On the construction of useful quantum kernels

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">     <html xmlns="http://www.w3.org/1999/xhtml" lang="de" xml:lang="de" xmlns:og="http://ogp.me/ns#" xmlns:fb="http://ogp.me/ns/fb#"> <head> <title>On the construction of useful quantum kernels - CERN Document Server</title> <link href='https://framework.web.cern.ch/framework/2.0/fonts/PTSansWeb/PTSansWeb.css' rel='stylesheet' type='text/css' /> <link rel="stylesheet" href="https://cds.cern.ch/img/invenio.css?v=20141127" type="text/css" /> <link rel="stylesheet" href="https://cds.cern.ch/img/cern_theme/css/cern_theme.css?v=20141127" type="text/css" /> <link rel="stylesheet"href="/css/font-awesome.min.css"> <meta http-equiv="X-UA-Compatible" content="IE=Edge"/> <link rel="stylesheet" href="https://cds.cern.ch/img/cern_toolbar/css/toolbar.css" type="text/css" />    <link rel="canonical" href="https://cds.cern.ch/record/2854770" /> <link rel="alternate" hreflang="el" href="https://cds.cern.ch/record/2854770?ln=el" /> <link rel="alternate" hreflang="fr" href="https://cds.cern.ch/record/2854770?ln=fr" /> <link rel="alternate" hreflang="bg" href="https://cds.cern.ch/record/2854770?ln=bg" /> <link rel="alternate" hreflang="zh-TW" href="https://cds.cern.ch/record/2854770?ln=zh_TW" /> <link rel="alternate" hreflang="pt" href="https://cds.cern.ch/record/2854770?ln=pt" /> <link rel="alternate" hreflang="no" href="https://cds.cern.ch/record/2854770?ln=no" /> <link rel="alternate" hreflang="hr" href="https://cds.cern.ch/record/2854770?ln=hr" /> <link rel="alternate" hreflang="ca" href="https://cds.cern.ch/record/2854770?ln=ca" /> <link rel="alternate" hreflang="de" href="https://cds.cern.ch/record/2854770?ln=de" /> <link rel="alternate" hreflang="it" href="https://cds.cern.ch/record/2854770?ln=it" /> <link rel="alternate" hreflang="zh-CN" href="https://cds.cern.ch/record/2854770?ln=zh_CN" /> <link rel="alternate" hreflang="sv" href="https://cds.cern.ch/record/2854770?ln=sv" /> <link rel="alternate" hreflang="sk" href="https://cds.cern.ch/record/2854770?ln=sk" /> <link rel="alternate" hreflang="en" href="https://cds.cern.ch/record/2854770?ln=en" /> <link rel="alternate" hreflang="pl" href="https://cds.cern.ch/record/2854770?ln=pl" /> <link rel="alternate" hreflang="ru" href="https://cds.cern.ch/record/2854770?ln=ru" /> <link rel="alternate" hreflang="ka" href="https://cds.cern.ch/record/2854770?ln=ka" /> <link rel="alternate" hreflang="ja" href="https://cds.cern.ch/record/2854770?ln=ja" /> <link rel="alternate" hreflang="es" href="https://cds.cern.ch/record/2854770?ln=es" /> <link rel="alternate" type="application/rss+xml" title="CERN Document Server RSS" href="/rss?ln=de" /> <link rel="search" type="application/opensearchdescription+xml" href="https://cds.cern.ch/opensearchdescription" title="CERN Document Server" /> <link rel="unapi-server" type="application/xml" title="unAPI" href="https://cds.cern.ch/unapi" /> <link rel="apple-touch-icon" href="/apple-touch-icon.png"/> <link rel="apple-touch-icon-precomposed" href="/apple-touch-icon-precomposed.png"/> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta http-equiv="Content-Language" content="de" /> <meta name="description" content="<p>The representation of data is of paramount importance for machine learning methods. Kernel methods are used to enrich the feature representation, allowing better generalization. Quantum kernels implement efficiently complex transformation encoding classical data in the Hilbert space of a quantum system, resulting in even exponential speedup. However, we need prior knowledge of the data to choose an appropriate parametric quantum circuit that can be used as quantum embedding.</p><p>We propose an algorithm that automatically selects the best quantum embedding through a combinatorial optimization procedure that modifies the structure of the circuit, changing the generators of the gates, their angles (which depend on the data points), and the qubits on which the various gates act. Since combinatorial optimization is computationally expensive, we have introduced a criterion based on the exponential concentration of kernel matrix coefficients around the mean to immediately discard an arbitrarily large portion of solutions that are believed to perform poorly.