{"id":6571,"date":"2023-09-13T15:57:15","date_gmt":"2023-09-13T06:57:15","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=6571"},"modified":"2023-09-13T15:57:15","modified_gmt":"2023-09-13T06:57:15","slug":"d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/","title":{"rendered":"D-Wave\u30de\u30b7\u30f3\u306e\u9650\u754c\u3092\u8d85\u3048\u308b&#8221;\u5927\u95a2\u6cd5&#8221;"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\" >\u6587\u732e\u60c5\u5831<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E6%A6%82%E8%A6%81\" >\u6982\u8981<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E8%83%8C%E6%99%AF\" >\u80cc\u666f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E6%BA%96%E5%82%99\" >\u6e96\u5099<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E5%A4%A7%E9%96%A2%E6%B3%95\" >\u5927\u95a2\u6cd5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E3%83%8F%E3%83%90%E3%83%BC%E3%83%89%E3%83%BB%E3%82%B9%E3%83%88%E3%83%A9%E3%83%88%E3%83%8E%E3%83%B4%E3%82%A3%E3%83%83%E3%83%81%E5%A4%89%E6%8F%9B\" >\u30cf\u30d0\u30fc\u30c9\u30fb\u30b9\u30c8\u30e9\u30c8\u30ce\u30f4\u30a3\u30c3\u30c1\u5909\u63db<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E9%9E%8D%E7%82%B9%E6%B3%95\" >\u978d\u70b9\u6cd5<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E5%AE%9F%E9%A8%93\" >\u5b9f\u9a13<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave%e3%83%9e%e3%82%b7%e3%83%b3%e3%81%ae%e9%99%90%e7%95%8c%e3%82%92%e8%b6%85%e3%81%88%e3%82%8b%e5%a4%a7%e9%96%a2%e6%b3%95\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb: Breaking limitation of quantum annealer in solving optimization problems under constraints<\/li>\n<li>\u8457\u8005: Ohzeki, M<\/li>\n<li>\u66f8\u8a8c\u60c5\u5831: Sci Rep 10, 3126 (2020).<\/li>\n<li>DOI: <a href=\"https:\/\/doi.org\/10.1038\/s41598-020-60022-5\">https:\/\/doi.org\/10.48550\/arXiv.2201.04877<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73fe\u72b6\u306eD-Wave\u30de\u30b7\u30f3\u3067\u306f\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u4e0a\u306b\u89e3\u304d\u305f\u3044\u554f\u984c\u306e\u30b0\u30e9\u30d5\u3092\u57cb\u3081\u8fbc\u3080\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u30b0\u30e9\u30d5\u304c\u5bc6\u306b\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u306f\u5c11\u306a\u304f\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u554f\u984c\u3092QUBO\u5f62\u5f0f\u3067\u8868\u73fe\u3059\u308b\u969b\u3001\u5236\u7d04\u3092\u7f70\u91d1\u9805\u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u7f70\u91d1\u9805\u306f2\u6b21\u9805\u3067\u3042\u308b\u305f\u3081\u5fc5\u7136\u7684\u306b\u30b0\u30e9\u30d5\u306f\u5bc6\u306b\u306a\u3063\u3066\u3057\u307e\u3044\u3001\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u3092\u5c11\u306a\u304f\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u672c\u8ad6\u6587\u3067\u306f\u3001\u3053\u306e\u3088\u3046\u306aD-Wave\u30de\u30b7\u30f3\u3092\u4f7f\u7528\u3059\u308b\u969b\u306b\u751f\u3058\u3066\u3057\u307e\u3046\u5236\u9650\u3092\u89e3\u6d88\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u3053\u306e\u624b\u6cd5\u306f\u3001\u8ad6\u6587\u306e\u8457\u8005\u306b\u3061\u306a\u3093\u3067\u300c\u5927\u95a2\u6cd5\u300d\u3068\u547c\u3070\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF\"><\/span>\u80cc\u666f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3067\u3042\u308bD-Wave 