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class="vector-toc-link" href="#Quil"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Quil</span> </div> </a> <ul id="toc-Quil-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Quantum_software_development_kits" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Quantum_software_development_kits"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Quantum software development kits</span> </div> </a> <button aria-controls="toc-Quantum_software_development_kits-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Quantum software development kits subsection</span> </button> <ul id="toc-Quantum_software_development_kits-sublist" class="vector-toc-list"> <li id="toc-SDKs_with_access_to_quantum_processors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#SDKs_with_access_to_quantum_processors"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>SDKs with access to quantum processors</span> </div> </a> <ul id="toc-SDKs_with_access_to_quantum_processors-sublist" class="vector-toc-list"> <li id="toc-Cirq" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Cirq"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Cirq</span> </div> </a> <ul id="toc-Cirq-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Classiq" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Classiq"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Classiq</span> </div> </a> <ul id="toc-Classiq-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Forest" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Forest"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.3</span> <span>Forest</span> </div> </a> <ul id="toc-Forest-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-MindQuantum" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#MindQuantum"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.4</span> <span>MindQuantum</span> </div> </a> <ul id="toc-MindQuantum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ocean" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ocean"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.5</span> <span>Ocean</span> </div> </a> <ul id="toc-Ocean-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-PennyLane" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#PennyLane"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.6</span> <span>PennyLane</span> </div> </a> <ul id="toc-PennyLane-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Perceval" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Perceval"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.7</span> <span>Perceval</span> </div> </a> <ul id="toc-Perceval-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ProjectQ" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#ProjectQ"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.8</span> <span>ProjectQ</span> </div> </a> <ul id="toc-ProjectQ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Qibo" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Qibo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.9</span> <span>Qibo</span> </div> </a> <ul id="toc-Qibo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Qiskit" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Qiskit"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.10</span> <span>Qiskit</span> </div> </a> <ul id="toc-Qiskit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Qrisp" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Qrisp"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.11</span> <span>Qrisp</span> </div> </a> <ul id="toc-Qrisp-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_Development_Kit" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Quantum_Development_Kit"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.12</span> <span>Quantum Development Kit</span> </div> </a> <ul id="toc-Quantum_Development_Kit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strawberry_Fields" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Strawberry_Fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.13</span> <span>Strawberry Fields</span> </div> </a> <ul id="toc-Strawberry_Fields-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-t|ket>" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#t|ket>"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.14</span> <span>t|ket></span> </div> </a> <ul id="toc-t|ket>-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Quantum_programming_languages" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Quantum_programming_languages"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Quantum programming languages</span> </div> </a> <button aria-controls="toc-Quantum_programming_languages-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Quantum programming languages subsection</span> </button> <ul id="toc-Quantum_programming_languages-sublist" class="vector-toc-list"> <li id="toc-Imperative_languages" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Imperative_languages"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Imperative languages</span> </div> </a> <ul id="toc-Imperative_languages-sublist" class="vector-toc-list"> <li id="toc-Ket" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ket"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Ket</span> </div> </a> <ul id="toc-Ket-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-LQP" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#LQP"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>LQP</span> </div> </a> <ul id="toc-LQP-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Q_language" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Q_language"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span>Q language</span> </div> </a> <ul id="toc-Q_language-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Q#" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Q#"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.4</span> <span>Q#</span> </div> </a> <ul id="toc-Q#-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-QCL" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#QCL"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.5</span> <span>QCL</span> </div> </a> <ul id="toc-QCL-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-qGCL" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#qGCL"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.6</span> <span>qGCL</span> </div> </a> <ul id="toc-qGCL-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-QMASM" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#QMASM"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.7</span> <span>QMASM</span> </div> </a> <ul id="toc-QMASM-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Qmod" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Qmod"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.8</span> <span>Qmod</span> </div> </a> <ul id="toc-Qmod-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Q|SI>" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Q|SI>"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.9</span> <span>Q|SI></span> </div> </a> <ul id="toc-Q|SI>-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_pseudocode" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Quantum_pseudocode"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.10</span> <span>Quantum pseudocode</span> </div> </a> <ul id="toc-Quantum_pseudocode-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Scaffold" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Scaffold"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.11</span> <span>Scaffold</span> </div> </a> <ul id="toc-Scaffold-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Silq" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Silq"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.12</span> <span>Silq</span> </div> </a> <ul id="toc-Silq-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Functional_languages" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Functional_languages"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Functional languages</span> </div> </a> <ul id="toc-Functional_languages-sublist" class="vector-toc-list"> <li id="toc-LIQUi|>" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#LIQUi|>"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>LIQUi|></span> </div> </a> <ul id="toc-LIQUi|>-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-QFC_and_QPL" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#QFC_and_QPL"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>QFC and QPL</span> </div> </a> <ul id="toc-QFC_and_QPL-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-QML" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#QML"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.3</span> <span>QML</span> </div> </a> <ul id="toc-QML-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_lambda_calculi" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Quantum_lambda_calculi"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.4</span> <span>Quantum lambda calculi</span> </div> </a> <ul id="toc-Quantum_lambda_calculi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quipper" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Quipper"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.5</span> <span>Quipper</span> </div> </a> <ul id="toc-Quipper-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" 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class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 13 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-13" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">13 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B1%D9%85%D8%AC%D8%A9_%D9%83%D9%85%D9%88%D9%85%D9%8A%D8%A9" title="برمجة كمومية – Arabic" lang="ar" hreflang="ar" data-title="برمجة كمومية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Programaci%C3%B3_qu%C3%A0ntica" title="Programació quàntica – Catalan" lang="ca" hreflang="ca" data-title="Programació quàntica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%D8%A7%D9%85%D9%87%E2%80%8C%D9%86%D9%88%DB%8C%D8%B3%DB%8C_%DA%A9%D9%88%D8%A7%D9%86%D8%AA%D9%88%D9%85%DB%8C" title="برنامه‌نویسی کوانتومی – Persian" lang="fa" hreflang="fa" data-title="برنامه‌نویسی کوانتومی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%96%91%EC%9E%90_%ED%94%84%EB%A1%9C%EA%B7%B8%EB%9E%98%EB%B0%8D" title="양자 프로그래밍 – Korean" lang="ko" hreflang="ko" data-title="양자 프로그래밍" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%9F%E3%83%B3%E3%82%B0%E8%A8%80%E8%AA%9E" title="量子プログラミング言語 – Japanese" lang="ja" hreflang="ja" data-title="量子プログラミング言語" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/QCL" title="QCL – Polish" lang="pl" hreflang="pl" data-title="QCL" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Programa%C3%A7%C3%A3o_qu%C3%A2ntica" title="Programação quântica – Portuguese" lang="pt" hreflang="pt" data-title="Programação quântica" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D0%B3%D1%80%D0%B0%D0%BC%D0%BC%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5" title="Квантовое программирование – Russian" lang="ru" hreflang="ru" data-title="Квантовое программирование" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kvanttiohjelmointi" title="Kvanttiohjelmointi – Finnish" lang="fi" hreflang="fi" data-title="Kvanttiohjelmointi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kuantum_programlama" title="Kuantum programlama – Turkish" lang="tr" hreflang="tr" data-title="Kuantum programlama" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82%D0%BE%D0%B2%D0%B5_%D0%BF%D1%80%D0%BE%D0%B3%D1%80%D0%B0%D0%BC%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F" title="Квантове програмування – Ukrainian" lang="uk" hreflang="uk" data-title="Квантове програмування" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a 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href="https://www.google.com/search?tbm=nws&q=%22Quantum+programming%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Quantum+programming%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Quantum+programming%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Quantum+programming%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Quantum+programming%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">August 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p> <b>Quantum programming</b> is the process of designing or <a href="/wiki/Assembly_language" title="Assembly language">assembling</a> sequences of instructions, called quantum circuits, using gates, switches, and operators to manipulate a quantum system for a desired outcome or results of a given experiment. <a href="/wiki/Quantum_algorithms" class="mw-redirect" title="Quantum algorithms">Quantum circuit algorithms</a> can be implemented on integrated circuits, conducted with instrumentation, or written in a programming language for use with a <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computer</a> or a quantum processor. </p><p>With quantum processor based systems, quantum <a href="/wiki/Programming_language" title="Programming language">programming languages</a> help express <a href="/wiki/Quantum_algorithm" title="Quantum algorithm">quantum algorithms</a> using high-level constructs.