</p><p>Contrary to the gradient-based optimization (e.g. trainable quantum kernels), our approach is not affected by the barren plateau by construction. We have used both artificial and real-world datasets to demonstrate the increased performance of our approach with respect to randomly generated PQC. We have also compared the effect of different optimization algorithms, including greedy local search, simulated annealing, and genetic algorithms, showing that the algorithm choice largely affects the result.</p><p><strong>About the speaker</strong>&nbsp;<br><span style="color:hsl(210,75%,60%);"><strong>Massimiliano Incudin</strong></span>i is PhD student at the Dep. of Computer Science, University of Verona. In his studies, he is focused on the development of quantum kernels for real-world applications.</p><p><strong>Collaborators</strong>&nbsp;<br>The presentation is based on the joint work with Alessandra Di Pierro and Francesco Martini available at&nbsp;<a href="https://arxiv.org/abs/2209.11144">arxiv.org/abs/2209.11144</a>.</p> Incudini, Massimiliano" /> <meta name="keywords" content="CERN Document Server, WebSearch, CERN Document Server" /> <script type="text/javascript" src="https://cds.cern.ch/js/jquery.min.js"></script>  <link rel="stylesheet" href="https://cds.cern.ch/img/webnews.css" type="text/css" />  <script type="text/javascript" src="https://cds.cern.ch/js/webnews.js?v=20131009"></script> <meta property="fb:app_id" content="137353533001720"/> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$']], processEscapes: true}, showProcessingMessages: false, messageStyle: "none" }); </script> <script src="/MathJax/MathJax.js?config=TeX-AMS_CHTML" type="text/javascript"> </script>  <meta content="On the construction of useful quantum kernels" name="citation_title" /> <meta content="2023/03/29" name="citation_publication_date" /> <meta name="citation_online_date" content="2023/03/30">  <meta content="On the construction of useful quantum kernels" property="og:title" /> <meta content="website" property="og:type" /> <meta content="website" property="og:type" /> <meta content="https://cds.cern.ch/record/2854770" property="og:url" /> <meta property="og:video:height" content="360" /> <meta property="og:video:width" content="640" /> <meta property="og:video" content="https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-720p-quality.mp4" /> <meta property="og:video:type" content="video/mp4" /> <meta property="og:image" content="https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-cover.jpg" /> <meta name="twitter:player:height" content="360" /> <meta name="twitter:player:width" content="640" /> <link rel="image_src" href="https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-cover.jpg" /> <link rel="video_src" href="https://cds.cern.ch/mediaplayer.swf?file=/1251853/1251853-presenter-720p-quality.mp4&streamer=rtmp://wowza.cern.ch:1935/vod&provider=rtmp&stretching=exactfit&image=https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-cover.jpg"/> <meta name="twitter:player" content="https://cds.cern.ch/video/?"/> <meta content="CERN Document Server" property="og:site_name" /> <meta content="The representation of data is of paramount importance for machine learning methods. Kernel methods are used to enrich the feature representation, allowing better generalization. Quantum kernels implement efficiently complex transformation encoding classical data in the Hilbert space of a quantum system, resulting in even exponential speedup. However, we need prior knowledge of the data to choose an appropriate parametric quantum circuit that can be used as quantum embedding.We propose an algorithm that automatically selects the best quantum embedding through a combinatorial optimization procedure that modifies the structure of the circuit, changing the generators of the gates, their angles (which depend on the data points), and the qubits on which the various gates act. Since combinatorial optimization is computationally expensive, we have introduced a criterion based on the exponential concentration of kernel matrix coefficients around the mean to immediately discard an arbitrarily large portion of solutions that are believed to perform poorly.Contrary to the gradient-based optimization (e.g. trainable quantum kernels), our approach is not affected by the barren plateau by construction. We have used both artificial and real-world datasets to demonstrate the