2000Q\u3067\u306f\u3001\u7269\u7406\u7684\u306a\u91cf\u5b50\u30d3\u30c3\u30c8\u306f\u30ad\u30e1\u30e9\u30b0\u30e9\u30d5\u3068\u3044\u3046\u72ec\u7279\u306a\u69cb\u9020\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u304f\u969b\u306b\u306f\u3001\u56f31\u306e\u30ad\u30e1\u30e9\u30b0\u30e9\u30d5\u4e0a\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<div id=\"attachment_6546\" style=\"width: 235px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6546\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/09\/chimera.png\" alt=\"\" width=\"225\" height=\"231\" class=\" wp-image-6546\" \/><p id=\"caption-attachment-6546\" class=\"wp-caption-text\">\u3000\u56f31: \u30ad\u30e1\u30e9\u30b0\u30e9\u30d5<\/p><\/div>\n<p>\u4f8b\u3048\u3070\u3001\u56f32\u306e\u3088\u3046\u306a\u30b0\u30e9\u30d5\u69cb\u9020\u3092\u6301\u3064\u554f\u984c\u3067\u3042\u308c\u3070\u3001\u305d\u306e\u307e\u307e\u89e3\u304d\u305f\u3044\u554f\u984c\u3092\u30de\u30c3\u30d4\u30f3\u30b0\u3059\u308b\u3053\u3068\u304c\u51fa\u6765\u307e\u3059\u3002<\/p>\n<div id=\"attachment_6545\" style=\"width: 567px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6545\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/09\/embedding1.png\" alt=\"\" width=\"557\" height=\"267\" class=\" wp-image-6545\" \/><p id=\"caption-attachment-6545\" class=\"wp-caption-text\">\u56f32: \u30de\u30c3\u30d4\u30f3\u30b0\u304c\u5bb9\u6613\u306a\u4f8b<\/p><\/div>\n<p>\u3057\u304b\u3057\u3001\u56f33\u306e\u3088\u3046\u306b\u30ce\u30fc\u30c91\u3068\u30ce\u30fc\u30c93\u306e\u9593\u306b\u7d50\u5408\u304c\u3042\u308b\u5834\u5408\u3001\u30ad\u30e1\u30e9\u30b0\u30e9\u30d5\u4e0a\u306b\u76f4\u63a5\u30de\u30c3\u30d4\u30f3\u30b0\u3059\u308b\u3053\u3068\u304c\u51fa\u6765\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u3001\u56f33\u306e\u53f3\u56f3\u306e\u3088\u3046\u306b\u3001\u8907\u6570\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u30671\u3064\u306e\u30ce\u30fc\u30c9\u3092\u8868\u3059\u3088\u3046\u306a\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u884c\u3044\u307e\u3059\u3002\u3053\u308c\u3092\u3001\u30de\u30a4\u30ca\u30fc\u57cb\u3081\u8fbc\u307f\u3068\u8a00\u3044\u307e\u3059\u3002<\/p>\n<div id=\"attachment_6544\" style=\"width: 567px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6544\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/09\/embedding2.png\" alt=\"\" width=\"557\" height=\"268\" class=\" wp-image-6544\" \/><p id=\"caption-attachment-6544\" class=\"wp-caption-text\">\u56f33: \u30de\u30c3\u30d4\u30f3\u30b0\u304c\u8907\u96d1\u306a\u4f8b<\/p><\/div>\n<p>\u56f33\u306e\u5834\u5408\u3001\u89e3\u304d\u305f\u3044\u554f\u984c\u306e\u30ce\u30fc\u30c9\u6570\u306f4\u500b\u3067\u3059\u304c\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u4e0a\u3067\u306f6\u500b\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u4f7f\u7528\u3055\u308c\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u89e3\u304d\u305f\u3044\u554f\u984c\u306e\u30b0\u30e9\u30d5\u304c\u5bc6\u306b\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u4f7f\u7528\u3059\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u306f\u5897\u52a0\u3057\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u4e0a\u306e\u5236\u9650\u306b\u3088\u308a\u3001D-Wave 2000Q\u306f\u6700\u59272048\u500b\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u4f7f\u7528\u53ef\u80fd\u3067\u3059\u304c\u3001\u5b9f\u969b\u306b\u89e3\u3051\u308b\u554f\u984c\u30b5\u30a4\u30ba\u306f\u304b\u306a\u308a\u5c0f\u3055\u3044\u3082\u306e\u306b\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u73fe\u5728\u306fD-Wave 