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The field is deeply rooted in the <a href="/wiki/Open-source" class="mw-redirect" title="Open-source">open-source</a> philosophy and as a result most of the quantum software discussed in this article is freely available as <a href="/wiki/Open-source_software" title="Open-source software">open-source software</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Quantum computers, such as those based on the <a href="/wiki/KLM_protocol" title="KLM protocol">KLM protocol</a>, a <a href="/wiki/Linear_optical_quantum_computing" title="Linear optical quantum computing">linear optical quantum computing</a> (LOQC) model, use quantum algorithms (circuits) implemented with electronics, integrated circuits, instrumentation, sensors, and/or by other physical means.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources in the body of the article. (June 2023)">not verified in body</span></a></i>]</sup> </p><p>Other circuits designed for experimentation related to quantum systems can be instrumentation and sensor based.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources in the body of the article. (June 2023)">not verified in body</span></a></i>]</sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Quantum_instruction_sets">Quantum instruction sets</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=1" title="Edit section: Quantum instruction sets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum instruction sets are used to turn higher level algorithms into physical instructions that can be executed on quantum processors. Sometimes these instructions are specific to a given hardware platform, e.g. <a href="/wiki/Ion_trap" title="Ion trap">ion traps</a> or <a href="/wiki/Superconducting_quantum_computing" title="Superconducting quantum computing">superconducting qubits</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Blackbird">Blackbird</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=2" title="Edit section: Blackbird"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Blackbird<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> is a quantum instruction set and intermediate representation used by <a href="/wiki/Xanadu_Quantum_Technologies" title="Xanadu Quantum Technologies">Xanadu Quantum Technologies</a> and Strawberry Fields. It is designed to represent <a href="/wiki/Continuous-variable_quantum_information" title="Continuous-variable quantum information">continuous-variable</a> quantum programs that can run on photonic quantum hardware. </p> <div class="mw-heading mw-heading3"><h3 id="cQASM">cQASM</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=3" title="Edit section: cQASM"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>cQASM,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> also known as common QASM, is a hardware-agnostic quantum assembly language which guarantees the interoperability between all the quantum compilation and simulation tools. It was introduced by the QCA Lab at <a href="/wiki/TUDelft" class="mw-redirect" title="TUDelft">TUDelft</a>. </p> <div class="mw-heading mw-heading3"><h3 id="OpenQASM">OpenQASM</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=4" title="Edit section: OpenQASM"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/OpenQASM" title="OpenQASM">OpenQASM</a></div> <p><a href="/wiki/OpenQASM" title="OpenQASM">OpenQASM</a><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> is the intermediate representation introduced by IBM for use with <a href="#Qiskit">Qiskit</a> and the <a href="/wiki/IBM_Q_Experience" class="mw-redirect" title="IBM Q Experience">IBM Q Experience</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Quil">Quil</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=5" title="Edit section: Quil"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Quil_(instruction_set_architecture)" title="Quil (instruction set architecture)">Quil (instruction set architecture)</a></div> <p><a href="/wiki/Quil_(instruction_set_architecture)" title="Quil (instruction set architecture)">Quil</a> is an instruction set architecture for quantum computing that first introduced a shared quantum/classical memory model. It was introduced by Robert Smith, Michael Curtis, and William Zeng in <i>A Practical Quantum Instruction Set Architecture</i>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Many quantum algorithms (including <a href="/wiki/Quantum_teleportation" title="Quantum teleportation">quantum teleportation</a>, <a href="/wiki/Quantum_error_correction" title="Quantum error correction">quantum error correction</a>, simulation,<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and optimization algorithms<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>) require a shared memory architecture. </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_software_development_kits">Quantum software development kits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=6" title="Edit section: Quantum software development kits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum <a href="/wiki/Software_development_kit" title="Software development kit">software development kits</a> provide collections of tools to create and manipulate quantum programs.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> They also provide the means to simulate the quantum programs or prepare them to be run using <a href="/wiki/Cloud-based_quantum_computing" title="Cloud-based quantum computing">cloud-based quantum devices</a> and self-hosted quantum devices. </p> <div class="mw-heading mw-heading3"><h3 id="SDKs_with_access_to_quantum_processors">SDKs with access to quantum processors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=7" title="Edit section: SDKs with access to quantum processors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following <a href="/wiki/Software_development_kit" title="Software development kit">software development kits</a> can be used to run quantum circuits on prototype quantum devices, as well as on simulators. </p> <div class="mw-heading mw-heading4"><h4 id="Cirq">Cirq</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=8" title="Edit section: Cirq"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cirq" title="Cirq">Cirq</a></div> <p>An open source project developed by <a href="/wiki/Google" title="Google">Google</a>, which uses the <a href="/wiki/Python_programming" class="mw-redirect" title="Python programming">Python programming</a> language to create and manipulate quantum circuits. Programs written in Cirq can be run on <a href="/wiki/IonQ" title="IonQ">IonQ</a>, <a href="/w/index.php?title=Pasqal&action=edit&redlink=1" class="new" title="Pasqal (page does not exist)">Pasqal</a>,<sup id="cite_ref-auto_12-0" class="reference"><a href="#cite_note-auto-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Rigetti_Computing" title="Rigetti Computing">Rigetti</a>, and <a href="/w/index.php?title=Alpine_Quantum_Technologies&action=edit&redlink=1" class="new" title="Alpine Quantum Technologies (page does not exist)">Alpine Quantum Technologies</a>.<sup id="cite_ref-auto2_13-0" class="reference"><a href="#cite_note-auto2-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Classiq">Classiq</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=9" title="Edit section: Classiq"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/w/index.php?title=Classiq&action=edit&redlink=1" class="new" title="Classiq (page does not exist)">Classiq</a></div> <p>A cloud-based quantum IDE developed by Classiq, uses a high-level quantum language, <a href="#Qmod">Qmod</a>, to generate scalable and efficient quantum circuits with a hardware-aware synthesis engine, that can be deployed across a wide range of QPUs. The platform includes a large library of quantum algorithms. </p> <div class="mw-heading mw-heading4"><h4 id="Forest">Forest</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=10" title="Edit section: Forest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An open source project developed by <a href="/wiki/Rigetti" class="mw-redirect" title="Rigetti">Rigetti</a>, which uses the <a href="/wiki/Python_programming" class="mw-redirect" title="Python programming">Python programming</a> language to create and manipulate quantum circuits. Results are obtained either using simulators or prototype quantum devices provided by Rigetti. As well as the ability to create programs using basic quantum operations, higher level algorithms are available within the Grove package.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Forest is based on the <a href="/wiki/Quil_(instruction_set_architecture)" title="Quil (instruction set architecture)">Quil</a> instruction set. </p> <div class="mw-heading mw-heading4"><h4 id="MindQuantum">MindQuantum</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=11" title="Edit section: MindQuantum"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MindQuantum is a quantum computing framework based on <a href="/wiki/MindSpore" title="MindSpore">MindSpore</a>, focusing on the implementation of <a href="/wiki/NISQ" class="mw-redirect" title="NISQ">NISQ</a> algorithms.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Ocean">Ocean</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=12" title="Edit section: Ocean"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An <a href="/wiki/Open_source" title="Open source">open source</a> suite of tools developed by D-Wave. Written mostly in the Python programming language, it enables users to formulate problems in Ising Model and Quadratic Unconstrained Binary Optimization formats (QUBO). Results can be obtained by submitting to an online quantum computer in Leap, D-Wave's real-time Quantum Application Environment, customer-owned machines, or classical samplers.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (June 2021)">citation needed</span></a></i>]</sup> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:QProg1-Refreshed.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/QProg1-Refreshed.png/500px-QProg1-Refreshed.png" decoding="async" width="350" height="168" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/QProg1-Refreshed.png/960px-QProg1-Refreshed.png 1.5x" data-file-width="1289" data-file-height="618" /></a><figcaption>A sample code using projectq with Python</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="PennyLane">PennyLane</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=13" title="Edit section: PennyLane"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An <a href="/wiki/Open-source_software" title="Open-source software">open-source</a> <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> library developed by <a href="/wiki/Xanadu_Quantum_Technologies" title="Xanadu Quantum Technologies">Xanadu Quantum Technologies</a> for <a href="/wiki/Differentiable_programming" title="Differentiable programming">differentiable programming</a> of quantum computers.