increased performance of our approach with respect to randomly generated PQC. We have also compared the effect of different optimization algorithms, including greedy local search, simulated annealing, and genetic algorithms, showing that the algorithm choice largely affects the result.About the speaker&nbsp;Massimiliano Incudini is PhD student at the Dep. of Computer Science, University of Verona. In his studies, he is focused on the development of quantum kernels for real-world applications.Collaborators&nbsp;The presentation is based on the joint work with Alessandra Di Pierro and Francesco Martini available at&nbsp;arxiv.org/abs/2209.11144." property="og:description" />  <meta content="summary" name="twitter:card" /> <style></style> </head> <body class="CERN32Document32Server search" lang="de">  <div id="cern-toolbar"> <h1><a href="http://cern.ch" title="CERN">CERN <span>Accelerating science</span></a></h1> <ul> <li class="cern-accountlinks"><a class="cern-account" href="https://cds.cern.ch/youraccount/login?ln=de&referer=https%3A//cds.cern.ch/record/2854770%3Fln%3Dde" title="Sign in to your CERN account">Sign in</a></li> <li><a class="cern-directory" href="http://cern.ch/directory" title="Search CERN resources and browse the directory">Directory</a></li> </ul> </div>   <div role="banner" class="clearfix" id="header"> <div class="header-inner inner"> <hgroup class="clearfix"> <h2 id="site-name"> <a rel="home" title="Home" href="/"><span>CERN Document Server</span></a> </h2> <h3 id="site-slogan">Access articles, reports and multimedia content in HEP</h3> </hgroup> <div role="navigation" id="main-navigation" class="cdsmenu"> <h2 class="element-invisible">Main menu</h2><ul class="links inline clearfix"> <li class="menu-386 first active-trail"><a class="active-trail" href="https://cds.cern.ch/?ln=de">Suchen</a></li> <li class="menu-444 "><a class="" title="" href="https://cds.cern.ch/submit?ln=de">Absenden</a></li> <li class="menu-426 "><a class="" href="https://cds.cern.ch/help/?ln=de">Hilfe</a></li> <li class="leaf hassubcdsmenu"> <a hreflang="en" class="header" href="https://cds.cern.ch/youraccount/display?ln=de">Personalisieren</a> <ul class="subsubcdsmenu"><li><a href="https://cds.cern.ch/youralerts/list?ln=de">Ihre Benachrichtigungen</a></li><li><a href="https://cds.cern.ch/yourbaskets/display?ln=de">Ihre Körbe</a></li><li><a href="https://cds.cern.ch/yourcomments?ln=de">Your comments</a></li><li><a href="https://cds.cern.ch/youralerts/display?ln=de">Ihre Suchanfragen</a></li></ul></li> </ul> </div> </div> </div>  <table class="navtrailbox"> <tr> <td class="navtrailboxbody"> <a href="/?ln=de" class="navtrail">Hauptseite</a> > On the construction of useful quantum kernels </td> </tr> </table> </div> <div class="pagebody"><div class="pagebodystripemiddle"> <div class="detailedrecordbox"> <div class="detailedrecordtabs"> <div> <ul class="detailedrecordtabs"><li class="on first"><a href="/record/2854770/?ln=de">Information </a></li><li class="disabled"><a>Dateien </a></li></ul> <div id="tabsSpacer" style="clear:both;height:0px"> </div></div> </div> <div class="detailedrecordboxcontent"> <div class="top-left-folded"></div> <div class="top-right-folded"></div> <div class="inside">  <abbr class="unapi-id" title="2854770"></abbr>  <link href="/img/download_and_embed_buttons.css" rel="stylesheet" type="text/css" /> <style type="text/css">  .video_talk_wrapper{ max-width: 640px; min-height: 360px; } </style> <table class="formatRecordTableFullWidth"> <tr> <td class="formatRecordHeader" style="background-image: url('/img/journals.jpg');" colspan="2">  Talk </td> </tr> <tr><td class="formatRecordLabel"> Title </td><td style="padding-left:5px;"><b>On the construction of useful quantum kernels</b></td></tr> <tr><td class="formatRecordLabel"> Video </td><td style="padding-left:5px;"><div class='video_talk_wrapper'><iframe id="iframe-1251853" src="https://lecturemedia.cern.ch/2023/1251853/" width="1020px" height="600px" allowfullscreen scrolling="no" frameborder="0"></iframe></div> <meta http-equiv="X-UA-Compatible" content="IE=edge" /> <style type="text/css"> /* .video_controlbutton, .video_controlbutton:link{ margin-right : 20px; padding-left : 20px; padding-right : 20px; color : #4D94CC; font-size : 16px; font-weight : bold; position : relative; } .video_controlbutton:hover, .video_controlbutton.hover{ cursor : pointer; text-decoration : none; color : #333; } .video_controlbutton:after{ content : " "; width : 0; right : 0; top : 9px; position : absolute; height : 0; border-left : 5px solid transparent; border-right : 5px solid transparent; border-top : 5px solid #4D94CC; } .video_controlbutton.hover:after{ content : " "; width : 0; right : 0; top : 9px; position : absolute; height : 0; border-left : 5px solid transparent; border-right : 5px solid transparent; border-bottom : 5px solid #333; border-top : none!important; }*/ </style> <script> $(document).ready(function(){ $('#video_detailbox_download').hide(); $('#video_detailbox_embed').hide(); $('#video_controlbutton_download').click(function(){ $('#video_detailbox_embed').hide(); $('#video_detailbox_download').toggle(); $('#video_controlbutton_embed').removeClass('hover'); if ($('#video_detailbox_download').is(':hidden')){ $(this).removeClass('hover'); }else{ $(this).addClass('hover'); } return false; }); $('#video_controlbutton_embed').click(function(){ $('#video_detailbox_download').hide(); $('#video_detailbox_embed').toggle(); $('#video_controlbutton_download').removeClass('hover'); if ($('#video_detailbox_embed').is(':hidden')){ $(this).removeClass('hover'); }else{ $(this).addClass('hover'); } return false; });}); </script> <div class="video_control_container"> <div style="box-sizing: inherit;position: relative;min-height: 1em;margin: 1em 0;background: #f8f8f9;padding: 1em 1.5em;line-height: 1.4285em;transition: opacity .1s ease,color .1s ease,background .1s ease,box-shadow .1s ease,-webkit-box-shadow .1s ease;border-radius: .28571429rem;font-size: 1.1em;margin-top: 0;margin-bottom: 6px;background-color: #f8ffff;color: #276f86;box-shadow: 0 0 0 1px #a9d5de inset,0 0 0 0 transparent;"> <i class="fa fa-info"></i><span style="padding-left: 9px;">If you experience any problem watching the video, click the download button below</span> </div> <a id="video_controlbutton_download" rel="download_button" class="video_controlbutton" href="#">Download</a> <a id="video_controlbutton_embed" class="video_controlbutton" href="#">Embed</a> <div style="font-size:small;color:#999;float:right; margin-right:50px"> <span id="record-stats-container"> <a href="#" id="record-stats-link" rel="nofollow">Show n. of views</a> <img id="record-stats-loading" src="/img/loading.gif" style="display:none;" /> </span> <script type="text/javascript"> function getStats() { var $container = $("#record-stats-container"); var $containerLoading = $("#record-stats-loading"); var $containerLink = $("#record-stats-link"); $containerLink.remove() $containerLoading.css('display', 'inline-block'); $.get("/api/record-stats/2854770?display=total_nb_views").done(function(response) { var nViews = "n_views" in response ? response["n_views"] : 0; $container.html(nViews + " views (not distinct)"); }) .fail(function(error) { $container.html("Error loading stats"); console.warn(error); }); }; document.getElementById("record-stats-link").addEventListener('click', function(event) { event.preventDefault(); getStats(); }); </script> </div> </div> <div id="video_detailbox_download" style="margin:10px"> <meta http-equiv="X-UA-Compatible" content="IE=edge" /> <style type="text/css"> #download_movie_box_internal_link, .more_avail_bitrates_link{ background-color: #FAFAFA; border-radius: 5px; box-shadow: 1px 1px 1px 1px #CCCCCC; margin: 5px 2px; padding: 3px; color: #222222; text-align: center; display: inline-block; line-height: 110%; vertical-align: middle; } #download_movie_box_internal_link:hover, .more_avail_bitrates_link:hover, #more_avail_bitrates_links:hover{ color: #FFFFFF; cursor: pointer; text-decoration: none; background: rgb(58,58,58); /* Old browsers */ background: -moz-linear-gradient(top, rgba(58,58,58,1) 0%, rgba(125,126,125,1) 100%); /* FF3.6+ */ background: -webkit-gradient(linear, left top, left bottom, color-stop(0%,rgba(58,58,58,1)), color-stop(100%,rgba(125,126,125,1))); /* Chrome,Safari4+ */ background: -webkit-linear-gradient(top, rgba(58,58,58,1) 0%,rgba(125,126,125,1) 100%); /* Chrome10+,Safari5.1+ */ background: -o-linear-gradient(top, rgba(58,58,58,1) 0%,rgba(125,126,125,1) 100%); /* Opera11.10+ */ background: -ms-linear-gradient(top, rgba(58,58,58,1) 0%,rgba(125,126,125,1) 100%); /* IE10+ */ filter: progid:DXImageTransform.Microsoft.gradient( startColorstr='#3a3a3a', endColorstr='#7d7e7d',GradientType=0 ); /* IE6-9 */ background: linear-gradient(top, rgba(58,58,58,1) 0%,rgba(125,126,125,1) 100%); /* W3C */ -webkit-box-shadow: 0px 0px 0px 0px #b3b3b3; -moz-box-shadow: 0px 0px 0px 0px #b3b3b3; box-shadow: 0px 0px 0px 0px #b3b3b3; } .more_avail_bitrates_link:active{ background-color: #FAFAFA; color: #222222; } span#download_movie_box_internal_link_item{ font-size: x-small; } .more_avail_bitrates_box{ background-color: #FAFAFA; color: #222222; font-size: x-small; box-shadow: 1px 1px 1px 1px #CCCCCC; border-radius: 5px; padding: 2px; margin: 5px 2px; } #highres_box{ background-color: #FAFAFA; color: #222222; font-size: x-small; box-shadow: 1px 1px 1px 1px #CCCCCC; border-radius: 5px; padding: 2px; margin: 5px 2px; display: inline-block; } a.more_avail_bitrates_link{ color: #222222; background-color: #FAFAFA; } #more_avail_bitrates_links{ padding: 3px 7px; border-radius: 3px; color: #222222; vertical-align: middle; } #high_res_ext{ font-size: small; } #high_res_help_img{ vertical-align: middle; } #download_movie_box_title{ text-align: center; } #download_movie_box_part_label{ font-weight: bold; text-align: center; } #download_movie_box_format_label{ font-size: small; font-weight: bold; padding-right: 15px; padding-left: 15px; vertical-align: middle; } #download_movie_box_high_res_link{ color: #444; } #download_movie_box{ border: #CCCCCC solid 1px; margin: 0 auto; width: 90%; } </style> <script> $(document).ready(function(){ $('.more_avail_bitrates_box').hide(); $('a.more_avail_bitrates_link').click(function(){ var id_box = $(this).attr('id').replace('link', 'box'); $('#' + id_box).slideToggle(); $(this).text($(this).text() == 'More..'? 'Less..' : 'More..'); return false; }); }); </script><table id="download_movie_box"><tr><td align="right" valign="top" id="download_movie_box_format_label">Mp4:</td><td><a id="download_movie_box_internal_link" href="https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-720p-quality.mp4">720p<br/><span>(presenter)</span></a></td><td><a id="download_movie_box_internal_link" href="https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-1080p-quality.mp4">1080p<br/><span>(presenter)</span></a></td><td><a id="download_movie_box_internal_link" href="https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-480p-quality.mp4">360p<br/><span>(presenter)</span></a></td><td><a id="download_movie_box_internal_link" href="https://lecturemedia.cern.ch/2023/1251853/1251853-presenter-360p-quality.mp4">270p<br/><span>(presenter)</span></a></td><tr><td align="right" valign="top" id="download_movie_box_format_label">Subtitles:</td><td colspan='4' align='left'><div class='cds-video-subtitles'><a id='download_movie_box_internal_link' href='/2023/1251853/1251853_en.vtt'>English</a></td><td colspan='4' align='left'><div class='cds-video-subtitles'><a id='download_movie_box_internal_link' href='/2023/1251853/1251853_fr.vtt'>FrançAis</a></td></tr/></table> </div> <div id="video_detailbox_embed" style="margin:10px"> <style type="text/css"> #embed_video_box{ background-color: #EEE; border: #DDD solid 1px; margin:0 auto; width: 90%; } #embed_video_box_header{ text-align: center; font-size:small; } </style><table id="embed_video_box"> <tr><th colspan="4" id="embed_video_box_header">Copy-paste this code into your page: </th></tr> <tr><td><textarea readonly="readonly" rows="3" cols="60"><iframe width="640" height="360" frameborder="0" src="https://cds.cern.ch/video/2854770?" allowfullscreen></iframe></textarea></td></tr> </table> </div> <tr><td class="formatRecordLabel"> <span style="white-space:nowrap;">Author(s)</span> </td><td style="padding-left:5px;"><a href="https://cds.cern.ch/search?f=author&p=Incudini%2C%20Massimiliano&ln=de">Incudini, Massimiliano</a> (speaker) (Univ.Verona)</td></tr> <tr><td class="formatRecordLabel"> Corporate <span style="white-space:nowrap;">author(s)</span> </td><td style="padding-left:5px;">CERN. Geneva</td></tr>  <script type="text/javascript"> /* * Changes the Imprint title to Date - Duration as requested by RQF0820114 * This is a hack not to touch the general imprint format element */ $(document).ready(function() { var collections = 'Indico'; if (collections.indexOf('E-LEARNING') > -1) { $('.cern-imprint-label').text('Date - Duration'); } }) </script> <tr><td class="formatRecordLabel cern-imprint-label"> Imprint </td><td style="padding-left:5px;">2023-03-29. - 4512.