Scientific Publications

<!DOCTYPE html> <html lang="en-US">  <head> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> <script>(function (i, s, o, g, r, a, m) { i["GoogleAnalyticsObject"] = r; i[r] = i[r] || function () { (i[r].q = i[r].q || []).push(arguments) }, i[r].l = 1 * new Date(); a = s.createElement(o), m = s.getElementsByTagName(o)[0]; a.async = 1; a.src = g; m.parentNode.insertBefore(a, m) })(window, document, "script", "https://www.google-analytics.com/analytics.js", "ga"); ga("create", "UA-124167090-6", { "cookieDomain": "auto" }); ga("send", "pageview");</script>   <script async src="https://www.googletagmanager.com/gtag/js?id=AW-606193534"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'AW-606193534'); </script>  <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-TG454ZB');</script>  <script src=https://www.googleoptimize.com/optimize.js?id=OPT-K2NJGQV></script> <script type="text/javascript"> (function () { var didInit = false; function initMunchkin() { if (didInit === false) { didInit = true; Munchkin.init('100-UBX-183'); } } var s = document.createElement('script'); s.type = 'text/javascript'; s.async = true; s.src = '//munchkin.marketo.net/munchkin.js'; s.onreadystatechange = function () { if (this.readyState == 'complete' || this.readyState == 'loaded') { initMunchkin(); } }; s.onload = initMunchkin; document.getElementsByTagName('head')[0].appendChild(s); })(); </script> <title>Scientific Publications | D-Wave</title> <link rel="shortcut icon" href="https://www.dwavesys.com/favicon.ico" type="image/x-icon" /> <meta name="description" content="Learn more about the science behind our cutting-edge quantum technology and the use cases it can be applied to." /> <meta name="keywords" content="Quantum publications, quantum computing publications, quantum papers, quantum computing papers, quantum whitepaper, quantum white paper, quantum physics, D-Wave publications, D-Wave papers" /> <link rel="canonical" href="" /> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1 user-scalable=no"> <meta http-equiv="X-UA-Compatible" content="IE=edge" /> <link rel="shortcut icon" type="image/x-icon" href="https://www.dwavesys.com/favicon.ico"> <meta property="og:locale" content="en_US" /> <meta property="og:type" content="website" /> <meta property="og:title" content="Scientific Publications | D-Wave" /> <meta property="og:description" content="Learn more about the science behind our cutting-edge quantum technology and the use cases it can be applied to." /> <meta property="og:url" content="https://www.dwavesys.com/learn/publications/" /> <meta property="og:site_name" /> <meta property='og:image' content='https://www.dwavesys.com/media/cdqdvcaa/dwave-gerneric-open-graph-image.png?anchor=center&mode=crop&width=1200&height=630' /> <meta name="twitter:card" content="summary_large_image" /> <meta name="twitter:site" /> <meta name="twitter:title" content="Scientific Publications | D-Wave"> <meta name="twitter:description" content="Learn more about the science behind our cutting-edge quantum technology and the use cases it can be applied to."> <meta name="twitter:image" content="https://www.dwavesys.com/media/cdqdvcaa/dwave-gerneric-open-graph-image.png?anchor=center&mode=crop&width=600&height=314" /> <link href="/css/styles.css" rel="stylesheet"/> <link rel="preconnect" href="https://fonts.gstatic.com"> <link href="https://fonts.googleapis.com/css2?family=Open+Sans:ital,wght@0,300;0,400;0,600;0,700;0,800;1,400;1,600;1,800&display=swap" rel="stylesheet"> <link rel="stylesheet" href="/css/frameworks-libraries/animate-it/animations.css" type="text/css"> <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.0.13/css/all.css" integrity="sha384-DNOHZ68U8hZfKXOrtjWvjxusGo9WQnrNx2sqG0tfsghAvtVlRW3tvkXWZh58N9jp" crossorigin="anonymous"> <script> function showAllItems(formKey) { $('#div-'+formKey).children().removeClass("resources-hide"); $('#btn-'+ formKey).addClass("resources-hide"); } // Picture element HTML5 shiv document.createElement("picture"); </script> <style> .cta__medium:hover { color: #FFF !important; } .cta__link i { display: none; } </style> </head> <body class="page-bg-image"> <style> body.page-bg-image { background-color: #000; background-position: center 0px; background-image: url('/media/qpqhf5qp/lines-publications-desktop-c.png'); background-repeat:no-repeat; overflow-x: hidden; } @media (min-width: 1920px) { body.page-bg-image { background-color: #000; background-position: center 0px; background-size: 1920px; background-image: url('/media/qpqhf5qp/lines-publications-desktop-c.png'); background-repeat: no-repeat; overflow-x: hidden; } } @media (max-width: 768px) { body.page-bg-image { background-color: #000; background-position: center 0px; background-size: cover; background-image: url('/media/facdiyev/lines-generic-tablet-2-c.png'); background-repeat: no-repeat; overflow-x: hidden; } } @media (max-width: 480px) { body.page-bg-image { background-color: #000; background-position: center 0px; background-size: cover; background-image: url('/media/rlggrv0j/lines-generic-mobile-2-c.png'); background-repeat: no-repeat; overflow-x: hidden; } } </style> <nav class="navbar navbar-expand-lg dwave__menu"> <div class="container"> <div class="row menu__row--fix"> <button class="navbar-toggler dwave__menu--toggler" type="button" data-toggle="collapse" data-target="#navbarNavDropdown" aria-controls="navbarNavDropdown" aria-expanded="false" aria-label="Toggle navigation"> <span></span> <span></span> <span></span> </button> <div class="col-md-3"> <div class="logo"> <a class="navbar-brand" href="/"> <img src="/media/j31olsrx/d-wave.svg" width="170" alt="Logo" /> </a> </div> </div> <div class="col-md-9 collapse navbar-collapse menu__mobile--container" id="navbarNavDropdown"> <div class="menu menu__main--block"> <div class="navigation"> <div class="search"> <ul class="menu__search--block"> <li class=""> <a class="" href="https://ir.dwavesys.com/overview/default.aspx">INVESTORS</a> </li> <li class=""> <a class="" href="/company/careers/">CAREERS</a> </li> <li class=""> <a class="" href="/company/contact/">CONTACT</a> </li> <li class=""> <a class="" href="https://cloud.dwavesys.com/leap/login/?next=/leap/" target="_blank" rel="noopener noreferrer">Log In</a> </li> <li class="c-navigation__top-nav__search"> <div class="desktop-search-container search-hidden"> <span class="search-btn glyphicon glyphicon-search"></span> <div class="desktop-search-container__wrapper"> <input id="desktop-search-box" class="search-box" type="text" maxlength="40" name="query" data-search-url="/gaining/" /> <input id="desktop-search-button" type="submit" class="submit-btn search-submit-btn" value="Go" /> </div> </div> </li> </ul> </div> <ul id="MainMenu" class="menu__bottom--block menu_link"> <li class="menu__item--block dropdown"> <a data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Products</a> <div class="sub_menu dropdown-menu"> <div class="container"> <div class="row submenu__col--divider"> <div class="col-md-4 menu-item-info"> <h3>Products</h3> <p>Discover how you can use quantum computing today</p> </div> <div class="menu-item-links menu__col--right"> <div class="row menu-items-row"> <div class="col-md-12 sub__menu--inner-col"> <div class="row"> <ul class="width-50-item " > <li class="submenu-item-info"> <a href="/solutions-and-products/cloud-platform/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Cloud Platform </span> <span class="submenu-item-info__link--desc"> The Leap™ quantum cloud service provides real-time quantum access </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/product-overview/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Product Overview </span> <span class="submenu-item-info__link--desc"> The only full-stack, cross-platform quantum ecosystem built for business </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/professional-services/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Professional Services </span> <span class="submenu-item-info__link--desc"> The D-Wave Launch™ program on-boards your business to quantum computing </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/systems/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Systems </span> <span class="submenu-item-info__link--desc"> The Advantage™ quantum system is the first and only quantum computer built for business </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/training/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Learning Solutions </span> <span class="submenu-item-info__link--desc"> Start your journey! Explore D-Wave applications, events, and resources </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/ocean/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Software & Tools </span> <span class="submenu-item-info__link--desc"> The Ocean™ suite of open-source tools are accessible via the Ocean SDK for rapid quantum development </span> </a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> </li> <li class="menu__item--block dropdown"> <a data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Solutions</a> <div class="sub_menu dropdown-menu"> <div class="container"> <div class="row submenu__col--divider"> <div class="col-md-3 menu-item-info"> <h3>Solutions</h3> <p>Discover how you can use quantum computing today</p> </div> <div class="menu-item-links col-md-9"> <div class="row menu-items-row"> <div class="col-md-8 sub__menu--inner-col"> <h4>By Use Case</h4> <div class="row"> <ul class=" col-md-6" > <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/quantum-optimization-landing-page/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Quantum Optimization Summary </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/workforce-scheduling/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Workforce Scheduling </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/production-scheduling/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Production Scheduling </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/logistics-routing/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Logistics Routing </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/resource-optimization/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Resource Optimization </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/cargo-loading/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Cargo Loading </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/featured-applications/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Additional Use Cases </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> </ul> </div> </div> <div class="col-md-4 sub__menu--inner-col"> <h4>By Role</h4> <div class="row"> <ul class=" " > <li class="submenu-item-info"> <a href="/solutions-and-products/developer/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Developer </span> <span class="submenu-item-info__link--desc"> Get started building real quantum applications </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/technology-business-leader/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Tech & Business Leaders </span> <span class="submenu-item-info__link--desc"> Learn how quantum computing fits into your technology portfolio </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/researcher/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Researcher </span> <span class="submenu-item-info__link--desc"> Explore the boundaries of quantum computing </span> </a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> </li> <li class="menu__item--block dropdown"> <a data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Sectors</a> <div class="sub_menu dropdown-menu"> <div class="container"> <div class="row submenu__col--divider"> <div class="col-md-4 menu-item-info"> <h3>Sectors</h3> <p>Discover how you can use quantum computing today</p> </div> <div class="menu-item-links menu__col--right"> <div class="row menu-items-row"> <div class="col-md-12 sub__menu--inner-col"> <div class="row"> <ul class="width-50-item " > <li class="submenu-item-info"> <a href="/solutions-and-products/manufacturing-logistics/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Manufacturing & Logistics </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/public-sector/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Public Sector </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/quantum-research-landing-page/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Quantum Research </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/quantum-optimization/quantum-ai-landing-page/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Quantum AI </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> </li> <li class="menu__item--block dropdown"> <a data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Learn</a> <div class="sub_menu dropdown-menu"> <div class="container"> <div class="row submenu__col--divider"> <div class="col-md-4 menu-item-info"> <h3>Learn</h3> <p>Start your journey! Explore D-Wave applications, events, and resources.</p> </div> <div class="menu-item-links menu__col--right"> <div class="row menu-items-row"> <div class="col-md-12 sub__menu--inner-col"> <div class="row"> <ul class="width-50-item " > <li class="submenu-item-info"> <a href="/learn/featured-applications/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Featured Applications </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/quantum-computing/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Quantum Computing </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/resource-library/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Resource Library </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/d-wave-s-approach/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> D-Wave's Approach </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/publications/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Publications </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/customer-success-stories/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Customer Success Stories </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/events-and-webinars/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Events & Webinars </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/learn/training/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Training </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> </li> <li class="menu__item--block dropdown"> <a data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Build</a> <div class="sub_menu dropdown-menu"> <div class="container"> <div class="row submenu__col--divider"> <div class="col-md-4 menu-item-info"> <h3>Build</h3> <p>Unlock your quantum skills and start building quantum applications today</p> </div> <div class="menu-item-links menu__col--right"> <div class="row menu-items-row"> <div class="col-md-12 sub__menu--inner-col"> <div class="row"> <ul class="width-50-item " > <li class="submenu-item-info"> <a href="https://support.dwavesys.com/hc/en-us/community/topics" class="submenu-item-info__link" target="_blank"> <span class="submenu-item-info__link--header"> Community Forums <i class="fas fa-arrow-up new-window-arrow"></i> </span> <span class="submenu-item-info__link--desc"> Connect with and learn from other quantum developers. </span> </a> </li> <li class="submenu-item-info"> <a href="/build/getting-started/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Getting Started </span> <span class="submenu-item-info__link--desc"> Step-by-step approach to building quantum applications today. </span> </a> </li> <li class="submenu-item-info"> <a href="https://github.com/dwave-examples" class="submenu-item-info__link" target="_blank"> <span class="submenu-item-info__link--header"> Code Samples <i class="fas fa-arrow-up new-window-arrow"></i> </span> <span class="submenu-item-info__link--desc"> Search for and run working examples by industry, problem type, and tools or techniques. </span> </a> </li> <li class="submenu-item-info"> <a href="/solutions-and-products/developer/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Developer </span> <span class="submenu-item-info__link--desc"> Start here! </span> </a> </li> <li class="submenu-item-info"> <a href="https://docs.dwavesys.com/docs/latest/index.html" class="submenu-item-info__link" target="_blank"> <span class="submenu-item-info__link--header"> Documentation <i class="fas fa-arrow-up new-window-arrow"></i> </span> <span class="submenu-item-info__link--desc"> Find out more about D-Wave’s quantum technologies and how they work. </span> </a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> </li> <li class="menu__item--block dropdown"> <a data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Company</a> <div class="sub_menu dropdown-menu"> <div class="container"> <div class="row submenu__col--divider"> <div class="col-md-4 menu-item-info"> <h3>Company</h3> <p>We are the practical quantum computing company. Learn more about who we are and what we do.