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> PennyLane provides users the ability to create models using <a href="/wiki/TensorFlow" title="TensorFlow">TensorFlow</a>, <a href="/wiki/NumPy" title="NumPy">NumPy</a>, or <a href="/wiki/PyTorch" title="PyTorch">PyTorch</a>, and connect them with quantum computer backends available from <a href="/wiki/IBM_Quantum_Experience" class="mw-redirect" title="IBM Quantum Experience">IBMQ</a>, <a href="/wiki/Google" title="Google">Google Quantum</a>, <a href="/wiki/Rigetti_Computing" title="Rigetti Computing">Rigetti</a>, <a href="/wiki/Quantinuum" title="Quantinuum">Quantinuum</a><sup id="cite_ref-auto1_22-0" class="reference"><a href="#cite_note-auto1-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> and <a href="/w/index.php?title=Alpine_Quantum_Technologies&action=edit&redlink=1" class="new" title="Alpine Quantum Technologies (page does not exist)">Alpine Quantum Technologies</a>.<sup id="cite_ref-auto2_13-1" class="reference"><a href="#cite_note-auto2-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Perceval">Perceval</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=14" title="Edit section: Perceval"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An open-source project created by <a href="/w/index.php?title=Quandela&action=edit&redlink=1" class="new" title="Quandela (page does not exist)">Quandela</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://fr.wikipedia.org/wiki/Quandela" class="extiw" title="fr:Quandela">fr</a>]</span> for designing photonic quantum circuits and developing quantum algorithms, based on <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>. Simulations are run either on the user's own computer or on the <a href="/wiki/Cloud_computing" title="Cloud computing">cloud</a>. Perceval is also used to connect to Quandela's cloud-based <a href="/wiki/List_of_quantum_processors" title="List of quantum processors">photonic quantum processor</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="ProjectQ">ProjectQ</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=15" title="Edit section: ProjectQ"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An open source project developed at the Institute for Theoretical Physics at <a href="/wiki/ETH" class="mw-redirect" title="ETH">ETH</a>, which uses the <a href="/wiki/Python_programming" class="mw-redirect" title="Python programming">Python programming</a> language to create and manipulate quantum circuits.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Results are obtained either using a simulator, or by sending jobs to IBM quantum devices. </p> <div class="mw-heading mw-heading4"><h4 id="Qibo">Qibo</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=16" title="Edit section: Qibo"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An open source full-stack API for quantum simulation, quantum hardware control and calibration developed by multiple research laboratories, including <a href="/wiki/Technology_Innovation_Institute" title="Technology Innovation Institute">QRC</a>, <a href="/wiki/Centre_for_Quantum_Technologies" title="Centre for Quantum Technologies">CQT</a> and <a href="/wiki/Istituto_Nazionale_di_Fisica_Nucleare" title="Istituto Nazionale di Fisica Nucleare">INFN</a>. <a rel="nofollow" class="external text" href="https://github.com/qiboteam/qibo">Qibo</a> is a modular framework which includes multiple backends for quantum simulation and hardware control.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> This project aims at providing a platform agnostic quantum hardware control framework with drivers for multiple instruments<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> and tools for quantum calibration, characterization and validation.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> This framework focuses on self-hosted quantum devices by simplifying the software development required in labs. </p> <div class="mw-heading mw-heading4"><h4 id="Qiskit">Qiskit</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=17" title="Edit section: Qiskit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Qiskit" title="Qiskit">Qiskit</a></div> <p>An open source project developed by <a href="/wiki/IBM" title="IBM">IBM</a>.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Quantum circuits are created and manipulated using <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>. Results are obtained either using simulators that run on the user's own device, simulators provided by IBM or prototype quantum devices provided by IBM. As well as the ability to create programs using basic quantum operations, higher level tools for algorithms and benchmarking are available within specialized packages.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Qiskit is based on the <a href="/wiki/OpenQASM" title="OpenQASM">OpenQASM</a> standard for representing quantum circuits. It also supports pulse level control of quantum systems via QiskitPulse standard.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Qrisp">Qrisp</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=18" title="Edit section: Qrisp"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Eclipse_Qrisp&action=edit&redlink=1" class="new" title="Eclipse Qrisp (page does not exist)">Qrisp</a><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> is an open source project coordinated by the <a href="/wiki/Eclipse_Foundation" title="Eclipse Foundation">Eclipse Foundation</a><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> and developed in <a href="/wiki/Python_programming" class="mw-redirect" title="Python programming">Python programming</a> by <a href="/w/index.php?title=Fraunhofer_FOKUS&action=edit&redlink=1" class="new" title="Fraunhofer FOKUS (page does not exist)">Fraunhofer FOKUS</a><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> Qrisp is a high-level programming language for creating and compiling quantum algorithms. Its structured programming model enables scalable development and maintenance. The expressive syntax is based on variables instead of qubits, with the QuantumVariable as core class, and functions instead of gates. Additional tools, such as a performant simulator and automatic uncomputation, complement the extensive framework. Furthermore, it is platform independent, since it offers alternative compilation of elementary functions down to the circuit level, based on device-specific gate sets. </p> <div class="mw-heading mw-heading4"><h4 id="Quantum_Development_Kit">Quantum Development Kit</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=19" title="Edit section: Quantum Development Kit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A project developed by <a href="/wiki/Microsoft" title="Microsoft">Microsoft</a><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> as part of the <a href="/wiki/.NET_Framework" title=".NET Framework">.NET Framework</a>. Quantum programs can be written and run within <a href="/wiki/Visual_Studio" title="Visual Studio">Visual Studio</a> and <a href="/wiki/VSCode" class="mw-redirect" title="VSCode">VSCode</a> using the quantum programming language Q#. Programs developed in the QDK can be run on Microsoft's <a href="/wiki/Microsoft_Azure_Quantum" title="Microsoft Azure Quantum"> Azure Quantum</a>,<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> and run on quantum computers from <a href="/wiki/Quantinuum" title="Quantinuum">Quantinuum</a>,<sup id="cite_ref-auto1_22-1" class="reference"><a href="#cite_note-auto1-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <a href="/wiki/IonQ" title="IonQ">IonQ</a>, and <a href="/w/index.php?title=Pasqal&action=edit&redlink=1" class="new" title="Pasqal (page does not exist)">Pasqal</a>.<sup id="cite_ref-auto_12-1" class="reference"><a href="#cite_note-auto-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Strawberry_Fields">Strawberry Fields</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=20" title="Edit section: Strawberry Fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An <a href="/wiki/Open-source_software" title="Open-source software">open-source</a> <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> <a href="/wiki/Library_(computing)" title="Library (computing)">library</a> developed by <a href="/wiki/Xanadu_Quantum_Technologies" title="Xanadu Quantum Technologies">Xanadu Quantum Technologies</a> for designing, simulating, and optimizing <a href="/wiki/Continuous-variable_quantum_information" title="Continuous-variable quantum information">continuous variable</a> (CV) <a href="/wiki/Quantum_optics" title="Quantum optics">quantum optical</a> circuits.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Three simulators are provided - one in the <a href="/wiki/Fock_state" title="Fock state">Fock basis</a>, one using the Gaussian formulation of quantum optics,<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> and one using the <a href="/wiki/TensorFlow" title="TensorFlow">TensorFlow</a> machine learning library. Strawberry Fields is also the library for executing programs on Xanadu's quantum photonic hardware.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="t|ket>"><span id="t.7Cket.3E"></span>t|ket></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=21" title="Edit section: t|ket>"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A quantum programming environment and optimizing compiler developed by <a href="/wiki/Cambridge_Quantum_Computing" class="mw-redirect" title="Cambridge Quantum Computing">Cambridge Quantum Computing</a> that targets simulators and several quantum hardware back-ends, released in December 2018.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Quantum_programming_languages">Quantum programming languages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=22" title="Edit section: Quantum programming languages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are two main groups of quantum programming languages: <a href="/wiki/Imperative_programming" title="Imperative programming">imperative</a> quantum programming languages and <a href="/wiki/Functional_programming" title="Functional programming">functional</a> quantum programming languages. </p> <div class="mw-heading mw-heading3"><h3 id="Imperative_languages">Imperative languages</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=23" title="Edit section: Imperative languages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The most prominent representatives of the imperative languages are QCL,<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> LanQ<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> and Q|SI>.