</td></tr>  <tr><td class="formatRecordLabel"> Series </td><td style="padding-left:5px;">(<a href="/search?f=490__a&p=QTI%20Lectures">QTI Lectures</a>)</td></tr> <tr><td class="formatRecordLabel"> Lecture note </td><td style="padding-left:5px;"> on 2023-03-29T14:30:00<br/></td></tr> <tr><td class="formatRecordLabel"> Subject category </td><td style="padding-left:5px;">QTI Lectures</td></tr> <tr><td class="formatRecordLabel"> Abstract </td><td style="padding-left:5px;"><p>The representation of data is of paramount importance for machine learning methods. Kernel methods are used to enrich the feature representation, allowing better generalization. Quantum kernels implement efficiently complex transformation encoding classical data in the Hilbert space of a quantum system, resulting in even exponential speedup. However, we need prior knowledge of the data to choose an appropriate parametric quantum circuit that can be used as quantum embedding.</p><p>We propose an algorithm that automatically selects the best quantum embedding through a combinatorial optimization procedure that modifies the structure of the circuit, changing the generators of the gates, their angles (which depend on the data points), and the qubits on which the various gates act. Since combinatorial optimization is computationally expensive, we have introduced a criterion based on the exponential concentration of kernel matrix coefficients around the mean to immediately discard an arbitrarily large portion of solutions that are believed to perform poorly.</p><p>Contrary to the gradient-based optimization (e.g. trainable quantum kernels), our approach is not affected by the barren plateau by construction. We have used both artificial and real-world datasets to demonstrate the increased performance of our approach with respect to randomly generated PQC. We have also compared the effect of different optimization algorithms, including greedy local search, simulated annealing, and genetic algorithms, showing that the algorithm choice largely affects the result.</p><p><strong>About the speaker</strong> <br><span style="color:hsl(210,75%,60%);"><strong>Massimiliano Incudin</strong></span>i is PhD student at the Dep. of Computer Science, University of Verona. In his studies, he is focused on the development of quantum kernels for real-world applications.</p><p><strong>Collaborators</strong> <br>The presentation is based on the joint work with Alessandra Di Pierro and Francesco Martini available at <a href="https://arxiv.org/abs/2209.11144">arxiv.org/abs/2209.11144</a>.</p></td></tr> <tr><td class="formatRecordLabel"> Copyright/License </td><td style="padding-left:5px;"><a href="https://copyright.web.cern.ch/">© 2023-2024 CERN</a></td></tr> <tr><td class="formatRecordLabel"> Submitted by </td><td style="padding-left:5px;"><a href="mailto:miguel.marquina@cern.ch">miguel.marquina@cern.ch</a></td></tr> </table> <br/><div><div style="clear: both;"> </div></div> <script type="text/javascript"> // Initially hide: $(".longCaption").hide(); // Allow to toggle visibility: $(".toggleLongCaption").toggle(function(){ $(this).siblings(".longCaption").show('fast'); var thisElem = $(this); thisElem.text(thisElem.text() === "more" ? "less" : "more"); },function(){ $(this).siblings(".longCaption").hide('fast'); var thisElem = $(this); thisElem.text(thisElem.text() === "more" ? "less" : "more"); }); </script> <br/><br/><div align="right"><div style="padding-bottom:2px;padding-top:30px;"><span class="moreinfo" style="margin-right:10px;"> <a href="" class="moreinfo">Zurück zur Suche</a> </span></div></div> <div class="bottom-left-folded"><div class="recordlastmodifiedbox" style="position:relative;margin-left:1px"> Datensatz erzeugt am 2023-03-30, letzte Änderung am 2024-06-26</div></div> <div class="bottom-right-folded" style="text-align:right;padding-bottom:2px;"> <span class="moreinfo" style="margin-right:10px;"><a href="/search?ln=de&p=recid%3A2854770&rm=wrd" class="moreinfo">Ähnliche Datensätze</a></span></div> </div> </div> </div> <br/> <br /> <div class="detailedrecordminipanel"> <div class="top-left"></div><div class="top-right"></div> <div class="inside"> <div id="detailedrecordminipanelfile" style="width:33%;float:left;text-align:center;margin-top:0"> <small class="detailedRecordActions">Externer