</p> </div> <div class="menu-item-links menu__col--right"> <div class="row menu-items-row"> <div class="col-md-12 sub__menu--inner-col"> <div class="row"> <ul class="width-50-item " > <li class="submenu-item-info"> <a href="/learn/events-and-webinars/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Events & Webinars </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/company/about-d-wave/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> About D-Wave </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/company/newsroom/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Newsroom </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/company/leadership/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Leadership </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/company/media-resources/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Media Resources </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/company/careers/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Careers </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> <li class="submenu-item-info"> <a href="/company/contact/" class="submenu-item-info__link"> <span class="submenu-item-info__link--header"> Contact </span> <span class="submenu-item-info__link--desc"> </span> </a> </li> </ul> </div> </div> </div> </div> </div> </div> </div> </li> </ul> </div> <div class="right_btn"> <div class="right_arrow"> <a href="/build/getting-started/">Get Started<span><i class="fas fa-chevron-right"></i></span></a> </div> </div> </div> </div> </div> </div> </nav> <main role="main"> <div class="umb-grid"> <div class="grid-section"> <section class="grid__row-section "><div class="grid__container-outer " style="background-color:transparent;" ><div class="grid__container container grid-container--wrapped "><div class="grid__container-inner pb-5 "> <div class="row clearfix row-type--1Column"> <div class="grid__column col-lg-12 col-md-12 col-sm-12 column "> <div class="grid__component-wrapper pt-5 " style="background-color:transparent;">  <div id="element_1" class="optional-marquee l2-marquee-alt"> <div class="content_center"> <div class="marquee-title"> <h1> Scientific Publications </h1> </div> </div> <div class="content_center"> <div class="marquee-body"> <p><span class="NormalTextRun SCXW206447712 BCX0">D-Wave is the world’s first commercial supplier of quantum computers. Learn more about the science behind our cutting-edge quantum technology and the use cases it can be applied to. </span><span class="NormalTextRun SCXW206447712 BCX0">Visit our <a href="/learn/resource-library/" title="Resource Library">resource library</a> to read our technical white papers or see a list of the most important research papers <a href="/learn/select-research-papers/" title="Select Research Papers">here</a>. </span></p> </div> </div> </div> </div> </div> </div> </div></div></div></section><section class="grid__row-section "><div class="grid__container-outer " style="background-color:#eeeeee;" ><div class="grid__container container grid-container--wrapped "><div class="grid__container-inner "> <div class="row clearfix row-type--1Column"> <div class="grid__column col-lg-12 col-md-12 col-sm-12 column publication--block"> <div class="grid__component-wrapper " style="background-color:#eeeeee;"> <style> html { scroll-behavior: unset; } </style> <div id="resource-list"> <section class="container py-5 light-bg-tiles"> <div class="search__filter--cont"> <div class="sf__left--block"> <div class="sf__input--block"> <form action="#resource-list" method="GET" id="search"> <div class="search__feature--cont"> <input type="text" class="sf__input--box" maxlength="40" name="query" value="" /> <input type="hidden" class="sf__input--box" placeholder="Search" maxlength="40" value="-1" name="thirdParty" /> <div class="sf__search--icon"> <button type="submit" class="btn"> </button> </div> </div> </form> </div> </div> <div class="full-cta-container"> <a href="?thirdParty=-1#resource-list" class="page-selector-links selected"> <span>All</span> </a> <a href="?thirdParty=0#resource-list" class="page-selector-links "> <span>D-Wave Publication </span> </a> <a href="?thirdParty=1#resource-list" class="page-selector-links "> <span>Third Party Publication </span> </a> </div> </div> <div class="row filtered-resources load-more-container" data-page-number="1" data-total-pages="14"> <div class="col-sm-12 header"> <div class="row"> <h3 style="color: #212529;"><strong>2024</strong></h3> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_11bcb1f4-c197-486c-b54e-16b59867214f"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_11bcb1f4-c197-486c-b54e-16b59867214f .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/t4umjft4/publications-thumb-12.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865765100000" alt="Publications Thumb 12" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Optimization Applications as Quantum Performance Benchmarks</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Optimization Applications as Quantum Performance Benchmarks </div> <div class="resource-modal-body" style="color: #000 !important;"> <p style="font-weight: 400;">Thomas Lubinski, Carleton Coffrin, Catherine McGeoch, Pratik Sathe, Joshua Apanavicius, David Bernal Neira, Quantum Economic Development Consortium(QED-C) Collaboration</p> <p><span>ACM Transactions on Quantum Computing</span>, Volume <span>5</span>, Issue <span>3</span></p> <div class="core-self-citation"> <div data-type="acm-number">Article No.: 18, Pages 1 - 44 <a href="https://doi.org/10.1145/3678184">https://doi.org/10.1145/3678184</a></div> <div data-type="acm-number"></div> <div data-type="acm-number">Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm and Quantum Annealing can potentially demonstrate significant run-time performance benefits over current state-of-the-art solutions. Inspired by existing methods to characterize classical optimization algorithms, we analyze the solution quality obtained by solving Max-cut problems using gate-model quantum devices and a quantum annealing device. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through compelling visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. As an illustration, we explore the factors that influence quantum computing system throughput, using results obtained through execution on various quantum simulators and quantum hardware systems.</div> </div> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_160b5d26-7646-4e9e-bbd2-2e7abcc51799"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_160b5d26-7646-4e9e-bbd2-2e7abcc51799 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/iitf2mpl/publications-thumb-20.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865687900000" alt="Publications Thumb 20" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Experience with Quantum Annealing Computation</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Experience with Quantum Annealing Computation </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Catherine McGeoch, D-Wave; David Esteban Bernal Neira, Purdue University; Susan Mniszewski, Los Alamos National Laboratory; Nicholas Chancellor, Durham University </p> <div class="Ibar__journalName__container"> <div class="Ibar__journalName"><a href="https://www.frontiersin.org/research-topics/53056/experience-with-quantum-annealing-computation/overview">Frontiers in Computer Science</a></div> </div> <p>The past decade has seen four generations of quantum annealing processors, with qubit counts increasing from 512 on the D-Wave Two (released in 2013), to over 5000 on Advantage processors available in 2023. During this time, expanding access for researchers has sparked enormous growth in publications and in the body of knowledge surrounding capabilities, applications, and best practices in use of these novel computing systems. <br /><br />This Research Topic will invite submissions on all aspects of empirical experience with annealing-based quantum computers. The intention is to present a broad survey of the current state of knowledge about quantum annealing hardware, performance, software infrastructures, and application</p> </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">COMPANY </b>: D-Wave </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_eebc8731-1a80-413c-b4a6-1d2023063d03"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_eebc8731-1a80-413c-b4a6-1d2023063d03 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/frgppke5/publications-thumb-33.