<sup id="cite_ref-:0_47-0" class="reference"><a href="#cite_note-:0-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Ket">Ket</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=24" title="Edit section: Ket"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Ket<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> is an open-source embedded language designed to facilitate quantum programming, leveraging the familiar syntax and simplicity of Python. It serves as an integral component of the Ket Quantum Programming Platform,<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> seamlessly integrating with a Rust runtime library and a quantum simulator. Maintained by Quantuloop, the project emphasizes accessibility and versatility for researchers and developers. The following example demonstrates the implementation of a <a href="/wiki/Bell_state" title="Bell state">Bell state</a> using Ket:</p><div class="mw-highlight mw-highlight-lang-python mw-content-ltr mw-highlight-lines" dir="ltr"><pre><span></span><span class="linenos" data-line="1"></span><span class="kn">from</span> <span class="nn">ket</span> <span class="kn">import</span> <span class="o">*</span> <span class="linenos" data-line="2"></span><span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">quant</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Allocate two quantum bits</span> <span class="linenos" data-line="3"></span><span class="n">H</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1"># Put qubit `a` in a superposition</span> <span class="linenos" data-line="4"></span><span class="n">cnot</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="c1"># Entangle the two qubits in the Bell state</span> <span class="linenos" data-line="5"></span><span class="n">m_a</span> <span class="o">=</span> <span class="n">measure</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1"># Measure qubit `a`, collapsing qubit `b` as well</span> <span class="linenos" data-line="6"></span><span class="n">m_b</span> <span class="o">=</span> <span class="n">measure</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="c1"># Measure qubit `b`</span> <span class="linenos" data-line="7"></span><span class="c1"># Assert that the measurement of both qubits will always be equal</span> <span class="linenos" data-line="8"></span><span class="k">assert</span> <span class="n">m_a</span><span class="o">.</span><span class="n">value</span> <span class="o">==</span> <span class="n">m_b</span><span class="o">.</span><span class="n">value</span> </pre></div> <div class="mw-heading mw-heading4"><h4 id="LQP">LQP</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=25" title="Edit section: LQP"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Logic of Quantum Programs (LQP) is a dynamic quantum logic, capable of expressing important features of quantum measurements and unitary evolutions of multi-partite states, and provides logical characterizations of various forms of entanglement. The logic has been used to specify and verify the correctness of various protocols in quantum computation.<sup id="cite_ref-LQP_50-0" class="reference"><a href="#cite_note-LQP-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-PLQP_51-0" class="reference"><a href="#cite_note-PLQP-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Q_language">Q language</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=26" title="Edit section: Q language"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Q Language is the second implemented imperative quantum programming language.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Q Language was implemented as an extension of C++ programming language. It provides classes for basic quantum operations like QHadamard, QFourier, QNot, and QSwap, which are derived from the base class Qop. New operators can be defined using C++ class mechanism. </p><p>Quantum memory is represented by class Qreg. </p> <div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre><span></span><span class="n">Qreg</span><span class="w"> </span><span class="n">x1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1-qubit quantum register with initial value 0</span> <span class="n">Qreg</span><span class="w"> </span><span class="nf">x2</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 2-qubit quantum register with initial value 0</span> </pre></div> <p>The computation process is executed using a provided simulator. Noisy environments can be simulated using parameters of the simulator. </p> <div class="mw-heading mw-heading4"><h4 id="Q#"><span id="Q.23"></span>Q#</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=27" title="Edit section: Q#"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Q_Sharp" title="Q Sharp">Q Sharp</a></div> <p>A language developed by <a href="/wiki/Microsoft" title="Microsoft">Microsoft</a> to be used with the <a href="#Quantum_Development_Kit">Quantum Development Kit</a>.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="QCL">QCL</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=28" title="Edit section: QCL"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Quantum_Computation_Language" title="Quantum Computation Language">Quantum Computation Language</a></div> <p><a href="/wiki/Quantum_Computation_Language" title="Quantum Computation Language">Quantum Computation Language</a> (QCL) is one of the first implemented quantum <a href="/wiki/Programming_languages" class="mw-redirect" title="Programming languages">programming languages</a>.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> The most important feature of QCL is the support for user-defined operators and functions. Its <a href="/wiki/Syntax" title="Syntax">syntax</a> resembles the syntax of the <a href="/wiki/C_(programming_language)" title="C (programming language)">C programming language</a> and its classical <a href="/wiki/Data_type" title="Data type">data types</a> are similar to primitive data types in C. One can combine classical code and quantum code in the same program. </p> <div class="mw-heading mw-heading4"><h4 id="qGCL">qGCL</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=29" title="Edit section: qGCL"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum Guarded Command Language (qGCL) was defined by P. Zuliani in his PhD thesis. It is based on <a href="/wiki/Guarded_Command_Language" title="Guarded Command Language">Guarded Command Language</a> created by <a href="/wiki/Edsger_Dijkstra" class="mw-redirect" title="Edsger Dijkstra">Edsger Dijkstra</a>. </p><p>It can be described as a language of quantum programs specification. </p> <div class="mw-heading mw-heading4"><h4 id="QMASM">QMASM</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=30" title="Edit section: QMASM"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum Macro Assembler (QMASM) is a low-level language specific to quantum annealers such as the D-Wave.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Qmod">Qmod</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=31" title="Edit section: Qmod"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum Modeling (Qmod) language is a high-level language that abstracts away the gate-level qubit operation, providing a functional approach to the implementation of quantum algorithms on quantum registers. The language is part of the <a rel="nofollow" class="external text" href="https://classiq.io">Classiq</a> platform and can be used directly with its native syntax, through a Python SDK, or with a visual editor, all methods can take advantage of the larger library of algorithms and the efficient circuit optimization. </p> <div class="mw-heading mw-heading4"><h4 id="Q|SI>"><span id="Q.7CSI.3E"></span>Q|SI></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=32" title="Edit section: Q|SI>"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Q|SI> is a platform embedded in <a href="/wiki/.NET_Framework" title=".NET Framework">.Net</a> language supporting quantum programming in a quantum extension of while-language.<sup id="cite_ref-:0_47-1" class="reference"><a href="#cite_note-:0-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> This platform includes a compiler of the quantum while-language<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> and a chain of tools for the simulation of quantum computation, optimisation of quantum circuits, termination analysis of quantum programs,<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> and verification of quantum programs.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Quantum_pseudocode">Quantum pseudocode</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=33" title="Edit section: Quantum pseudocode"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum pseudocode proposed by E. Knill is the first formalized language for description of <a href="/wiki/Quantum_algorithm" title="Quantum algorithm">quantum algorithms</a>. It was introduced and, moreover, was tightly connected with a model of quantum machine called <a href="/wiki/Quantum_Random_Access_Machine" class="mw-redirect" title="Quantum Random Access Machine">Quantum Random Access Machine</a> (QRAM). </p> <div class="mw-heading mw-heading4"><h4 id="Scaffold">Scaffold</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=34" title="Edit section: Scaffold"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Scaffold is C-like language, that compiles to QASM and OpenQASM. It is built on top of the <a href="/wiki/LLVM" title="LLVM">LLVM</a> Compiler Infrastructure to perform optimizations on Scaffold code before generating a specified instruction set.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Silq">Silq</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=35" title="Edit section: Silq"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Silq is a high-level programming language for quantum computing with a strong static type system, developed at <a href="/wiki/ETH_Zurich" title="ETH Zurich">ETH Zürich</a>.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Functional_languages">Functional languages</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=36" title="Edit section: Functional languages"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Efforts are underway to develop <a href="/wiki/Functional_programming_languages" class="mw-redirect" title="Functional programming languages">functional programming languages</a> for <a href="/wiki/Quantum_computing" title="Quantum computing">quantum computing</a>. Functional programming languages are well-suited for reasoning about programs. Examples include Selinger's QPL,<sup id="cite_ref-qpl_65-0" class="reference"><a href="#cite_note-qpl-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Haskell" title="Haskell">Haskell</a>-like language QML by Altenkirch and Grattage.<sup id="cite_ref-qml1_66-0" class="reference"><a href="#cite_note-qml1-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-qml2_67-0" class="reference"><a href="#cite_note-qml2-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> Higher-order quantum programming languages, based on <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>, have been proposed by van Tonder,<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> Selinger and Valiron<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> and by Arrighi and Dowek.<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="LIQUi|>"><span id="LIQUi.7C.3E"></span>LIQUi|></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=37" title="Edit section: LIQUi|>"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>LIQUi|> (pronounced <i>liquid</i>) is a quantum simulation extension on the <a href="/wiki/F_Sharp_(programming_language)" title="F Sharp (programming language)">F#</a> programming language.<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> It is currently being developed by the Quantum Architectures and Computation Group (QuArC)<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> part of the StationQ efforts at Microsoft Research. LIQUi|> seeks to allow theorists to experiment with quantum algorithm design before physical quantum computers are available for use.<sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </p><p>It includes a programming language, optimization and scheduling algorithms, and quantum simulators. LIQUi|> can be used to translate a quantum algorithm written in the form of a high-level program into the low-level machine instructions for a quantum device.<sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup> </p><p><br /> </p> <div class="mw-heading mw-heading4"><h4 id="QFC_and_QPL">QFC and QPL</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=38" title="Edit section: QFC and QPL"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>QFC and QPL are two closely related quantum programming languages defined by Peter Selinger. They differ only in their syntax: QFC uses a flow chart syntax, whereas QPL uses a textual syntax. These languages have classical control flow but can operate on quantum or classical data. Selinger gives a denotational semantics for these languages in a category of <a href="/wiki/Superoperator" title="Superoperator">superoperators</a>. </p> <div class="mw-heading mw-heading4"><h4 id="QML">QML</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=39" title="Edit section: QML"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>QML is a <a href="/wiki/Haskell" title="Haskell">Haskell</a>-like quantum programming language by Altenkirch and Grattage.<sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-qml1_66-1" class="reference"><a href="#cite_note-qml1-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> Unlike Selinger's QPL, this language takes duplication, rather than discarding, of quantum information as a primitive operation. Duplication in this context is understood to be the operation that maps <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\phi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ϕ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\phi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/312d43de853a9e6ca74888e63394fc8081f56a43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.937ex; height:2.843ex;" alt="{\displaystyle |\phi \rangle }" /></span> to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |\phi \rangle \otimes |\phi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ϕ</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>⊗</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ϕ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |\phi \rangle \otimes |\phi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f829c95befccd04865f8e850ca65719f2b643a6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.714ex; height:2.843ex;" alt="{\displaystyle |\phi \rangle \otimes |\phi \rangle }" /></span>, and is not to be confused with the impossible operation of <a href="/wiki/No-cloning_theorem" title="No-cloning theorem">cloning</a>; the authors claim it is akin to how sharing is modeled in classical languages. QML also introduces both classical and quantum control operators, whereas most other languages rely on classical control. </p><p>An <a href="/wiki/Operational_semantics" title="Operational semantics">operational semantics</a> for QML is given in terms of <a href="/wiki/Quantum_circuit" title="Quantum circuit">quantum circuits</a>, while a <a href="/wiki/Denotational_semantics" title="Denotational semantics">denotational semantics</a> is presented in terms of <a href="/wiki/Superoperator" title="Superoperator">superoperators</a>, and these are shown to agree. Both the operational and denotational semantics have been implemented (classically) in Haskell.<sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Quantum_lambda_calculi">Quantum lambda calculi</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=40" title="Edit section: Quantum lambda calculi"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Quantum lambda calculi are extensions of the classical <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a> introduced by <a href="/wiki/Alonzo_Church" title="Alonzo Church">Alonzo Church</a> and <a href="/wiki/Stephen_Cole_Kleene" title="Stephen Cole Kleene">Stephen Cole Kleene</a> in the 1930s. The purpose of quantum lambda calculi is to extend quantum programming languages with a theory of <a href="/wiki/Higher-order_function" title="Higher-order function">higher-order functions</a>. </p><p>The first attempt to define a quantum lambda calculus was made by Philip Maymin in 1996.<sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> His lambda-q calculus is powerful enough to express any quantum computation. However, this language can efficiently solve <a href="/wiki/NP-complete" class="mw-redirect" title="NP-complete">NP-complete</a> problems, and therefore appears to be strictly stronger than the standard quantum computational models (such as the <a href="/wiki/Quantum_Turing_machine" title="Quantum Turing machine">quantum Turing machine</a> or the <a href="/wiki/Quantum_circuit" title="Quantum circuit">quantum circuit</a> model). Therefore, Maymin's lambda-q calculus is probably not implementable on a physical device <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2019)">citation needed</span></a></i>]</sup>. </p><p>In 2003, André van Tonder defined an extension of the <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a> suitable for proving correctness of quantum programs. He also provided an implementation in the <a href="/wiki/Scheme_(programming_language)" title="Scheme (programming language)">Scheme</a> programming language.<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup> </p><p>In 2004, Selinger and Valiron defined a <a href="/wiki/Strongly_typed" class="mw-redirect" title="Strongly typed">strongly typed</a> lambda calculus for quantum computation with a type system based on <a href="/wiki/Linear_logic" title="Linear logic">linear logic</a>.<sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Quipper">Quipper</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=41" title="Edit section: Quipper"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">For the education technology company, see <a href="/wiki/Quipper_(company)" title="Quipper (company)">Quipper (company)</a>.</div> <p>Quipper was published in 2013.<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup> It is implemented as an embedded language, using <a href="/wiki/Haskell" title="Haskell">Haskell</a> as the host language.<sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> For this reason, quantum programs written in Quipper are written in Haskell using provided libraries. For example, the following code implements preparation of a superposition </p> <div class="mw-highlight mw-highlight-lang-haskell mw-content-ltr" dir="ltr"><pre><span></span><span class="kr">import</span><span class="w"> </span><span class="nn">Quipper</span> <span class="nf">spos</span><span class="w"> </span><span class="ow">::</span><span class="w"> </span><span class="kt">Bool</span><span class="w"> </span><span class="ow">-></span><span class="w"> </span><span class="kt">Circ</span><span class="w"> </span><span class="kt">Qubit</span> <span class="nf">spos</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="ow">=</span><span class="w"> </span><span class="kr">do</span><span class="w"> </span><span class="n">q</span><span class="w"> </span><span class="ow"><-</span><span class="w"> </span><span class="n">qinit</span><span class="w"> </span><span class="n">b</span> <span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="ow"><-</span><span class="w"> </span><span class="n">hadamard</span><span class="w"> </span><span class="n">q</span> <span class="w"> </span><span class="n">return</span><span class="w"> </span><span class="n">r</span> </pre></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=42" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite 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Archived from <a rel="nofollow" class="external text" href="http://sneezy.cs.nott.ac.uk/QML/">the original</a> on September 26, 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=QML%3A+A+Functional+Quantum+Programming+Language&rft.date=2007-09-26&rft_id=http%3A%2F%2Fsneezy.cs.nott.ac.uk%2FQML%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+programming" class="Z3988"></span></span> </li> <li id="cite_note-76"><span class="mw-cite-backlink"><b><a href="#cite_ref-76">^</a></b></span> <span class="reference-text">Jonathan Grattage, <a rel="nofollow" class="external text" href="http://sneezy.cs.nott.ac.uk/qml/compiler">QML: A Functional Quantum Programming Language (compiler)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160305052237/http://sneezy.cs.nott.ac.uk/qml/compiler/">Archived</a> 2016-03-05 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, 2005–2008</span> </li> <li id="cite_note-77"><span class="mw-cite-backlink"><b><a href="#cite_ref-77">^</a></b></span> <span class="reference-text">Philip Maymin, <a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/9612052">"Extending the Lambda Calculus to Express Randomized and Quantumized Algorithms"</a>, 1996</span> </li> <li id="cite_note-78"><span class="mw-cite-backlink"><b><a href="#cite_ref-78">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAndré_van_Tonder" class="citation web cs1">André van Tonder. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160305100936/http://www.het.brown.edu/people/andre/qlambda/">"A lambda calculus for quantum computation (website)"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.het.brown.edu/people/andre/qlambda">the original</a> on March 5, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">October 2,</span> 2007</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+lambda+calculus+for+quantum+computation+%28website%29&rft.au=Andr%C3%A9+van+Tonder&rft_id=http%3A%2F%2Fwww.het.brown.edu%2Fpeople%2Fandre%2Fqlambda&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+programming" class="Z3988"></span></span> </li> <li id="cite_note-79"><span class="mw-cite-backlink"><b><a href="#cite_ref-79">^</a></b></span> <span class="reference-text">Peter Selinger, Benoˆıt Valiron, <a rel="nofollow" class="external text" href="https://www.mscs.dal.ca/~selinger/papers/qlambdabook.pdf">"Quantum Lambda Calculus"</a></span> </li> <li id="cite_note-80"><span class="mw-cite-backlink"><b><a href="#cite_ref-80">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.mathstat.dal.ca/~selinger/quipper/">"The Quipper Language"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Quipper+Language&rft_id=http%3A%2F%2Fwww.mathstat.dal.ca%2F~selinger%2Fquipper%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+programming" class="Z3988"></span></span> </li> <li id="cite_note-81"><span class="mw-cite-backlink"><b><a href="#cite_ref-81">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAlexander_S._GreenPeter_LeFanu_LumsdaineNeil_J._RossPeter_Selinger" class="citation web cs1">Alexander S. Green; Peter LeFanu Lumsdaine; Neil J. Ross; Peter Selinger; Benoît Valiron. <a rel="nofollow" class="external text" href="http://www.mathstat.dal.ca/~selinger/quipper/">"The Quipper Language (website)"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Quipper+Language+%28website%29&rft.au=Alexander+S.+Green&rft.au=Peter+LeFanu+Lumsdaine&rft.au=Neil+J.+Ross&rft.au=Peter+Selinger&rft.au=Beno%C3%AEt+Valiron&rft_id=http%3A%2F%2Fwww.mathstat.dal.ca%2F~selinger%2Fquipper%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+programming" class="Z3988"></span></span> </li> <li id="cite_note-82"><span class="mw-cite-backlink"><b><a href="#cite_ref-82">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAlexander_S._GreenPeter_LeFanu_LumsdaineNeil_J._RossPeter_Selinger2013" class="citation book cs1">Alexander S. Green; Peter LeFanu Lumsdaine; Neil J. Ross; Peter Selinger; Benoît Valiron (2013). "An Introduction to Quantum Programming in Quipper". <i>Reversible Computation</i>. Lecture Notes in Computer Science. Vol. 7948. pp. <span class="nowrap">110–</span>124. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1304.5485">1304.5485</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-38986-3_10">10.1007/978-3-642-38986-3_10</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-38985-6" title="Special:BookSources/978-3-642-38985-6"><bdi>978-3-642-38985-6</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:9135905">9135905</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=An+Introduction+to+Quantum+Programming+in+Quipper&rft.btitle=Reversible+Computation&rft.series=Lecture+Notes+in+Computer+Science&rft.pages=%3Cspan+class%3D%22nowrap%22%3E110-%3C%2Fspan%3E124&rft.date=2013&rft_id=info%3Aarxiv%2F1304.5485&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9135905%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2F978-3-642-38986-3_10&rft.isbn=978-3-642-38985-6&rft.au=Alexander+S.