2000Q\u306e\u30b5\u30fc\u30d3\u30b9\u306f\u7d42\u4e86\u3057\u3066\u3057\u307e\u3044\u307e\u3057\u305f\u304c\u3001\u6700\u65b0\u306eD-Wave Advatage\u3067\u3082\u4f9d\u7136\u3053\u306e\u554f\u984c\u306f\u6b8b\u3063\u3066\u3044\u307e\u3059\u3002 \u305d\u3053\u3067\u672c\u8ad6\u6587\u3067\u306f\u3001\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u3092\u6e1b\u3089\u3055\u305a\u306b\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u51fa\u6765\u308b\u3001\u65b0\u305f\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u6848\u3057\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E6%BA%96%E5%82%99\"><\/span>\u6e96\u5099<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u9069\u5316\u554f\u984c\u3092\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3067\u89e3\u304f\u306b\u306f\u3001\u554f\u984c\u3092<b>Quadratic Unconstrained Binary Optimization(QUBO)<\/b>\u3067\u8868\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001QUBO\u3092\u30b3\u30b9\u30c8\u9805\u3068\u5236\u7d04\u9805\u306e\u548c\u3067\u8868\u3059\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{1}<br \/>\nf(\\boldsymbol q) = f_0(\\boldsymbol q) + \\frac{1}{2}\\sum_{k} \\lambda_{k} \\left( F_{k}(\\boldsymbol q) &#8211; C_{k}\\right)^2<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$q_i \\in \\{0, 1\\}$\u3001$f_{0}(\\boldsymbol q)$\u304c\u30b3\u30b9\u30c8\u9805\u3001$\\frac{1}{2}\\sum_{i} \\lambda_{i} \\left( F_{i}(\\boldsymbol q) &#8211; C_{i}\\right)^2$\u306f\u5236\u7d04\u9805\u3067\u3059\u3002\u5236\u7d04\u9805\u306f\u7b49\u5f0f\u5236\u7d04\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u4e00\u822c\u5f62\u3067\u306f\u5206\u304b\u308a\u306b\u304f\u3044\u306e\u3067\u3001\u6b21\u306e\u3088\u3046\u306a\u5177\u4f53\u7684\u306a\u554f\u984c\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>N\u500b\u306e\u4e71\u6570\u304b\u3089K\u500b\u9078\u3073\u51fa\u3057\u3001\u305d\u306e\u7dcf\u548c\u304c\u6700\u5c0f\u3068\u306a\u308b\u7d44\u307f\u5408\u308f\u305b\u3092\u63a2\u7d22\u3059\u308b\u554f\u984c<\/li>\n<\/ul>\n<p>\u3053\u306e\u554f\u984c\u306e\u5834\u5408\u3001QUBO\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{2}<br \/>\nf(\\boldsymbol q) = \\sum_{i=1}^{N}h_iq_i + \\frac{\\lambda}{2}\\left( \\sum_{i=1}^{N}q_{i} &#8211; K \\right)^2<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$q_{i}$\u306f\u30d0\u30a4\u30ca\u30ea\u5909\u6570\u3067\u3001$h_{i}$\u306f\u4e71\u6570\u306e\u5024\u3001$\\lambda$\u306f\u30cf\u30a4\u30d1\u30fc\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3059\u3002<br \/>\n\u7b2c2\u9805\u304c\u5236\u7d04\u9805\u306b\u306a\u3063\u3066\u304a\u308a\u3001\u554f\u984c\u6587\u306e\u300cN\u500b\u306e\u4e71\u6570\u304b\u3089K\u500b\u9078\u3073\u51fa\u3057\u300d\u3068\u3044\u3046\u90e8\u5206\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u6570\u5f0f\u3067\u66f8\u304f\u3068\u3001$\\sum_{i=1}^{N}q_{i} = K$\u3068\u3044\u3046\u7b49\u5f0f\u5236\u7d04\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u5236\u7d04\u9805\u3092\u5c55\u958b\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{3}<br \/>\n\\frac{\\lambda}{2}\\left( \\sum_{i=1}^{N}q_{i} &#8211; K \\right)^2=\\frac{\\lambda}{2}\\left( \\sum_{i=1}^{N}\\sum_{j=1}^{N}q_{i}q_{j} -2K\\sum_{i=1}^{N}q_{i} + K^2 \\right)<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u7b2c1\u9805\u306e$\\sum_{i=1}^{N}\\sum_{j=1}^{N}q_{i}q_{j}$\u306b\u6ce8\u76ee\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u306f\u3001\u5168\u3066\u306e$q_{i}$\u3068\u5168\u3066\u306e$q_{j}$\u306e\u9593\u306b$\\frac{\\lambda}{2}$\u306e\u91cd\u307f\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u3053\u306e\u554f\u984c\u306f\u5168\u7d50\u5408\u306e\u30b0\u30e9\u30d5\u3067\u8868\u3055\u308c\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u524d\u8ff0\u3057\u305f\u3088\u3046\u306b\u3001\u7d50\u5408\u304c\u591a\u304f\u306a\u308b\u307b\u3069\u7121\u99c4\u306b\u4f7f\u7528\u3059\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u5897\u3048\u3066\u3057\u307e\u3044\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u304b\u3089\u7d39\u4ecb\u3059\u308b\u300c\u5927\u95a2\u6cd5\u300d\u3067\u306f\u3001\u554f\u984c\u306e\u6839\u6e90\u3067\u3042\u308b2\u6b21\u5f0f\u306e\u5236\u7d04\u9805\u3092\u4e0a\u624b\u304f\u5909\u5f62\u3059\u308b\u3053\u3068\u3067\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u3092\u7121\u99c4\u306a\u304f\u6700\u5927\u9650\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%A4%A7%E9%96%A2%E6%B3%95\"><\/span>\u5927\u95a2\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u307e\u305a\u306f\u30012\u6b21\u5f0f\u30921\u6b21\u5f0f\u306b\u5909\u63db\u3059\u308b\u516c\u5f0f\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E3%83%8F%E3%83%90%E3%83%BC%E3%83%89%E3%83%BB%E3%82%B9%E3%83%88%E3%83%A9%E3%83%88%E3%83%8E%E3%83%B4%E3%82%A3%E3%83%83%E3%83%81%E5%A4%89%E6%8F%9B\"><\/span>\u30cf\u30d0\u30fc\u30c9\u30fb\u30b9\u30c8\u30e9\u30c8\u30ce\u30f4\u30a3\u30c3\u30c1\u5909\u63db<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u3053\u306e\u5909\u63db\u5f0f\u306f\u30ac\u30a6\u30b9\u7a4d\u5206\u304b\u3089\u5c0e\u304b\u308c\u307e\u3059\u3002\u307e\u305a\u306f\u3001\u30ac\u30a6\u30b9\u7a4d\u5206\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u30ac\u30a6\u30b9\u7a4d\u5206\uff1a<br \/>\n$$<br \/>\n\\begin{equation}\\tag{4}<br \/>\n\\int_{-\\infty}^{\\infty}\\exp\\left({-ax^2}\\right)dx=\\sqrt{\\frac{\\pi}{a}}<br \/>\n\\end{equation}<br \/>\n$$<\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u3001$\\exp$\u306e\u4e2d\u8eab\u3092$-\\frac{1}{2}ax^2+bx$\u3068\u3057\u3066\u5f0f\u5909\u5f62\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{5}<br \/>\n\\begin{split}<br \/>\n\\int_{-\\infty}^{\\infty}\\exp\\left({-\\frac{1}{2}ax^2+bx}\\right)dx<br \/>\n&amp;= \\int_{-\\infty}^{\\infty}\\exp\\left({-\\frac{1}{2}a\\left( x- \\frac{b}{a} \\right)^2+ \\frac{b^2}{2a}}\\right)dx \\\\<br \/>\n&amp;= \\sqrt{\\frac{2\\pi}{a}}\\exp{\\left( \\frac{b^2}{2a} \\right)}<br \/>\n\\end{split}<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>1\u884c\u76ee\u3067\u306f\u5e73\u65b9\u5b8c\u6210\u30012\u884c\u76ee\u3067\u306f\u30ac\u30a6\u30b9\u7a4d\u5206\u3092\u3057\u3066\u3044\u307e\u3059\u3002$b$\u3092\u5909\u6570\u3068\u3057\u3066\u9006\u304b\u3089\u8aad\u3080\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u51fa\u6765\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{6}<br \/>\n\\exp{\\left( \\frac{b^2}{2a} \\right)} = \\sqrt{\\frac{a}{2\\pi}}\\int_{-\\infty}^{\\infty}\\exp\\left({-\\frac{1}{2}ax^2+bx}\\right)dx<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>$b$\u306e2\u6b21\u5f0f\u304c1\u6b21\u5f0f\u306b\u5909\u63db\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u3001\u30cf\u30d0\u30fc\u30c9\u30fb\u30b9\u30c8\u30e9\u30c8\u30ce\u30f4\u30a3\u30c3\u30c1\u5909\u63db\u3068\u8a00\u3044\u307e\u3059\u3002\u65e9\u901f\u30012\u6b21\u306e\u5236\u7d04\u9805\u306b\u9069\u7528\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