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865783730000" alt="Publications Thumb 33" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Quantum Annealing-Based Algorithm for Efficient Coalition Formation Among LEO Satellites</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Quantum Annealing-Based Algorithm for Efficient Coalition Formation Among LEO Satellites </div> <div class="resource-modal-body" style="color: #000 !important;"> <div> <p>Supreeth Mysore Venkatesh, Antonio Macaluso, Marlon Nuske, Matthias Klusch, Andreas Dengel </p> <p>Deutsches Forschungszentrum für Künstliche</p> <p><a href="https://arxiv.org/abs/2408.06007" target="_top">https://arxiv.org/abs/2408.06007</a></p> <p>The increasing number of Low Earth Orbit (LEO) satellites, driven by lower manufacturing and launch costs, is proving invaluable for Earth observation missions and low-latency internet connectivity. However, as the number of satellites increases, the number of communication links to maintain also rises, making the management of this vast network increasingly challenging and highlighting the need for clustering satellites into efficient groups as a promising solution. This paper formulates the clustering of LEO satellites as a coalition structure generation (CSG) problem and leverages quantum annealing to solve it. We represent the satellite network as a graph and obtain the optimal partitions using a hybrid quantum-classical algorithm called GCS-Q. The algorithm follows a top-down approach by iteratively splitting the graph at each step using a quadratic unconstrained binary optimization (QUBO) formulation. To evaluate our approach, we utilize real-world three-line element set (TLE/3LE) data for Starlink satellites from Celestrak. Our experiments, conducted using the D-Wave Advantage annealer and the state-of-the-art solver Gurobi, demonstrate that the quantum annealer significantly outperforms classical methods in terms of runtime while maintaining the solution quality. The performance achieved with quantum annealers surpasses the capabilities of classical computers, highlighting the transformative potential of quantum computing in optimizing the management of large-scale satellite networks.</p> </div> </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">COMPANY </b>: Deutsches Forschungszentrum für Künstliche </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">DISCIPLINE </b>: Optimization </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_fd36fcf0-c197-482f-9d68-0e87ef340310"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_fd36fcf0-c197-482f-9d68-0e87ef340310 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/fb0b2dqu/publications-thumb-16.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865662670000" alt="Publications Thumb 16" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Real World Application of Quantum-Classical Optimization for Production Scheduling</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Real World Application of Quantum-Classical Optimization for Production Scheduling </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Abhishek Awasthi∗, Nico Kraus†, Florian Krellner‡, David Zambrano† ∗BASF Digital Solutions GmbH, Ludwigshafen am Rhein, Germany †<span>Aqarios GmbH, Munich, Germany<br /></span>‡SAP SE, Walldorf, Germany</p> <p>This work is a benchmark study for quantum- classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We first present the motivation and the problem description, along with different modeling techniques for classical and quantum computing. The modeling for classical solvers has been done as a mixed-integer convex program, while for the quantum-classical solver we model the problem as a binary quadratic program, which is best suited to the D-Wave Leap’s Hybrid Solver. This ensures that all the solvers we use are fetched with dedicated and most suitable model(s). Henceforth, we carry out benchmarking and comparisons between classical and quantum-classical methods, on problem sizes ranging till approximately 150, 000 variables. We utilize an industry grade classical solver and compare its results with D-Wave Leap’s Hybrid Solver. The results we obtain from D-Wave are highly competitive and sometimes offer speedups, compared to the classical solver.</p> </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">COMPANY </b>: BASF Digital Solutions GmbH, SAP SE, Aqarios GmbH </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">INDUSTRY </b>: Manufacturing </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">DISCIPLINE </b>: Optimization </div> <div class="cta__links--cont"> <ul> <li> <a href="https://arxiv.org/pdf/2408.01641" target="_blank" rel="noopener noreferrer" class="cta__link--code">Paper <i class="far fa-sticky-note"></i></a> </li> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_28c3eeef-3557-42a4-83b0-56130135b807"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_28c3eeef-3557-42a4-83b0-56130135b807 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/dl2cs2kn/publications-thumb-7.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865741200000" alt="Publications Thumb 7" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Solving the resource constrained project scheduling problem with quantum annealing</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Solving the resource constrained project scheduling problem with quantum annealing </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Pérez Armas, L.F., Creemers, S. & Deleplanque, S. Solving the resource constrained project scheduling problem with quantum annealing. <a href="https://doi.org/10.1038/s41598-024-67168-6"><em>Scientific Reports</em><strong>14</strong>, 16784</a> (2024). </p> <p>Quantum annealing emerges as a promising approach for tackling complex scheduling problems such as the resource-constrained project scheduling problem (RCPSP). This study represents the first application of quantum annealing to solve the RCPSP, analyzing 12 well-known mixed integer linear programming (MILP) formulations and converting the most qubit-efficient one into a quadratic unconstrained binary optimization (QUBO) model. We then solve this model using the D-wave advantage 6.3 quantum annealer, comparing its performance against classical computer solvers. Our results indicate significant potential, particularly for small to medium-sized instances. Further, we introduce time-to-target and Atos Q-score metrics to evaluate the effectiveness of quantum annealing and reverse quantum annealing. The paper also explores advanced quantum optimization techniques, such as customized anneal schedules, enhancing our understanding and application of quantum computing in operations researc</p> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_4aa5b6de-fd3a-4b07-9e75-6d3697f6bc9b"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_4aa5b6de-fd3a-4b07-9e75-6d3697f6bc9b .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/frwhhtiy/publications-thumb-10.