+Green&rft.au=Peter+LeFanu+Lumsdaine&rft.au=Neil+J.+Ross&rft.au=Peter+Selinger&rft.au=Beno%C3%AEt+Valiron&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+programming" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=43" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMingsheng2024" class="citation book cs1">Mingsheng, Ying (2024). <i>Foundations of quantum programming</i> (2nd ed.). Cambridge, Massachusetts: Morgan Kaufmann. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-4431-5942-8" title="Special:BookSources/978-0-4431-5942-8"><bdi>978-0-4431-5942-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1406095194">1406095194</a>. 978-0-4431-5943-5 (eBook).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+quantum+programming&rft.place=Cambridge%2C+Massachusetts&rft.edition=2nd&rft.pub=Morgan+Kaufmann&rft.date=2024&rft_id=info%3Aoclcnum%2F1406095194&rft.isbn=978-0-4431-5942-8&rft.aulast=Mingsheng&rft.aufirst=Ying&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+programming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSerranoPérez-CastilloPiattini2022" class="citation book cs1">Serrano, Manuel A.; Pérez-Castillo, Ricardo; Piattini, Mario, eds. (2022). <i>Quantum Software Engineering</i> (1st ed.). Cham, Switzerland: Springer. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-031-05324-5">10.1007/978-3-031-05324-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-031-05323-8" title="Special:BookSources/978-3-031-05323-8"><bdi>978-3-031-05323-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1347696597">1347696597</a>. 978-3-031-05326-9 (softcover) & 978-3-031-05324-5 (eBook).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+Software+Engineering&rft.place=Cham%2C+Switzerland&rft.edition=1st&rft.pub=Springer&rft.date=2022&rft_id=info%3Aoclcnum%2F1347696597&rft_id=info%3Adoi%2F10.1007%2F978-3-031-05324-5&rft.isbn=978-3-031-05323-8&rfr_id=info%3Asid%2Fen.wikipedia.org%3AQuantum+programming" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Quantum_programming&action=edit&section=44" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://github.com/qosf/awesome-quantum-software">Curated list</a> of all quantum open-source software projects</li> <li><a rel="nofollow" class="external text" href="http://www.dcs.gla.ac.uk/~simon/quantum/">Bibliography on Quantum Programming Languages</a> (updated in May 2007)</li> <li><a rel="nofollow" class="external text" href="https://www.mathstat.dal.ca/~selinger/qpl/">Quantum Physics and Logic (QPL) Conference Series</a> (L stood for 'Languages' until 2006)</li> <li><a rel="nofollow" class="external text" href="https://quantiki.org/wiki/quantum-programming-language">Quantum programming language</a> in <a rel="nofollow" class="external text" href="http://www.quantiki.org/">Quantiki</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/lanl/qmasm/wiki">QMASM documentation</a></li> <li><a rel="nofollow" class="external text" href="https://pyquil.readthedocs.io/en/stable/index.html">pyQuil documentation</a> including <a rel="nofollow" class="external text" href="https://pyquil.readthedocs.io/en/stable/intro.html">Introduction to Quantum Computing</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180718165337/https://pyquil.readthedocs.io/en/stable/intro.html">Archived</a> July 18, 2018, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/epiqc/ScaffCC">Scaffold Source</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output 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aria-labelledby="Quantum_information_science667" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output 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title="Special:EditPage/Template:Quantum information"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_information_science667" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/DiVincenzo%27s_criteria" title="DiVincenzo's criteria">DiVincenzo's criteria</a></li> <li><a href="/wiki/Noisy_intermediate-scale_quantum_era" title="Noisy intermediate-scale quantum era">NISQ era</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a> <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">timeline</a></li></ul></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a class="mw-selflink selflink">Quantum programming</a></li> <li><a href="/wiki/Quantum_simulator" title="Quantum simulator">Quantum simulation</a></li> <li><a href="/wiki/Qubit" title="Qubit">Qubit</a> <ul><li><a href="/wiki/Physical_and_logical_qubits" title="Physical and logical qubits">physical vs. logical</a></li></ul></li> <li><a href="/wiki/List_of_quantum_processors" title="List of quantum processors">Quantum processors</a> <ul><li><a href="/wiki/Cloud-based_quantum_computing" title="Cloud-based quantum computing">cloud-based</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bell%27s_theorem" title="Bell's theorem">Bell's</a></li> <li><a href="/wiki/Eastin%E2%80%93Knill_theorem" title="Eastin–Knill theorem">Eastin–Knill</a></li> <li><a href="/wiki/Gleason%27s_theorem" title="Gleason's theorem">Gleason's</a></li> <li><a href="/wiki/Gottesman%E2%80%93Knill_theorem" title="Gottesman–Knill theorem">Gottesman–Knill</a></li> <li><a href="/wiki/Holevo%27s_theorem" title="Holevo's theorem">Holevo's</a></li> <li><a href="/wiki/No-broadcasting_theorem" title="No-broadcasting theorem">No-broadcasting</a></li> <li><a href="/wiki/No-cloning_theorem" title="No-cloning theorem">No-cloning</a></li> <li><a href="/wiki/No-communication_theorem" title="No-communication theorem">No-communication</a></li> <li><a href="/wiki/No-deleting_theorem" title="No-deleting theorem">No-deleting</a></li> <li><a href="/wiki/No-hiding_theorem" title="No-hiding theorem">No-hiding</a></li> <li><a href="/wiki/No-teleportation_theorem" title="No-teleportation theorem">No-teleportation</a></li> <li><a href="/wiki/PBR_theorem" class="mw-redirect" title="PBR theorem">PBR</a></li> <li><a href="/wiki/Quantum_speed_limit_theorems" class="mw-redirect" title="Quantum speed limit theorems">Quantum speed limit</a></li> <li><a href="/wiki/Threshold_theorem" title="Threshold theorem">Threshold</a></li> <li><a href="/wiki/Solovay%E2%80%93Kitaev_theorem" title="Solovay–Kitaev theorem">Solovay–Kitaev</a></li> <li><a href="/wiki/Schr%C3%B6dinger%E2%80%93HJW_theorem" title="Schrödinger–HJW theorem">Purification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantum<br />communication</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_capacity" title="Classical capacity">Classical capacity</a> <ul><li><a href="/wiki/Entanglement-assisted_classical_capacity" title="Entanglement-assisted classical capacity">entanglement-assisted</a></li> <li><a href="/wiki/Quantum_capacity" title="Quantum capacity">quantum capacity</a></li></ul></li> <li><a href="/wiki/Entanglement_distillation" title="Entanglement distillation">Entanglement distillation</a></li> <li><a href="/wiki/Entanglement_swapping" title="Entanglement swapping">Entanglement swapping</a></li> <li><a href="/wiki/Monogamy_of_entanglement" title="Monogamy of entanglement">Monogamy of entanglement</a></li> <li><a href="/wiki/LOCC" title="LOCC">LOCC</a></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">Quantum channel</a> <ul><li><a href="/wiki/Quantum_network" title="Quantum network">quantum network</a></li></ul></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">Quantum teleportation</a> <ul><li><a href="/wiki/Quantum_gate_teleportation" title="Quantum gate teleportation">quantum gate teleportation</a></li></ul></li> <li><a href="/wiki/Superdense_coding" title="Superdense coding">Superdense coding</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Quantum_cryptography24" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Post-quantum_cryptography" title="Post-quantum cryptography">Post-quantum cryptography</a></li> <li><a href="/wiki/Quantum_coin_flipping" title="Quantum coin flipping">Quantum coin flipping</a></li> <li><a href="/wiki/Quantum_money" title="Quantum money">Quantum money</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a> <ul><li><a href="/wiki/BB84" title="BB84">BB84</a></li> <li><a href="/wiki/SARG04" title="SARG04">SARG04</a></li> <li><a href="/wiki/List_of_quantum_key_distribution_protocols" title="List of quantum key distribution protocols">other protocols</a></li></ul></li> <li><a href="/wiki/Quantum_secret_sharing" title="Quantum secret sharing">Quantum secret sharing</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_algorithm" title="Quantum algorithm">Quantum algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amplitude_amplification" title="Amplitude amplification">Amplitude amplification</a></li> <li><a href="/wiki/Bernstein%E2%80%93Vazirani_algorithm" title="Bernstein–Vazirani algorithm">Bernstein–Vazirani</a></li> <li><a href="/wiki/BHT_algorithm" title="BHT algorithm">BHT</a></li> <li><a href="/wiki/Boson_sampling" title="Boson sampling">Boson sampling</a></li> <li><a href="/wiki/Deutsch%E2%80%93Jozsa_algorithm" title="Deutsch–Jozsa algorithm">Deutsch–Jozsa</a></li> <li><a href="/wiki/Grover%27s_algorithm" title="Grover's algorithm">Grover's</a></li> <li><a href="/wiki/HHL_algorithm" title="HHL algorithm">HHL</a></li> <li><a href="/wiki/Hidden_subgroup_problem" title="Hidden subgroup problem">Hidden subgroup</a></li> <li><a href="/wiki/Quantum_annealing" title="Quantum annealing">Quantum annealing</a></li> <li><a href="/wiki/Quantum_counting_algorithm" title="Quantum counting algorithm">Quantum counting</a></li> <li><a href="/wiki/Quantum_Fourier_transform" title="Quantum Fourier transform">Quantum Fourier transform</a></li> <li><a href="/wiki/Quantum_optimization_algorithms" title="Quantum optimization algorithms">Quantum optimization</a></li> <li><a href="/wiki/Quantum_phase_estimation_algorithm" title="Quantum phase estimation algorithm">Quantum phase estimation</a></li> <li><a href="/wiki/Shor%27s_algorithm" title="Shor's algorithm">Shor's</a></li> <li><a href="/wiki/Simon%27s_problem" title="Simon's problem">Simon's</a></li> <li><a href="/wiki/Variational_quantum_eigensolver" title="Variational quantum eigensolver">VQE</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">Quantum<br />complexity theory</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BQP" title="BQP">BQP</a></li> <li><a href="/wiki/Exact_quantum_polynomial_time" title="Exact quantum polynomial time">EQP</a></li> <li><a href="/wiki/QIP_(complexity)" title="QIP (complexity)">QIP</a></li> <li><a href="/wiki/QMA" title="QMA">QMA</a></li> <li><a href="/wiki/PostBQP" title="PostBQP">PostBQP</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantum <br /> processor benchmarks</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_supremacy" title="Quantum supremacy">Quantum supremacy</a></li> <li><a href="/wiki/Quantum_volume" title="Quantum volume">Quantum volume</a></li> <li><a href="/wiki/Randomized_benchmarking" title="Randomized benchmarking">Randomized benchmarking</a> <ul><li><a href="/wiki/Cross-entropy_benchmarking" title="Cross-entropy benchmarking">XEB</a></li></ul></li> <li><a href="/wiki/Relaxation_(NMR)" title="Relaxation (NMR)">Relaxation times</a> <ul><li><a href="/wiki/Spin%E2%80%93lattice_relaxation" title="Spin–lattice relaxation"><i>T</i><sub>1</sub></a></li> <li><a href="/wiki/Spin%E2%80%93spin_relaxation" title="Spin–spin relaxation"><i>T</i><sub>2</sub></a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantum<br /><a href="/wiki/Model_of_computation" title="Model of computation">computing models</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adiabatic_quantum_computation" title="Adiabatic quantum computation">Adiabatic quantum computation</a></li> <li><a