3068\u8a00\u3044\u305f\u3044\u3068\u3053\u308d\u3067\u3059\u304c\u3001\u30cf\u30d0\u30fc\u30c9\u30fb\u30b9\u30c8\u30e9\u30c8\u30ce\u30f4\u30a3\u30c3\u30c1\u5909\u63db\u306f$\\exp$\u306e\u4e2d\u8eab\u30921\u6b21\u5f0f\u306b\u5909\u63db\u3059\u308b\u3082\u306e\u3067\u3059\u3002\u5236\u7d04\u9805\u3092\u305d\u306e\u307e\u307e\u5909\u63db\u3059\u308b\u3053\u3068\u306f\u51fa\u6765\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001$f(\\boldsymbol{q})$\u306e\u5206\u914d\u95a2\u6570\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u5206\u914d\u95a2\u6570\uff1a<br \/>\n$$<br \/>\n\\begin{equation}\\tag{7}<br \/>\nZ \\equiv \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f(\\boldsymbol{q})\\right)}<br \/>\n\\end{equation}<br \/>\n$$<\/li>\n<\/ul>\n<p>\u3053\u306e\u5f62\u3067\u3042\u308c\u3070\u3001\u30cf\u30d0\u30fc\u30c9\u30fb\u30b9\u30c8\u30e9\u30c8\u30ce\u30f4\u30a3\u30c3\u30c1\u5909\u63db\u304c\u9069\u7528\u3067\u304d\u305d\u3046\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u5909\u63db\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{8}<br \/>\n\\begin{split}<br \/>\nZ &amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f(\\boldsymbol{q})\\right)}\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) &#8211; \\frac{\\beta}{2} \\sum_{k} \\lambda_{k} \\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k} \\right)^2\\right)} \\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)}\\prod_{k}\\exp{\\left( -\\frac{\\beta}{2}\\lambda_{k}\\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k} \\right)^2\\right)}\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)}\\prod_{k}\\frac{1}{\\sqrt{2\\pi}}\\int\\exp{\\left( -\\frac{1}{2}z_{k}^2 + i\\sqrt{\\beta\\lambda_{k}}\\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k} \\right)z_{k} \\right)}dz_{k}\\\\<br \/>\n&amp;= \\frac{1}{\\sqrt{2\\pi}}\\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)}\\prod_{k}\\int\\exp{\\left( -\\frac{1}{2}z_{k}^2 + i\\sqrt{\\beta\\lambda_{k}}z_{k}\\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k} \\right) \\right)}dz_{k}\\\\<br \/>\n&amp;\\propto \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)}\\prod_{k}\\int\\exp{\\left(\\frac{\\beta}{2\\lambda_{k}}\\nu_{k}^2 + \\beta \\nu_{k} \\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k} \\right) \\right)}d\\nu_{k}\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)}\\prod_{k}\\int\\exp{\\left( g(\\nu_{k})\\right)d\\nu_{k}}<br \/>\n\\end{split}<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u5909\u5f62\u9014\u4e2d\u3067\u3059\u304c\u3001\u3053\u3053\u30671\u5ea6\u533a\u5207\u308a\u307e\u3059\u3002\u5404\u884c\u306e\u8aac\u660e\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>2~3\u884c\u76ee<\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u306e\u5177\u4f53\u4f8b\u306e\u3088\u3046\u306b\u3001$\\exp$\u306e\u4e2d\u306e\u7dcf\u548c\u3092$\\exp$\u306e\u5916\u5074\u306b\u7dcf\u7a4d\u3067\u66f8\u304f\u3053\u3068\u304c\u51fa\u6765\u308b\u3053\u3068\u3092\u5229\u7528\u3057\u307e\u3057\u305f\u3002<br \/>\n$$<br \/>\n\\exp{\\left( \\sum_{k=1}^3\u00a0 x_{k}\\right)}=\\exp{\\left( x_1 + x_2 + x_3 \\right)} = \\exp{\\left( x_1 \\right)}\\exp{\\left( x_2 \\right)}\\exp{\\left( x_3 \\right)}=\\prod_{k=1}^3\\exp{\\left(\u00a0 x_{k} \\right)}<br \/>\n$$<\/p>\n<ul>\n<li>3~4\u884c\u76ee<\/li>\n<\/ul>\n<p>\u30cf\u30d0\u30fc\u30c9\u30fb\u30b9\u30c8\u30e9\u30c8\u30ce\u30f4\u30a3\u30c3\u30c1\u5909\u63db\u3092\u5229\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u5148\u7a0b\u306e\u5909\u63db\u5f0f(1)\u306b$a=1, b=\\sqrt{-\\beta \\lambda_{k} \\left( F_{k}(\\boldsymbol{q})- C_{k}\\right)^2}$\u3092\u5f53\u3066\u306f\u3081\u308b\u3053\u3068\u3067\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>5~6\u884c\u76ee<\/li>\n<\/ul>\n<p>$i\\sqrt{\\beta \\lambda_{k}}z_{k} = \\beta \\nu_{k}$\u3064\u307e\u308a\u3001$z_{k} = -i \\sqrt{\\frac{\\beta}{\\lambda_{k}}} \\nu_{k}$\u3068\u5909\u6570\u5909\u63db\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li>6~7\u884c\u76ee<\/li>\n<\/ul>\n<p>$\\frac{\\beta}{2\\lambda_{k}}\\nu_{k}^2 + \\beta \\nu_{k} \\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k}\\right)$\u3092$g(\\nu_k)$\u3068\u7f6e\u3044\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5909\u5f62\u306b\u623b\u308a\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{9}<br \/>\n\\begin{split}<br \/>\nZ &amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)}\\prod_{k}\\int\\exp{\\left( g(\\nu_{k})\\right)d\\nu_{k}}\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)}\\int\\exp{\\left( g(\\nu_{0})\\right)d\\nu_{0}}\\int\\exp{\\left( g(\\nu_{1})\\right)d\\nu_{1}} \\cdots\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)} \\prod_{k} \\int d\\nu_k\u00a0 \\exp{\\left( \\sum_{k} g(\\nu_k) \\right)}\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\exp{\\left( -\\beta f_{0}(\\boldsymbol{q}) \\right)} \\prod_{k} \\int d\\nu_k\u00a0 \\exp{\\left( \\sum_{k} \\frac{\\beta}{2\\lambda_{k}}\\nu_{k}^2 + \\beta \\nu_{k} \\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k}\\right) \\right)}\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\prod_{k} \\int d\\nu_k\u00a0 \\exp{\\left(-\\beta f_{0}(\\boldsymbol{q})+ \\sum_{k} \\frac{\\beta}{2\\lambda_{k}}\\nu_{k}^2 + \\beta \\nu_{k} \\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k}\\right) \\right)}\\\\<br \/>\n&amp;= \\sum_{\\boldsymbol{q}} \\prod_{k} \\int d\\nu_k\u00a0 \\exp{\\left( -\\beta H(\\boldsymbol{q}, \\boldsymbol{\\nu}) \\right)}<br \/>\n\\end{split}<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u308c\u306b\u3088\u308a\u3001\u6709\u52b9\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{10}<br \/>\nH(\\boldsymbol{q}, \\boldsymbol{\\nu})=f_{0}(\\boldsymbol{q}) &#8211; \\sum_{k} \\frac{\\nu_{k}^2}{2\\lambda_{k}} &#8211; \\nu_{k} \\left( F_{k}(\\boldsymbol{q}) &#8211; C_{k}\\right)<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u308c\u3092\u6700\u5c0f\u5316\u3059\u308b\u3088\u3046\u306a$(\\boldsymbol{q}, \\boldsymbol{\\nu})$\u304c\u6700\u7d42\u7684\u306b\u6c42\u3081\u305f\u3044\u89e3\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u978d\u70b9\u6cd5\u3092\u7528\u3044\u3066$H(\\boldsymbol{q}, \\boldsymbol{\\nu})$\u3092\u6700\u5c0f\u5316\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E9%9E%8D%E7%82%B9%E6%B3%95\"><\/span>\u978d\u70b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>$f(t)$\u304c\u6b63\u5247\u3067\u3001$\\beta \\rightarrow \\infty$ \u306e\u6642\u3001\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{11}<br \/>\n\\int d t \\exp (\\beta f(t)) \\propto \\exp \\left(\\beta f(t^*)\\right)<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$t^*$\u306f\u978d\u70b9\u3067\u3042\u308a\u3001$f(t^*)$\u306f\u6700\u5927\u5024\u3068\u306a\u308a\u307e\u3059\u3002<br \/>\n\u3053\u308c\u3092\u5f0f(9)\u306b\u9069\u7528\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{12}<br \/>\nZ \\propto \\exp \\left(- \\beta