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865804570000" alt="Publications Thumb 10" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Quantum Annealing-Infused Microgrids Formation: Distribution System Restoration and Resilience Enhancement</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Quantum Annealing-Infused Microgrids Formation: Distribution System Restoration and Resilience Enhancement </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>N. Nikmehr, P. Zhang, H. Zheng, T. -C. Wei, G. He and Y. A. Shamash, "Quantum Annealing-Infused Microgrids Formation: Distribution System Restoration and Resilience Enhancement," in <em>IEEE Transactions on Power Systems, <strong>DOI: </strong><a rel="noopener" href="https://doi.org/10.1109/TPWRS.2024.3399122" target="_blank">10.1109/TPWRS.2024.3399122</a></em></p> <p>In this paper, the use of quantum computing is explored to solve a crucial optimization problem in the formation of microgrids (MGs), which can enhance the resilience of distribution networks against natural disasters or faults. The study focuses on developing a quantum-inspired optimization model for critical load restoration via MGs formation, leveraging the power of quantum annealing to solve complex combinatorial problems that classical methods struggle with. The Constrained Quadratic Model (CQM) solver from D-Wave is used to merge classical and quantum optimization approaches, delivering improved solutions to complex optimization problems. The solver has been optimized to take advantage of quantum computing's parallelism to provide high-performance solutions. The study compares outcomes from the D-Wave hybrid quantum-classical solver and the classical Gurobi solver, underscoring the effectiveness of quantum computing in addressing resilience-oriented optimization challenges. This assessment is validated through two case studies: the IEEE 37-bus system and the IEEE 240-bus distribution system.</p> <p> </p> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_e808ab0a-7b44-4aad-af26-ea3a8b6fc663"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_e808ab0a-7b44-4aad-af26-ea3a8b6fc663 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/0hlouyun/publications-thumb-4.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865729030000" alt="Publications Thumb 4" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Short-depth QAOA circuits and quantum annealing on higher-order ising models</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Short-depth QAOA circuits and quantum annealing on higher-order ising models </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Pelofske, E., Bärtschi, A. & Eidenbenz, S. Short-depth QAOA circuits and quantum annealing on higher-order ising models. <a href="https://doi.org/10.1038/s41534-024-00825-w"><em>npj Quantum Information</em> <strong>10</strong>, 30</a> (2024). </p> <p>We present a direct comparison between QAOA (Quantum Alternating Operator Ansatz), and QA (Quantum Annealing) on 127 qubit problem instances. QAOA with <em>p</em> = 1, 2 rounds is executed on the 127 qubit heavy-hex graph gate-model quantum computer ibm_washington, using on-device grid-searches for angle finding, and QA is executed on two Pegasus-chip D-Wave quantum annealers. The problems are random Ising models whose connectivity matches heavy-hex graphs and the Pegasus graph connectivity, and optionally include hardware-compatible cubic terms (<em>Z</em><em>Z</em><em>Z</em> terms). The QAOA circuits are heavily optimized and of extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of the heavy-hex lattice. QAOA and QA are both compared against simulated annealing and the optimal solutions are computed exactly using CPLEX. The noiseless mean QAOA expectation values for <em>p</em> = 1, 2 are computed using classical light-cone based simulations. We find QA outperforms QAOA on the evaluated devices.</p> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_5b41aede-2989-4de9-9c78-9ac1ada57979"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_5b41aede-2989-4de9-9c78-9ac1ada57979 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/iitf2mpl/publications-thumb-20.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865687900000" alt="Publications Thumb 20" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Computational supremacy in quantum simulation</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Computational supremacy in quantum simulation </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Andrew D. King, et al.</p> <p>Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. Establishing this capability, especially for impactful and meaningful problems, remains a central challenge. One such problem is the simulation of nonequilibrium dynamics of a magnetic spin system quenched through a quantum phase transition. State-of-the-art classical simulations demand resources that grow exponentially with system size. Here we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench in two-, three- and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for classical approaches. We assess approximate methods based on tensor networks and neural networks and conclude that no known approach can achieve the same accuracy as the quantum annealer within a reasonable timeframe. Thus quantum annealers can answer questions of practical importance that classical computers cannot.</p> </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">COMPANY </b>: D-Wave </div> <div class="cta__links--cont"> <ul> <li> <a href="https://arxiv.org/abs/2403.00910" target="_blank" rel="noopener noreferrer" class="cta__link--code">Paper <i class="far fa-sticky-note"></i></a> </li> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_52b3a430-6f01-4fa6-9efa-155d00473c5a"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_52b3a430-6f01-4fa6-9efa-155d00473c5a .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/dl2cs2kn/publications-thumb-7.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865741200000" alt="Publications Thumb 7" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Using quantum annealing to design lattice proteins</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Using quantum annealing to design lattice proteins </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Anders Irbäck, Lucas Knuthson, Sandipan Mohanty, and Carsten Peterson, Using quantum annealing to design lattice proteins, <a href="https://link.aps.org/doi/10.1103/PhysRevResearch.6.013162">Phys. Rev. Research <strong>6</strong>, 013162</a> </p> <p>Quantum annealing has shown promise for finding solutions to difficult optimization problems, including protein folding. Recently, we used the D-Wave Advantage quantum annealer to explore the folding problem in a coarse-grained lattice model, the HP model, in which amino acids are classified into two broad groups: hydrophobic (H) and polar (P). Using a set of 22 HP sequences with up to 64 amino acids, we demonstrated the fast and consistent identification of the correct HP model ground states using the D-Wave hybrid quantum-classical solver. An equally relevant biophysical challenge, called the protein design problem, is the inverse of the above, where the task is to predict protein sequences that fold to a given structure. Here, we approach the design problem by a two-step procedure implemented and executed on a D-Wave machine. In the first step, we perform a pure sequence-space search by varying the type of amino acid at each sequence position, and seek sequences which minimize the HP-model energy of the target structure. After mapping this task onto an Ising spin-glass representation, we employ a hybrid quantum-classical solver to deliver energy-optimal sequences for structures with 30–64 amino acids, with a 100% success rate. In the second step, we filter the optimized sequences from the first step according to their ability to fold to the intended structure. In addition, we try solving the sequence optimization problem using only the quantum processing unit (QPU), which confines us to sizes ≤20, due to exponentially decreasing success rates. To shed light on the pure QPU results, we investigate the effects of control errors caused by an imperfect implementation of the intended Hamiltonian on the QPU, by numerically analyzing the Schrödinger equation. We find that the simulated success rates in the presence of control noise semiquantitatively reproduce the modest pure QPU results for larger chains.</p> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_6cebe625-6906-47b1-8ea5-c7e9a02ac466"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_6cebe625-6906-47b1-8ea5-c7e9a02ac466 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/zn0nqx15/publications-thumb-31.