU.</p>
<a class="header" href="user-guide/operations.html#measurement" id="measurement"><h2>Measurement</h2></a>
<p>You can measure the register in two ways. You can either do a single measurement and return an integer with the measured value or you can measure multiple times and return a <code>HashMap<String, i32></code>, with the key being the bitstring, and the value being the number of times it was measured.</p>
<p>The measurements don't collapse the state.</p>
<p>They are used as follows:</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.measure(); // Returns an integer
state.measure_many(1000); // Measures 1000 times, returns a HashMap<String, i32>
#}</code></pre></pre>
<p>There is also a convenience method to measure the first \(n\) qubits in the register. Again, the state is not collapsed</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.measure_first(3, 1000); // Measures the first 3 qubits 1000 times, returns a HashMap<String, i32>
#}</code></pre></pre>
<a class="header" href="user-guide/operations.html#probability" id="probability"><h2>Probability</h2></a>
<p>QCGPU provides another method for getting the probability of each outcome.</p>
<p>The probability is calculated for a state \(\lvert \psi \rangle = \sum_{j = 0}^{2^n - 1} \alpha_j \lvert j \rangle\),</p>
<p>\[P(j) = |\alpha_j|^2\]</p>
<p>The method <code>get_probabilities</code> returns a <code>Vec<f32></code> with each of the values corresponding to \(|\alpha_j|^2\) for each index \(j\).</p>
<pre><pre class="playpen"><code class="language-rust">
# #![allow(unused_variables)]
#fn main() {
use qcgpu::State;
let mut state = State::new(1, 0);
state.h(0);
state.get_probabilities(); // [0.5, 0.5]
#}</code></pre></pre>
</main>
<nav class="nav-wrapper" aria-label="Page navigation">
<!-- Mobile navigation buttons -->
<a rel="prev" href="user-guide/gates.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/examples.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/gates.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/examples.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>
<!-- Local fallback for Font Awesome -->
<script>
if (getComputedStyle(document.querySelector(".fa")).fontFamily !== "FontAwesome") {
var link = document.createElement('link');
link.rel = 'stylesheet';
link.type = 'text/css';
link.href = '_FontAwesome/css/font-awesome.css';
document.head.insertBefore(link, document.head.firstChild)
}
</script>
<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="highlight.js"></script>
<script src="book.js"></script>
<!-- Custom JS script -->
</body>
</html>