link:</small><br /><small><a href="https://indico.cern.ch/event/1251853/"><img style="border:none" src="/img/file-icon-text-34x48.gif" alt="Volltext herunterladen" /><br />Event details</a></small> </div> <div id="detailedrecordminipanelreview" style="width:30%;float:left;text-align:center"> </div> <div id="detailedrecordminipanelactions" style="width:36%;float:right;text-align:right;"> <ul class="detailedrecordactions"> <li><a href="/yourbaskets/add?ln=de&recid=2854770">Zum persönlichen Korb hinzufügen</a></li> <li>Export als <a style="text-decoration:underline;font-weight:normal" href="/record/2854770/export/hx?ln=de">BibTeX</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2854770/export/hm?ln=de">MARC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2854770/export/xm?ln=de">MARCXML</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2854770/export/xd?ln=de">DC</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2854770/export/xe?ln=de">EndNote</a>,  <a style="text-decoration:underline;font-weight:normal" href="/record/2854770/export/xn?ln=de">NLM</a>, <a style="text-decoration:underline;font-weight:normal" href="/record/2854770/export/xw?ln=de">RefWorks</a> </li> </ul> <div style='padding-left: 13px;'>  <div id="bookmark"></div> <div id="bookmark_sciencewise"></div> <style type="text/css"> #bookmark_sciencewise, #bookmark {float: left;} #bookmark_sciencewise li {padding: 2px; width: 25px;} #bookmark_sciencewise ul, #bookmark ul {list-style-image: none;} </style> <script type="text/javascript" src="/js/jquery.bookmark.min.js"></script> <style type="text/css">@import "/css/jquery.bookmark.css";</style> <script type="text/javascript">// <![CDATA[ $.bookmark.addSite('sciencewise', 'ScienceWise.info', 'https://cds.cern.ch/img/sciencewise.png', 'en', 'bookmark', 'http://sciencewise.info/bookmarks/cds:2854770/add'); $('#bookmark_sciencewise').bookmark({sites: ['sciencewise']}); $('#bookmark').bookmark({ sites: ['facebook', 'twitter', 'linkedin', 'google_plusone'], icons: '/img/bookmarks.png', url: 'https://cds.cern.ch/record/2854770', addEmail: true, title: "On the construction of useful quantum kernels", description: "<p>The representation of data is of paramount importance for machine learning methods. Kernel methods are used to enrich the feature representation, allowing better generalization. Quantum kernels implement efficiently complex transformation encoding classical data in the Hilbert space of a quantum system, resulting in even exponential speedup. However, we need prior knowledge of the data to choose an appropriate parametric quantum circuit that can be used as quantum embedding.</p><p>We propose an algorithm that automatically selects the best quantum embedding through a combinatorial optimization procedure that modifies the structure of the circuit, changing the generators of the gates, their angles (which depend on the data points), and the qubits on which the various gates act. Since combinatorial optimization is computationally expensive, we have introduced a criterion based on the exponential concentration of kernel matrix coefficients around the mean to immediately discard an arbitrarily large portion of solutions that are believed to perform poorly.</p><p>Contrary to the gradient-based optimization (e.g. trainable quantum kernels), our approach is not affected by the barren plateau by construction. We have used both artificial and real-world datasets to demonstrate the increased performance of our approach with respect to randomly generated PQC. We have also compared the effect of different optimization algorithms, including greedy local search, simulated annealing, and genetic algorithms, showing that the algorithm choice largely affects the result.</p><p><strong>About the speaker</strong> <br><span style=\"color:hsl(210,75%,60%);\"><strong>Massimiliano Incudin</strong></span>i is PhD student at the Dep. of Computer Science, University of Verona. In his studies, he is focused on the development of quantum kernels for real-world applications.</p><p><strong>Collaborators</strong> <br>The presentation is based on the joint work with Alessandra Di Pierro and Francesco Martini available at <a href=\"https://arxiv.org/abs/2209.11144\">arxiv.org/abs/2209.11144</a>.