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865724170000" alt="Publications Thumb 31" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Quantum fluctuations drive nonmonotonic correlations in a qubit lattice</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Quantum fluctuations drive nonmonotonic correlations in a qubit lattice </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Alejandro Lopez-Bezanilla, Andrew D. King, Cristiano Nisoli, and Avadh Saxena </p> <p class="c-article-info-details" data-container-section="info"><em data-test="journal-title">Nature Communications</em> volume 15, Article number: 589 (2024) </p> <p class="c-article-info-details" data-container-section="info">Fluctuations may induce the degradation of order by overcoming ordering interactions, consequently leading to an increase of entropy. This is particularly evident in magnetic systems characterized by nontrivial, constrained disorder, where thermal or quantum fluctuations can yield counterintuitive forms of ordering. Using the proven efficiency of quantum annealers as programmable spin system simulators, we present a study based on entropy postulates and experiments on a platform of programmable superconducting qubits to show that a low level of uncertainty can promote ordering in a system impacted by both thermal and quantum fluctuations. A set of experiments is proposed on a lattice of interacting qubits arranged in a triangular geometry with precisely controlled disorder, effective temperature, and quantum fluctuations. Our results demonstrate the creation of ordered ferrimagnetic and layered anisotropic disordered phases, displaying characteristics akin to the elegant order-by-disorder phenomenon. Extensive experimental evidence is provided for the role of quantum fluctuations in lowering the total energy of the system by increasing entropy and defect clustering. Our thorough and comprehensive application of an intentionally introduced noise on a quantum platform provides insight into the dynamics of defects and fluctuations in quantum devices, which may help to reduce the cost associated with quantum processing.</p> </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">COMPANY </b>: D-Wave </div> <div class="cta__links--cont"> <ul> <li> <a href="https://www.nature.com/articles/s41467-023-44281-0#citeas" target="_blank" rel="noopener noreferrer" class="cta__link--code">Paper <i class="far fa-sticky-note"></i></a> </li> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_5646a766-4e77-4386-ab47-b276d216d5ea"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_5646a766-4e77-4386-ab47-b276d216d5ea .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/5fzodsgg/publications-thumb-3.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865802870000" alt="Publications Thumb 3" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Scaling Advantage in Approximate Optimization with Quantum Annealing</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Scaling Advantage in Approximate Optimization with Quantum Annealing </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Humberto Munoz Bauza, Daniel A. Lidar, Scaling Advantage in Approximate Optimization with Quantum Annealing, <a href="https://arxiv.org/abs/2401.07184">arXiv:2401.07184</a> </p> <p>Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected discrete optimization and quantum simulation problems. Nevertheless, despite numerous attempts, a computational quantum advantage in exact optimization using quantum annealing hardware has so far remained elusive. Here, we present evidence for a quantum annealing scaling advantage in approximate optimization. The advantage is relative to the top classical heuristic algorithm: parallel tempering with isoenergetic cluster moves (PT-ICM). The setting is a family of 2D spin-glass problems with high-precision spin-spin interactions. To achieve this advantage, we implement quantum annealing correction (QAC): an embedding of a bit-flip error-correcting code with energy penalties that leverages the properties of the D-Wave Advantage quantum annealer to yield over 1,300 error-suppressed logical qubits on a degree-5 interaction graph. We generate random spin-glass instances on this graph and benchmark their time-to-epsilon, a generalization of the time-to-solution metric for low-energy states. We demonstrate that with QAC, quantum annealing exhibits a scaling advantage over PT-ICM at sampling low energy states with an optimality gap of at least 1.0%. This amounts to the first demonstration of an algorithmic quantum speedup in approximate optimization.</p> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 header"> <div class="row"> <h3 style="color: #212529;"><strong>2023</strong></h3> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_5b9a2498-1b48-44f1-874f-9ccbb526bd7e"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_5b9a2498-1b48-44f1-874f-9ccbb526bd7e .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/frwhhtiy/publications-thumb-10.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865804570000" alt="Publications Thumb 10" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Kagome qubit ice</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Kagome qubit ice </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Lopez-Bezanilla, A., Raymond, J., Boothby, K. <em>et al.</em> Kagome qubit ice. <em>Nat Commun</em> <strong>14</strong>, 1105 (2023). <a href="https://doi.org/10.1038/s41467-023-36760-1">https://doi.org/10.1038/s41467-023-36760-1</a></p> <p>Topological phases of spin liquids with constrained disorder can host a kinetics of fractionalized excitations. However, spin-liquid phases with distinct kinetic regimes have proven difficult to observe experimentally. Here we present a realization of kagome spin ice in the superconducting qubits of a quantum annealer, and use it to demonstrate a field-induced kinetic crossover between spin-liquid phases. Employing fine control over local magnetic fields, we show evidence of both the Ice-I phase and an unconventional field-induced Ice-II phase. In the latter, a charge-ordered yet spin-disordered topological phase, the kinetics proceeds via pair creation and annihilation of strongly correlated, charge conserving, fractionalized excitations. As these kinetic regimes have resisted characterization in other artificial spin ice realizations, our results demonstrate the utility of quantum-driven kinetics in advancing the study of topological phases of spin liquids.</p> </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">COMPANY </b>: D-Wave </div> <div class="cta__links--cont"> <ul> <li> <a href="https://doi.org/10.1038/s41467-023-36760-1" target="_blank" rel="noopener noreferrer" class="cta__link--code">Paper <i class="far fa-sticky-note"></i></a> </li> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_6a49729c-4ac9-480a-ac51-748cac071601"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_6a49729c-4ac9-480a-ac51-748cac071601 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/iitf2mpl/publications-thumb-20.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865687900000" alt="Publications Thumb 20" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Quantum error mitigation in quantum annealing</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Quantum error mitigation in quantum annealing </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Mohammad H. Amin, et al.</p> <p>Quantum Error Mitigation (QEM) presents a promising near-term approach to reduce error when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using Zero-Noise Extrapolation (ZNE). We implement ZNE through zero-temperature extrapolation as well as energy-time rescaling. We conduct experimental investigations into the quantum critical dynamics of a transverse-field Ising spin chain, demonstrating the successful mitigation of thermal noise through both of these techniques. Moreover, we show that energy-time rescaling effectively mitigates control errors in the coherent regime where the effect of thermal noise is minimal. Our ZNE results agree with exact calculations of the coherent evolution over a range of annealing times that exceeds the coherent annealing range by almost an order of magnitude.</p> </div> <div style="color: #000;" class="mt-2"> <b style="font-size: 15px;color:#af4904;">COMPANY </b>: D-Wave </div> <div class="cta__links--cont"> <ul> <li> <a href="https://arxiv.org/abs/2311.01306" target="_blank" rel="noopener noreferrer" class="cta__link--code">Paper <i class="far fa-sticky-note"></i></a> </li> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_06bdbd04-99c5-4352-a393-6afd2cb94944"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_06bdbd04-99c5-4352-a393-6afd2cb94944 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/aznfzh40/publications-thumb-14.