href="/wiki/Continuous-variable_quantum_information" title="Continuous-variable quantum information">Continuous-variable quantum information</a></li> <li><a href="/wiki/One-way_quantum_computer" title="One-way quantum computer">One-way quantum computer</a> <ul><li><a href="/wiki/Cluster_state" title="Cluster state">cluster state</a></li></ul></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a> <ul><li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">quantum logic gate</a></li></ul></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a> <ul><li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">quantum neural network</a></li></ul></li> <li><a href="/wiki/Quantum_Turing_machine" title="Quantum Turing machine">Quantum Turing machine</a></li> <li><a href="/wiki/Topological_quantum_computer" title="Topological quantum computer">Topological quantum computer</a></li> <li><a href="/wiki/Hamiltonian_quantum_computation" title="Hamiltonian quantum computation">Hamiltonian quantum computation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_error_correction" title="Quantum error correction">Quantum<br />error correction</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Codes <ul><li><a href="/wiki/CSS_code" title="CSS code">CSS</a></li> <li><a href="/wiki/Quantum_convolutional_code" title="Quantum convolutional code">quantum convolutional</a></li> <li><a href="/wiki/Stabilizer_code" title="Stabilizer code">stabilizer</a></li> <li><a href="/wiki/Shor_code" class="mw-redirect" title="Shor code">Shor</a></li> <li><a href="/wiki/Bacon%E2%80%93Shor_code" title="Bacon–Shor code">Bacon–Shor</a></li> <li><a href="/wiki/Steane_code" title="Steane code">Steane</a></li> <li><a href="/wiki/Toric_code" title="Toric code">Toric</a></li> <li><a href="/wiki/Gnu_code" title="Gnu code"><i>gnu</i></a></li></ul></li> <li><a href="/wiki/Entanglement-assisted_stabilizer_formalism" title="Entanglement-assisted stabilizer formalism">Entanglement-assisted</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical<br />implementations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cavity_quantum_electrodynamics" title="Cavity quantum electrodynamics">Cavity QED</a></li> <li><a href="/wiki/Circuit_quantum_electrodynamics" title="Circuit quantum electrodynamics">Circuit QED</a></li> <li><a href="/wiki/Linear_optical_quantum_computing" title="Linear optical quantum computing">Linear optical QC</a></li> <li><a href="/wiki/KLM_protocol" title="KLM protocol">KLM protocol</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ultracold_atom" title="Ultracold atom">Ultracold atoms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Neutral_atom_quantum_computer" title="Neutral atom quantum computer">Neutral atom QC</a></li> <li><a href="/wiki/Trapped-ion_quantum_computer" title="Trapped-ion quantum computer">Trapped-ion QC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Spin_(physics)" title="Spin (physics)">Spin</a>-based</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kane_quantum_computer" title="Kane quantum computer">Kane QC</a></li> <li><a href="/wiki/Spin_qubit_quantum_computer" title="Spin qubit quantum computer">Spin qubit QC</a></li> <li><a href="/wiki/Nitrogen-vacancy_center" title="Nitrogen-vacancy center">NV center</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance_quantum_computer" title="Nuclear magnetic resonance quantum computer">NMR QC</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Superconducting_quantum_computing" title="Superconducting quantum computing">Superconducting</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Charge_qubit" title="Charge qubit">Charge qubit</a></li> <li><a href="/wiki/Flux_qubit" title="Flux qubit">Flux qubit</a></li> <li><a href="/wiki/Phase_qubit" title="Phase qubit">Phase qubit</a></li> <li><a href="/wiki/Transmon" title="Transmon">Transmon</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Quantum<br />programming</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/OpenQASM" title="OpenQASM">OpenQASM</a>–<a href="/wiki/Qiskit" title="Qiskit">Qiskit</a>–<a href="/wiki/IBM_Quantum_Experience" class="mw-redirect" title="IBM Quantum Experience">IBM QX</a></li> <li><a href="/wiki/Quil_(instruction_set_architecture)" title="Quil (instruction set architecture)">Quil</a>–<a href="/wiki/Rigetti_Computing" title="Rigetti Computing">Forest/Rigetti QCS</a></li> <li><a href="/wiki/Cirq" title="Cirq">Cirq</a></li> <li><a href="/wiki/Q_Sharp" title="Q Sharp">Q#</a></li> <li><a href="/wiki/Libquantum" title="Libquantum">libquantum</a></li> <li><a class="mw-selflink selflink">many others...</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Quantum_information_science" title="Category:Quantum information science">Quantum information science</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Template"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/16px-Symbol_template_class_pink.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/23px-Symbol_template_class_pink.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/31px-Symbol_template_class_pink.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics">Quantum mechanics topics</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Emerging_technologies167" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align: center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Emerging_technologies" title="Template:Emerging technologies"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Emerging_technologies" title="Template talk:Emerging technologies"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Emerging_technologies" title="Special:EditPage/Template:Emerging technologies"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Emerging_technologies167" style="font-size:114%;margin:0 4em"><a href="/wiki/Emerging_technologies" title="Emerging technologies">Emerging technologies</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Fields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Quantum_technology" class="mw-redirect" title="Quantum technology">Quantum</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_algorithm" title="Quantum algorithm">algorithms</a></li> <li><a href="/wiki/Quantum_amplifier" title="Quantum amplifier">amplifier</a></li> <li><a href="/wiki/Quantum_bus" title="Quantum bus">bus</a></li> <li><a href="/wiki/Quantum_cellular_automaton" title="Quantum cellular automaton">cellular automata</a></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">channel</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">circuit</a></li> <li><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">complexity theory</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">computing</a></li> <li><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">cryptography</a> <ul><li><a href="/wiki/Post-quantum_cryptography" title="Post-quantum cryptography">post-quantum</a></li></ul></li> <li><a href="/wiki/Quantum_dynamics" title="Quantum dynamics">dynamics</a></li> <li><a href="/wiki/Quantum_electronics" class="mw-redirect" title="Quantum electronics">electronics</a></li> <li><a href="/wiki/Quantum_error_correction" title="Quantum error correction">error correction</a></li> <li><a href="/wiki/Quantum_finite_automaton" title="Quantum finite automaton">finite automata</a></li> <li><a href="/wiki/Quantum_image_processing" title="Quantum image processing">image processing</a></li> <li><a href="/wiki/Quantum_imaging" title="Quantum imaging">imaging</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">information</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">key distribution</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">logic</a></li> <li><a href="/wiki/Quantum_logic_clock" title="Quantum logic clock">logic clock</a></li> <li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">logic gate</a></li> <li><a href="/wiki/Quantum_machine" title="Quantum machine">machine</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">machine learning</a></li> <li><a href="/wiki/Quantum_metamaterial" title="Quantum metamaterial">metamaterial</a></li> <li><a href="/wiki/Quantum_network" title="Quantum network">network</a></li> <li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">neural network</a></li> <li><a href="/wiki/Quantum_optics" title="Quantum optics">optics</a></li> <li><a class="mw-selflink selflink">programming</a></li> <li><a href="/wiki/Quantum_sensor" title="Quantum sensor">sensing</a></li> <li><a href="/wiki/Quantum_simulator" title="Quantum simulator">simulator</a></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">teleportation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acoustic_levitation" title="Acoustic levitation">Acoustic levitation</a></li> <li><a href="/wiki/Anti-gravity" title="Anti-gravity">Anti-gravity</a></li> <li><a href="/wiki/Cloak_of_invisibility" title="Cloak of invisibility">Cloak of invisibility</a></li> <li><a href="/wiki/Digital_scent_technology" title="Digital scent technology">Digital scent technology</a></li> <li><a href="/wiki/Force_field_(technology)" title="Force field (technology)">Force field</a> <ul><li><a href="/wiki/Plasma_window" title="Plasma window">Plasma window</a></li></ul></li> <li><a href="/wiki/Immersion_(virtual_reality)" title="Immersion (virtual reality)">Immersive virtual reality</a></li> <li><a href="/wiki/Magnetic_refrigeration" class="mw-redirect" title="Magnetic refrigeration">Magnetic refrigeration</a></li> <li><a href="/wiki/Phased-array_optics" title="Phased-array optics">Phased-array optics</a></li> <li><a href="/wiki/Thermoacoustic_heat_engine" title="Thermoacoustic heat engine">Thermoacoustic heat engine</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" 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style="font-size:114%;margin:0 4em"><a href="/wiki/Programming_paradigm" title="Programming paradigm">Programming paradigms</a> (<a href="/wiki/Comparison_of_multi-paradigm_programming_languages" title="Comparison of multi-paradigm programming languages">Comparison by language</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Imperative_programming" title="Imperative programming">Imperative</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Structured_programming" title="Structured programming">Structured</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jackson_structured_programming" title="Jackson structured programming">Jackson structures</a></li> <li><a href="/wiki/Block_(programming)" title="Block (programming)">Block-structured</a></li> <li><a href="/wiki/Modular_programming" title="Modular programming">Modular</a></li> <li><a href="/wiki/Non-structured_programming" title="Non-structured programming">Non-structured</a></li> <li><a href="/wiki/Procedural_programming" title="Procedural programming">Procedural</a></li> <li><a href="/wiki/Programming_in_the_large_and_programming_in_the_small" title="Programming in the large and programming in the small">Programming in the large and in the small</a></li> <li><a href="/wiki/Design_by_contract" title="Design by contract">Design by contract</a></li> <li><a href="/wiki/Invariant-based_programming" title="Invariant-based programming">Invariant-based</a></li> <li><a href="/wiki/Nested_function" title="Nested function">Nested function</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Object-oriented_programming" title="Object-oriented programming">Object-oriented</a><br />(<a href="/wiki/Comparison_of_programming_languages_(object-oriented_programming)" title="Comparison of programming languages (object-oriented programming)">comparison</a>, <a href="/wiki/List_of_object-oriented_programming_languages" title="List of object-oriented programming languages">list</a>)</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Class-based_programming" title="Class-based programming">Class-based</a>, <a href="/wiki/Prototype-based_programming" title="Prototype-based