</p>" }); // ]]> </script>  </div> </div> <div style="clear:both;margin-bottom: 0;"></div> </div> <div class="bottom-left"></div><div class="bottom-right"></div> </div> </div></div> <footer id="footer" class="pagefooter clearfix">  <div class="pagefooterstripeleft"> CERN Document Server :: <a class="footer" href="https://cds.cern.ch/?ln=de">Suchen</a> :: <a class="footer" href="https://cds.cern.ch/submit?ln=de">Absenden</a> :: <a class="footer" href="https://cds.cern.ch/youraccount/display?ln=de">Personalisieren</a> :: <a class="footer" href="https://cds.cern.ch/help/?ln=de">Hilfe</a> :: <a class="footer" href="https://cern.service-now.com/service-portal?id=privacy_policy&se=CDS-Service" target="_blank">Privacy Notice</a> <br /> Powered by <a class="footer" href="http://invenio-software.org/">Invenio</a> <br /> Verwaltet von <a class="footer" href="https://cern.service-now.com/service-portal?id=service_element&name=CDS-Service">CDS Service</a> - Need help? Contact <a href="https://cern.service-now.com/service-portal?id=service_element&name=CDS-Service">CDS Support</a>. <br /> </div> <div class="pagefooterstriperight"> <div class="cern-logo"> <a id="logo" href="http://cern.ch" title="CERN" rel="CERN" ><img src="https://cds.cern.ch/img/cern_theme/img/cern-logo-large.png" alt="CERN" /></a> </div> <div class="cern-languagebox"> Diese Seite gibt es auch in den folgenden Sprachen:<br /><a href="/record/2854770?ln=bg" class="langinfo">Български</a>  <a href="/record/2854770?ln=ca" class="langinfo">Català</a>  <span class="langinfo">Deutsch</span>  <a href="/record/2854770?ln=el" class="langinfo">Ελληνικά</a>  <a href="/record/2854770?ln=en" class="langinfo">English</a>  <a href="/record/2854770?ln=es" class="langinfo">Español</a>  <a href="/record/2854770?ln=fr" class="langinfo">Français</a>  <a href="/record/2854770?ln=hr" class="langinfo">Hrvatski</a>  <a href="/record/2854770?ln=it" class="langinfo">Italiano</a>  <a href="/record/2854770?ln=ja" class="langinfo">日本語</a>  <a href="/record/2854770?ln=ka" class="langinfo">ქართული</a>  <a href="/record/2854770?ln=no" class="langinfo">Norsk/Bokmål</a>  <a href="/record/2854770?ln=pl" class="langinfo">Polski</a>  <a href="/record/2854770?ln=pt" class="langinfo">Português</a>  <a href="/record/2854770?ln=ru" class="langinfo">Русский</a>  <a href="/record/2854770?ln=sk" class="langinfo">Slovensky</a>  <a href="/record/2854770?ln=sv" class="langinfo">Svenska</a>  <a href="/record/2854770?ln=zh_CN" class="langinfo">中文(简)</a>  <a href="/record/2854770?ln=zh_TW" class="langinfo">中文(繁)</a> </div> </div>  </footer> <script type="text/javascript"> var SyndeticsBookCovers = (function() { var SMALL_SIZE = "sc.gif", MEDIUM_SIZE = "mc.gif", RAW_URL = "https://secure.syndetics.com/index.aspx?isbn=THEISBN/THESIZE&client=cernlibrary"; replaceCover = function(imgElement, isbns, hdFormat) { var img = new Image(), size = hdFormat ? MEDIUM_SIZE : SMALL_SIZE; var _isbns = isbns.sort(function(a, b) { // sort from shortest to longest ISBN (more modern) return a.length > b.length ? 1 : -1; }); function next() { var isbn = _isbns.pop(); if (isbn) { var url = RAW_URL.replace("THEISBN", isbn).replace("THESIZE", size); img.src = url; } } function done() { imgElement.src = img.src; } img.onload = function() { if (this.width > 1) { done(); } else { next(); } }; next(); }; return { replaceCover: replaceCover }; })(); $(document).ready(function() { // get book covers $("img.book-cover").each(function() { var $this = $(this), strIsbns = $this.data("isbns") || "", isbnsArray = String(strIsbns).split(","), hdFormat = $this.hasClass("hd"); SyndeticsBookCovers.replaceCover(this, isbnsArray, hdFormat); }); // WebNews tooltips $.ajax({ url: "/news/tooltips", success: function(data) { create_tooltips(data); }, dataType: "json", cache: false }); }); </script>  <script src="//cds.cern.ch/js/feedback.js"></script>   <script> var _paq = window._paq = window._paq || []; /* tracker methods like "setCustomDimension" should be called before "trackPageView" */ _paq.push(['trackPageView']); _paq.push(['enableLinkTracking']); (function() { var u="https://webanalytics.web.cern.ch/"; _paq.push(['setTrackerUrl', u+'matomo.php']); _paq.push(['setSiteId', '756']); var d=document, g=d.createElement('script'), s=d.getElementsByTagName('script')[0]; g.async=true; g.src=u+'matomo.js'; s.parentNode.insertBefore(g,s); })(); </script>  </body> </html>

CINXE.COM

On the construction of useful quantum kernels - CERN Document Server