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865771030000" alt="Publications Thumb 14" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Inter-generational comparison of quantum annealers in solving hard scheduling problems</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Inter-generational comparison of quantum annealers in solving hard scheduling problems </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>Pokharel, B., Izquierdo, Z.G., Lott, P.A. <em>et al.</em> Inter-generational comparison of quantum annealers in solving hard scheduling problems. <a href="https://doi.org/10.1007/s11128-023-04077-z"><em>Quantum Inf Process</em> <strong>22</strong>, 364</a> (2023). </p> <p>We compare the performance of four quantum annealers, the D-Wave <em>Two</em>, <em>2X</em>, <em>2000Q</em>, and <em>Advantage</em> in solving an identical ensemble of a parametrized family of scheduling problems. These problems are NP-complete and, in fact, equivalent to vertex coloring problems. They are also practically motivated and closely connected to planning problems from artificial intelligence. We examine factors contributing to the performance differences while separating the contributions from hardware upgrades, support for shorter anneal times, and possible optimization of ferromagnetic couplings. While shorter anneal times can improve the time to solution (TTS) at any given problem size, the scaling of TTS with respect to the problem size worsens for shorter anneal times. In contrast, optimizing the ferromagnetic coupling improves both the absolute TTS and the scaling. There is a statistically significant improvement in performance between D-Wave Two and 2X and from all older generation annealers to Advantage, even when operated under identical anneal time and ferromagnetic couplings. However, the performance improvement from 2X to 2000Q requires the anneal time and ferromagnetic couplings to be optimized. Overall, owing to these inter-generational hardware improvements and optimizations, the scaling exponent reduces from 1.01 ± 0.01 on Two to 0.259 ± 0.008 on Advantage.</p> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="col-sm-12 col-md-6 col-lg-4 col-xl-3 js-resource-item"> <div class="publication-cards light-theme"> <div class="corsslink__card--block" id="el_a90fd6fc-4d18-4843-b59f-f9a730dd3410"> <div class="cursor-pointer" data-toggle="modal" data-target="#content-modal" data-modal-title="" data-modal-content-selector="#el_a90fd6fc-4d18-4843-b59f-f9a730dd3410 .c-image-tile-with-modal__modal-content"> <div class="corsslink__card--image"> <img class="img-fluid w-100" src="/media/jgyjsrxg/publications-thumb-32.jpg?anchor=center&mode=crop&width=720&height=404&rnd=132718865707100000" alt="Publications Thumb 32" /> </div> <div class="eyebrow__label_dots corsslink__card--eyebrow"> Publication </div> <div class="corsslink__card--title h_text__small"> <h4>Effectiveness of quantum annealing for continuous-variable optimization</h4> </div> </div> <div class="c-image-tile-with-modal__modal-content resource-modal" style="color: #000;"> <div class="resource-modal"> <div class="eyebrow__label"> Publication </div> <div class="h_text__small" style="color: #000;"> Effectiveness of quantum annealing for continuous-variable optimization </div> <div class="resource-modal-body" style="color: #000 !important;"> <p>S. Arai et al., Effectiveness of quantum annealing for continuous-variable optimization, <a href="https://doi.org/10.1103/PhysRevA.108.042403"><em>Physical Review A</em>, 108, 042403</a> (2023)</p> <p>The application of quantum annealing to the optimization of continuous-variable functions is a relatively unexplored area of research. We test the performance of quantum annealing applied to a one-dimensional continuous-variable function with a rugged energy landscape. After domain-wall encoding to map a continuous variable to discrete Ising variables, we first benchmark the performance of the real hardware, the D-Wave 2000Q, against several state-of-the-art classical optimization algorithms designed for continuous-variable problems to find that the D-Wave 2000Q matches the classical algorithms in a limited domain of computation time. Beyond this domain, classical global optimization algorithms outperform the quantum device. Next we examine several optimization algorithms that are applicable to the Ising formulation of the problem, such as the time-evolving block decimation (TEBD) to simulate ideal coherent quantum annealing, simulated annealing, simulated quantum annealing, and spin-vector Monte Carlo. The data show that TEBD's coherent quantum annealing achieves far better results than the other approaches, demonstrating the effectiveness of coherent tunneling. From these two types of benchmarks, we conclude that the hardware realization of quantum annealing has the potential to significantly outperform the best classical algorithms if thermal noise and other imperfections are sufficiently suppressed and the device operates coherently, as demonstrated in recent short-time quantum simulations</p> </div> <div class="cta__links--cont"> <ul> </ul> </div> </div> </div> </div> </div> </div> <div class="full-cta-container"> <a href="?items=all&thirdParty=-1#resource-list" class="Medium-CTA view-more-center"> <span>View All </span> <span> <i class="fas fa-chevron-right"></i> </span> </a> </div> </div> </section> </div> </div> </div> </div> </div></div></div></section> </div> </div> </main>  <style> footer.dwave__footer { background-position: center bottom; background-image: url('/media/cdyngmyb/lines-footer-desktop-2-c.png'); background-repeat: no-repeat; background-color: rgba(0,0,0,0.7); } @media (min-width: 1920px) { footer.dwave__footer { background-position: center bottom; background-image: url('/media/cdyngmyb/lines-footer-desktop-2-c.png'); background-repeat: no-repeat; } } @media (max-width: 768px) { footer.dwave__footer { background-position: center bottom; background-image: url('/media/w0ugfzye/lines-footer-tablet-c.png'); background-repeat: no-repeat; } } @media (max-width: 480px) { footer.dwave__footer { background-position: center bottom; background-image: url('/media/ghpluken/lines-footer-mobile-c.png'); background-repeat: no-repeat; } } </style> <footer class="c-footer dark-footer dwave__footer" role="contentinfo"> <div class="container desktop-footer"> <div class="row"> <div class="col-lg-12 footer-separator"> <div class="row footer__header--row"> <div class="col-12 soc-container"> <a href="https://www.aicpa.org/soc4so" target="_blank"><img src="/images/A-LIGN-SOC-Badge.png" class="soc-2" /></a> </div> </div> <div class="row footer__header--row"> <div class="col-12 col-md-6 col-lg-8 footer-logo--cont"> <div class="row"> <div class="col-md-12 col-lg-4"> <img src="/media/j31olsrx/d-wave.svg" width="170" alt="Footer Logo" class="footer-logo" /> </div> <div class="col-md-12 col-lg-8 c-footer__newsletter-wrapper"> <div class="c-footer__newsletter"> <a href="/website-marketing-opt-in/"> Join Our Email Marketing List <span><i class="fas fa-chevron-right"></i></span> </a> </div> </div> </div> </div> <div class="col-12 col-md-6 col-lg-4"> <div class="c-footer__social-links"> <div class="cp-social-page-links"> <div class="cp-social-page-links__links"> <span class="follow-us-label">Follow Us</span> <a class="facebook" data-network="Facebook" target="_blank" rel="noopener noreferrer" href="https://www.facebook.com/dwavequantum"><i class="fab fa-facebook-f"></i><span class="sr-only">Facebook</span></a> <a class="linkedin" data-network="LinkedIn" target="_blank" rel="noopener noreferrer" href="https://www.linkedin.com/company/d-wave-systems-inc."