programming">Prototype-based</a>, <a href="/wiki/Object-based_language" title="Object-based language">Object-based</a></li> <li><a href="/wiki/Agent-oriented_programming" title="Agent-oriented programming">Agent</a></li> <li><a href="/wiki/Immutable_object" title="Immutable object">Immutable object</a></li> <li><a href="/wiki/Persistent_programming_language" title="Persistent programming language">Persistent</a></li> <li><a href="/wiki/Uniform_Function_Call_Syntax" title="Uniform Function Call Syntax">Uniform Function Call Syntax</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Declarative_programming" title="Declarative programming">Declarative</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Functional_programming" title="Functional programming">Functional</a><br />(<a href="/wiki/Comparison_of_functional_programming_languages" title="Comparison of functional programming languages">comparison</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Recursion_(computer_science)" title="Recursion (computer science)">Recursive</a></li> <li><a href="/wiki/Anonymous_function" title="Anonymous function">Anonymous function</a> (<a href="/wiki/Partial_application" title="Partial application">Partial application</a>)</li> <li><a href="/wiki/Higher-order_programming" title="Higher-order programming">Higher-order</a></li> <li><a href="/wiki/Purely_functional_programming" title="Purely functional programming">Purely functional</a></li> <li><a href="/wiki/Total_functional_programming" title="Total functional programming">Total</a></li> <li><a href="/wiki/Strict_programming_language" title="Strict programming language">Strict</a></li> <li><a href="/wiki/Generalized_algebraic_data_type" title="Generalized algebraic data type">GADTs</a></li> <li><a href="/wiki/Dependent_type" title="Dependent type">Dependent types</a></li> <li><a href="/wiki/Functional_logic_programming" title="Functional logic programming">Functional logic</a></li> <li><a href="/wiki/Tacit_programming" title="Tacit programming">Point-free style</a></li> <li><a href="/wiki/Expression-oriented_programming_language" title="Expression-oriented programming language">Expression-oriented</a></li> <li><a href="/wiki/Applicative_programming_language" title="Applicative programming language">Applicative</a>, <a href="/wiki/Concatenative_programming_language" title="Concatenative programming language">Concatenative</a></li> <li><a href="/wiki/Function-level_programming" title="Function-level programming">Function-level</a>, <a href="/wiki/Value-level_programming" title="Value-level programming">Value-level</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Dataflow_programming" title="Dataflow programming">Dataflow</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Flow-based_programming" title="Flow-based programming">Flow-based</a></li> <li><a href="/wiki/Reactive_programming" title="Reactive programming">Reactive</a> (<a href="/wiki/Functional_reactive_programming" title="Functional reactive programming">Functional reactive</a>)</li> <li><a href="/wiki/Signal_programming" class="mw-redirect" title="Signal programming">Signals</a></li> <li><a href="/wiki/Stream_processing" title="Stream processing">Streams</a></li> <li><a href="/wiki/Synchronous_programming_language" title="Synchronous programming language">Synchronous</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Logic_programming" title="Logic programming">Logic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abductive_logic_programming" title="Abductive logic programming">Abductive logic</a></li> <li><a href="/wiki/Answer_set_programming" title="Answer set programming">Answer set</a></li> <li><a href="/wiki/Constraint_programming" title="Constraint programming">Constraint</a> (<a href="/wiki/Constraint_logic_programming" title="Constraint logic programming">Constraint logic</a>)</li> <li><a href="/wiki/Inductive_logic_programming" title="Inductive logic programming">Inductive logic</a></li> <li><a href="/wiki/Nondeterministic_programming" title="Nondeterministic programming">Nondeterministic</a></li> <li><a href="/wiki/Ontology_language" title="Ontology language">Ontology</a></li> <li><a href="/wiki/Probabilistic_logic_programming" title="Probabilistic logic programming">Probabilistic logic</a></li> <li><a href="/wiki/Query_language" title="Query language">Query</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Domain-specific_language" title="Domain-specific language">DSL</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algebraic_modeling_language" title="Algebraic modeling language">Algebraic modeling</a></li> <li><a href="/wiki/Array_programming" title="Array programming">Array</a></li> <li><a href="/wiki/Automata-based_programming" title="Automata-based programming">Automata-based</a> (<a href="/wiki/Action_language" title="Action language">Action</a>)</li> <li><a href="/wiki/Command_language" title="Command language">Command</a> (<a href="/wiki/Spacecraft_command_language" title="Spacecraft command language">Spacecraft</a>)</li> <li><a href="/wiki/Differentiable_programming" title="Differentiable programming">Differentiable</a></li> <li><a href="/wiki/End-user_development" title="End-user development">End-user</a></li> <li><a href="/wiki/Grammar-oriented_programming" title="Grammar-oriented programming">Grammar-oriented</a></li> <li><a href="/wiki/Interface_description_language" title="Interface description language">Interface description</a></li> <li><a href="/wiki/Language-oriented_programming" title="Language-oriented programming">Language-oriented</a></li> <li><a href="/wiki/List_comprehension" title="List comprehension">List comprehension</a></li> <li><a href="/wiki/Low-code_development_platform" title="Low-code development platform">Low-code</a></li> <li><a href="/wiki/Modeling_language" title="Modeling language">Modeling</a></li> <li><a href="/wiki/Natural-language_programming" title="Natural-language programming">Natural language</a></li> <li><a href="/wiki/Non-English-based_programming_languages" title="Non-English-based programming languages">Non-English-based</a></li> <li><a href="/wiki/Page_description_language" title="Page description language">Page description</a></li> <li><a href="/wiki/Pipeline_(software)" title="Pipeline (software)">Pipes</a> and <a href="/wiki/Filter_(software)" title="Filter (software)">filters</a></li> <li><a href="/wiki/Probabilistic_programming" title="Probabilistic programming">Probabilistic</a></li> <li><a class="mw-selflink selflink">Quantum</a></li> <li><a href="/wiki/Scientific_programming_language" title="Scientific programming language">Scientific</a></li> <li><a href="/wiki/Scripting_language" title="Scripting language">Scripting</a></li> <li><a href="/wiki/Set_theoretic_programming" title="Set theoretic programming">Set-theoretic</a></li> <li><a href="/wiki/Simulation_language" title="Simulation language">Simulation</a></li> <li><a href="/wiki/Stack-oriented_programming" title="Stack-oriented programming">Stack-based</a></li> <li><a href="/wiki/System_programming_language" title="System programming language">System</a></li> <li><a href="/wiki/Tactile_programming_language" title="Tactile programming language">Tactile</a></li> <li><a href="/wiki/Template_processor" title="Template processor">Templating</a></li> <li><a href="/wiki/Transformation_language" title="Transformation language">Transformation</a> (<a href="/wiki/Graph_rewriting" title="Graph rewriting">Graph rewriting</a>, <a href="/wiki/Production_system_(computer_science)" title="Production system (computer science)">Production</a>, <a href="/wiki/Pattern_matching" title="Pattern matching">Pattern</a>)</li> <li><a href="/wiki/Visual_programming_language" title="Visual programming language">Visual</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Concurrent_computing" title="Concurrent computing">Concurrent</a>,<br /><a href="/wiki/Distributed_computing" title="Distributed computing">distributed</a>,<br /><a href="/wiki/Parallel_computing" title="Parallel computing">parallel</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Actor_model" title="Actor model">Actor-based</a></li> <li><a href="/wiki/Automatic_mutual_exclusion" title="Automatic mutual exclusion">Automatic mutual exclusion</a></li> <li><a href="/wiki/Choreographic_programming" title="Choreographic programming">Choreographic programming</a></li> <li><a href="/wiki/Concurrent_logic_programming" title="Concurrent logic programming">Concurrent logic</a> (<a href="/wiki/Concurrent_constraint_logic_programming" title="Concurrent constraint logic programming">Concurrent constraint logic</a>)</li> <li><a href="/wiki/Concurrent_object-oriented_programming" title="Concurrent object-oriented programming">Concurrent OO</a></li> <li><a href="/wiki/Macroprogramming" title="Macroprogramming">Macroprogramming</a></li> <li><a href="/wiki/Multitier_programming" title="Multitier programming">Multitier programming</a></li> <li><a href="/wiki/Organic_computing" title="Organic computing">Organic computing</a></li> <li><a href="/wiki/Parallel_programming_model" title="Parallel programming model">Parallel programming models</a></li> <li><a href="/wiki/Partitioned_global_address_space" title="Partitioned global address space">Partitioned global address space</a></li> <li><a href="/wiki/Process-oriented_programming" title="Process-oriented programming">Process-oriented</a></li> <li><a href="/wiki/Relativistic_programming" title="Relativistic programming">Relativistic programming</a></li> <li><a href="/wiki/Service-oriented_programming" title="Service-oriented programming">Service-oriented</a></li> <li><a href="/wiki/Structured_concurrency" title="Structured concurrency">Structured concurrency</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Metaprogramming" title="Metaprogramming">Metaprogramming</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Attribute-oriented_programming" title="Attribute-oriented programming">Attribute-oriented</a></li> <li><a href="/wiki/Automatic_programming" title="Automatic programming">Automatic</a> (<a href="/wiki/Inductive_programming" title="Inductive programming">Inductive</a>)</li> <li><a href="/wiki/Dynamic_programming_language" title="Dynamic programming language">Dynamic</a></li> <li><a href="/wiki/Extensible_programming" title="Extensible programming">Extensible</a></li> <li><a href="/wiki/Generic_programming" title="Generic programming">Generic</a></li> <li><a href="/wiki/Homoiconicity" title="Homoiconicity">Homoiconicity</a></li> <li><a href="/wiki/Interactive_programming" title="Interactive programming">Interactive</a></li> <li><a href="/wiki/Macro_(computer_science)" title="Macro (computer science)">Macro</a> (<a href="/wiki/Hygienic_macro" title="Hygienic macro">Hygienic</a>)</li> <li><a href="/wiki/Metalinguistic_abstraction" title="Metalinguistic abstraction">Metalinguistic abstraction</a></li> <li><a href="/wiki/Multi-stage_programming" title="Multi-stage programming">Multi-stage</a></li> <li><a href="/wiki/Program_synthesis" title="Program synthesis">Program synthesis</a> (<a href="/wiki/Bayesian_program_synthesis" title="Bayesian program synthesis">Bayesian</a>, <a href="/wiki/Inferential_programming" title="Inferential programming">Inferential</a>, <a href="/wiki/Programming_by_demonstration" title="Programming by demonstration">by demonstration</a>, <a href="/wiki/Programming_by_example" title="Programming by example">by example</a>)</li> <li><a href="/wiki/Reflective_programming" title="Reflective programming">Reflective</a></li> <li><a href="/wiki/Self-modifying_code" title="Self-modifying code">Self-modifying code</a></li> <li><a href="/wiki/Symbolic_programming" title="Symbolic programming">Symbolic</a></li> <li><a href="/wiki/Template_metaprogramming" title="Template metaprogramming">Template</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a 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