><i class="fab fa-linkedin-in"></i><span class="sr-only">LinkedIn</span></a> <a class="youtube" data-network="YouTube" target="_blank" rel="noopener noreferrer" href="https://youtube.com/user/dwavesystems"><i class="fab fa-youtube"></i><span class="sr-only">YouTube</span></a> <a class="twitter" data-network="Twitter" target="_blank" rel="noopener noreferrer" href="https://twitter.com/dwavequantum"><i class="fab fa-twitter"></i><span class="sr-only">Twitter</span></a> </div> </div> </div> </div> </div> </div>  <div class="col-lg-12 footer-separator footer-main-menu"> <div class="footer_main_block"> <div class="footer__inner--block"> <div class="row footer__lbc--cont"> <div class="col-sm-4 col-12"> <h3> Products </h3> <ul class="footer-main-link-ul"> <li class="mobile-50-percent"> <a href="/solutions-and-products/product-overview/" alt="Product Overview">Product Overview</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/cloud-platform/" alt="Cloud Platform">Cloud Platform</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/systems/" alt="Systems">Systems</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/professional-services/" alt="Professional Services">Professional Services</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/ocean/" alt="Software & Tools">Software & Tools</a> </li> <li class="mobile-50-percent"> <a href="/learn/training/" alt="Learning Solutions">Learning Solutions</a> </li> </ul> </div> <div class="col-sm-4 col-12"> <h3> Solutions </h3> <ul class="footer-main-link-ul"> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/quantum-optimization-landing-page/" alt="Quantum Optimization Summary">Quantum Optimization Summary</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/workforce-scheduling/" alt="Workforce Scheduling">Workforce Scheduling</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/production-scheduling/" alt="Production Scheduling">Production Scheduling</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/logistics-routing/" alt="Vehicle Routing">Vehicle Routing</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/resource-optimization/" alt="Resource Optimization">Resource Optimization</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/cargo-loading/" alt="Cargo Loading">Cargo Loading</a> </li> </ul> </div> <div class="col-sm-4 col-12"> <h3> Sectors </h3> <ul class="footer-main-link-ul"> <li class="mobile-50-percent"> <a href="/solutions-and-products/manufacturing-logistics/" alt="Manufacturing & Logistics">Manufacturing & Logistics</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/public-sector/" alt="Public Sector">Public Sector</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/quantum-research-landing-page/" alt="Quantum Research">Quantum Research</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/quantum-optimization/quantum-ai-landing-page/" alt="Quantum AI">Quantum AI</a> </li> </ul> </div> <div class="col-sm-4 col-12"> <h3> Learn </h3> <ul class="footer-main-link-ul"> <li class="mobile-50-percent"> <a href="/learn/quantum-computing/" alt="Quantum Computing">Quantum Computing</a> </li> <li class="mobile-50-percent"> <a href="/learn/d-wave-s-approach/" alt="D-Wave's Approach">D-Wave's Approach</a> </li> <li class="mobile-50-percent"> <a href="/learn/customer-success-stories/" alt="Customer Success Stories">Customer Success Stories</a> </li> <li class="mobile-50-percent"> <a href="/learn/featured-applications/" alt="Featured Applications">Featured Applications</a> </li> <li class="mobile-50-percent"> <a href="/learn/resource-library/" alt="Resource Library">Resource Library</a> </li> <li class="mobile-50-percent"> <a href="/learn/publications/" alt="Publications">Publications</a> </li> <li class="mobile-50-percent"> <a href="/learn/events-and-webinars/" alt="Events & Webinars">Events & Webinars</a> </li> <li class="mobile-50-percent"> <a href="/learn/training/" alt="Training">Training</a> </li> </ul> </div> <div class="col-sm-4 col-12"> <h3> Build </h3> <ul class="footer-main-link-ul"> <li class="mobile-50-percent"> <a href="/build/getting-started/" alt="Getting Started">Getting Started</a> </li> <li class="mobile-50-percent"> <a href="/solutions-and-products/developer/" alt="Developer">Developer</a> </li> <li class="mobile-50-percent"> <a href="https://docs.dwavesys.com/docs/latest/index.html" alt="Documentation" target="_blank">Documentation</a> </li> <li class="mobile-50-percent"> <a href="https://support.dwavesys.com/hc/en-us/community/topics" alt="Community Forums" target="_blank">Community Forums</a> </li> <li class="mobile-50-percent"> <a href="https://github.com/dwave-examples" alt="Code Samples" target="_blank">Code Samples</a> </li> </ul> </div> <div class="col-sm-4 col-12"> <h3> Company </h3> <ul class="footer-main-link-ul"> <li class="mobile-50-percent"> <a href="/company/about-d-wave/" alt="About D-Wave">About D-Wave</a> </li> <li class="mobile-50-percent"> <a href="/company/leadership/" alt="Leadership">Leadership</a> </li> <li class="mobile-50-percent"> <a href="/company/careers/" alt="Careers">Careers</a> </li> <li class="mobile-50-percent"> <a href="/learn/events-and-webinars/" alt="Events & Webinars">Events & Webinars</a> </li> <li class="mobile-50-percent"> <a href="/company/newsroom/" alt="Newsroom">Newsroom</a> </li> <li class="mobile-50-percent"> <a href="/company/media-resources/" alt="Media Resources">Media Resources</a> </li> <li class="mobile-50-percent"> <a href="https://ir.dwavesys.com/overview/default.aspx" alt="Investor Relations">Investor Relations</a> </li> <li class="mobile-50-percent"> <a href="/company/contact/" alt="Contact">Contact</a> </li> </ul> </div> </div> </div> </div> </div>  <div class="col-lg-12 footer-separator footer__extlinks--cont"> <div class="footer_main_block"> <div class="footer__inner--block"> <div class="row footer__more--row"> <div class="col-sm-12 col-md-4"> <h3 class="footer__more_text">More D-Wave</h3> </div> <div class="col-sm-12 col-md-4"> <a href="https://dwavejapan.com/" target="_blank">D-Wave Japan <i class="fas fa-arrow-up new-window-arrow"></i></a> </div> </div> </div> </div> </div> <div class="col-lg-12 footer-separator footer__copyright--cont"> <div class="footer_main_block"> <div class="footer__inner--block"> <div class="row"> <div class="col-sm-5 col-md-4 col-xs-12"> <div class="c-footer__legal-text"><p>Copyright 2023 D-Wave Quantum Inc.</p></div> </div> <div class="col-sm-7 col-md-6 col-xs-12"> <ul class="c-footer--secondary-links list-unstyled"> <li><a href="/privacy-policy/">Privacy Policy</a></li> <li><a href="/terms-and-conditions/">Terms and Conditions</a></li> <li><a href="/patent-notice/">Patent Notice</a></li> </ul> </div> </div> </div> </div> </div> </div> </div> </footer> <script src="/js/frameworks-libraries/jquery-3.6.0.min.js"></script> <script src="/js/frameworks-libraries/popper-1.14.7.min.js"></script> <script src="/js/frameworks-libraries/bootstrap-4.1.3/bootstrap.min.js"></script> <script src="/js/common/loadMore.js"></script> <script src="/js/common/cookieHelper.js"></script> <script src="/js/components/placeholder.js"></script> <script src="/js/components/videomodal.js"></script> <script src="/js/components/contentmodal.js"></script> <script src="/js/components/alertMessageBlade.js"></script> <script src="/js/components/statItem.js"></script> <script src="/js/components/global.js"></script> <script src="/js/components/formCountryLogic.js"></script> <script src="/js/frameworks-libraries/css3-animate-it.js"></script> <script src="/js/frameworks-libraries/slick.min.js"></script> <script src="/js/components/carousel.js"></script> <script src="/js/components/global.js"></script> <script src="/js/components/formCountryLogic.js"></script> <script src="/js/frameworks-libraries/slick.min.js"></script> <script src="/js/components/carousel.js"></script>  <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "item": { "@id": "https://www.dwavesys.com/", "name": "Home Page" } } , { "@type": "ListItem", "position": 2, "item": { "@id": "https://www.dwavesys.com/learn/", "name": "Learn" } } , { "@type": "ListItem", "position": 3, "item": { "@id": "https://www.dwavesys.com/learn/publications/", "name": "Publications" } } ] } </script> <script src="/scripts/formValidations.js"></script>  <div class="modal fade c-video-modal" id="video-modal" tabindex="-1" role="dialog" aria-labelledby="video-modal"> <div class="modal-dialog" role="document"> <div class="modal-content"> <span class="closer" data-dismiss="modal"></span> <div class="modal-body clearfix"> <div> </div> </div> </div> </div> </div>  <div class="modal fade c-content-modal" id="content-modal" tabindex="-1" role="dialog" aria-labelledby="content-modal"> <div class="modal-dialog modal-lg " role="document"> <div class="modal-content"> <div class="modal-header"> <h5 class="modal-title"></h5> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> </div> </div> </div> </div> </body> </html>

CINXE.COM

Scientific Publications | D-Wave