H(\\boldsymbol{q}^*,\\boldsymbol{\\nu}^* )\\right)<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$(\\boldsymbol{q}^*,\\boldsymbol{\\nu}^* )$\u304c\u978d\u70b9\u3067\u3042\u308a\u3001$H(\\boldsymbol{q^*},\\boldsymbol{\\nu^*} )$\u306f\u6700\u5c0f\u5024\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u304b\u3089\u306f\u3001$(\\boldsymbol{q}^*,\\boldsymbol{\\nu}^* )$\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<br \/>\n\u307e\u305a\u3001\u978d\u70b9\u306e\u6027\u8cea\u306b\u3064\u3044\u3066\u78ba\u8a8d\u3057\u307e\u3059\u3002<br \/>\n\u978d\u70b9\u306f\u56f34\u306e\u3088\u3046\u306b\u3001\u3042\u308b\u65b9\u5411\u304b\u3089\u898b\u308b\u3068\u6975\u5c0f\u3067\u3042\u308a\u3001\u3042\u308b\u65b9\u5411\u304b\u3089\u898b\u308b\u3068\u6975\u5927\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<div id=\"attachment_6625\" style=\"width: 766px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6625\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/09\/saddle_point_plot.png\" alt=\"\" width=\"756\" height=\"253\" class=\" wp-image-6625\" \/><p id=\"caption-attachment-6625\" class=\"wp-caption-text\">\u56f34: \u978d\u70b9\u306e3D\u56f3<\/p><\/div>\n<p>\u305d\u308c\u3067\u306f\u3001$\\boldsymbol{q}^*$\u3084$\\boldsymbol{\\nu}^*$\u306f\u6975\u5927\u30fb\u6975\u5c0f\u306e\u3069\u3061\u3089\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002<br \/>\n$H(\\boldsymbol{q},\\boldsymbol{\\nu})$\u306b\u3064\u3044\u3066\u3001$\\nu_k$\u306e\uff12\u6b21\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{13}<br \/>\n\\frac{\\partial^2}{\\partial \\nu_k^{2}} H(\\boldsymbol{q},\\boldsymbol{\\nu}) =-\\frac{1}{\\lambda_k}<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>$\\lambda_k$\u306f\u6b63\u306e\u305f\u3081\u3001$\\frac{\\partial^2 H}{\\partial \\nu_k^2}&lt;0$\u3068\u306a\u308a\u307e\u3059\u3002\u5f93\u3063\u3066\u3001$H(\\boldsymbol{q},\\boldsymbol{\\nu})$\u306f\u3001$\\boldsymbol{\\nu}$\u8ef8\u65b9\u5411\u3067\u6975\u5927\u5024\u3092\u3082\u3061\u307e\u3059\u3002<br \/>\n\u307e\u305f\u3001$i\\sqrt{\\beta\\nu_k}z_{k}=\\beta \\nu_k$\u3068\u5909\u6570\u5909\u63db\u3057\u305f\u306e\u3067\u3001$\\boldsymbol{\\nu}$\u306f\u865a\u8ef8\u65b9\u5411\u3067\u3059\u3002\u5f93\u3063\u3066\u3001\u5b9f\u8ef8\u65b9\u5411\u3067\u3042\u308b$\\boldsymbol{q}$\u8ef8\u65b9\u5411\u304b\u3089\u898b\u308b\u3068\u3001\u978d\u70b9\u306f\u6975\u5c0f\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a\u306f\u3001$\\boldsymbol{\\nu}$\u8ef8\u65b9\u5411\u304b\u3089\u898b\u305f\u978d\u70b9\u3092\u52fe\u914d\u6cd5\u3067\u6c42\u3081\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002\u305d\u306e\u305f\u3081\u306b\u3001$Z$\u3092\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{14}<br \/>\n\\begin{aligned}<br \/>\nZ &amp; \\propto \\sum_{\\boldsymbol{q}}\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp (-\\beta H(\\boldsymbol{q}, \\boldsymbol{\\nu})) \\\\<br \/>\n&amp; =\\sum_{\\boldsymbol{q}}\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta f_0(\\boldsymbol{q})+\\sum_k\\left(\\frac{\\beta}{2 \\lambda_k} \\nu_k^2+\\beta \\nu_k\\left(F_k(\\boldsymbol{q})-C_k\\right)\\right)\\right) \\\\<br \/>\n&amp; =\\sum_{\\boldsymbol{q}}\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta f_0(\\boldsymbol{q})+\\beta \\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2+\\beta \\sum_k \\nu_k F_k(\\boldsymbol{q})-\\beta \\sum_k \\nu_k C_k\\right) \\\\<br \/>\n&amp; =\\sum_{\\boldsymbol{q}}\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta \\sum_k \\nu_k C_k+\\beta \\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2+\\beta \\sum_k \\nu_k F_k(\\boldsymbol{q})-\\beta f_0(\\boldsymbol{q})\\right) \\\\<br \/>\n&amp; =\\sum_{\\boldsymbol{q}}\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta \\sum_k \\nu_k C_k+\\beta \\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2\\right) \\exp \\left(\\beta \\sum_k \\nu_k F_k(\\boldsymbol{q})-\\beta f_0(\\boldsymbol{q})\\right) \\\\<br \/>\n&amp; =\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta \\sum_k \\nu_k C_k+\\beta \\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2\\right) \\sum_{\\boldsymbol{q}} \\exp \\left(-\\beta\\left(f_0(\\boldsymbol{q})-\\sum_k \\nu_k F_k(\\boldsymbol{q})\\right)\\right) \\\\<br \/>\n&amp; =\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta \\sum_k \\nu_k C_k+\\beta \\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2\\right) Z(\\boldsymbol{\\nu}) \\\\<br \/>\n&amp; =\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta \\sum_k \\nu_k C_k+\\beta \\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2\\right) \\exp (\\log (Z(\\boldsymbol{\\nu}))) \\\\<br \/>\n&amp; =\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta \\sum_k \\nu_k C_k+\\beta \\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2+\\log (Z(\\boldsymbol{\\nu}))\\right) \\\\<br \/>\n&amp; =\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp \\left(-\\beta\\left(\\sum_k \\nu_k C_k-\\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2-\\frac{1}{\\beta} \\log (Z(\\boldsymbol{\\nu}))\\right)\\right) \\\\<br \/>\n&amp; =\\prod_{\\boldsymbol{k}} \\int d \\nu_k \\exp (-\\beta(H(\\boldsymbol{\\nu})))<br \/>\n\\end{aligned}<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u308c\u306b\u3088\u308a\u3001$H(\\boldsymbol{\\nu})$\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{15}<br \/>\nH(\\boldsymbol{\\nu})=\\sum_k \\nu_k C_k-\\sum_k \\frac{1}{2 \\lambda_k} \\nu_k^2-\\frac{1}{\\beta} \\log (Z(\\boldsymbol{\\nu}))<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$Z(\\boldsymbol{\\nu}) := \\sum_{\\boldsymbol{q}} \\exp \\left(-\\beta\\left(f_0(\\boldsymbol{q})-\\sum_k \\nu_k F_k(\\boldsymbol{q})\\right)\\right)$\u3068\u7f6e\u3044\u3066\u3044\u307e\u3059\u3002$\\lambda_{k}$\u306f\u7f70\u91d1\u9805\u306e\u4fc2\u6570\u306a\u306e\u3067\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u5024\u3092\u6301\u3061\u307e\u3059\u3002\u305d\u3053\u3067\u3001$\\lambda_{k} \\to \\infty$\u3068\u3057\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002\u5f93\u3063\u3066\u3001\u6b21\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{16}<br \/>\nH(\\boldsymbol{\\nu})=\\sum_k \\nu_k C_k &#8211; \\frac{1}{\\beta} \\log (Z(\\boldsymbol{\\nu}))<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u308c\u3092$\\nu_{k}$\u3067\u504f\u5fae\u5206\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{17}<br \/>\n\\begin{aligned}<br \/>\n\\frac{\\partial}{\\partial \\nu_k} H(\\boldsymbol{\\nu}) &amp; =C_k-\\frac{1}{\\beta} \\frac{\\partial}{\\partial \\nu_k} \\log (Z(\\boldsymbol{\\nu})) \\\\<br \/>\n&amp; =C_k-\\frac{1}{\\beta} \\frac{1}{Z(\\boldsymbol{\\nu})} \\frac{\\partial Z(\\boldsymbol{\\nu})}{\\partial \\nu_k} \\\\<br \/>\n&amp; =C_k-\\frac{1}{\\beta} \\frac{\\sum_{\\boldsymbol{q}} \\beta F_k(\\boldsymbol{q}) \\exp \\left(-\\beta\\left(f_0(\\boldsymbol{q})-\\sum_k \\nu_k F_k(\\boldsymbol{q})\\right)\\right)}{\\sum_{\\boldsymbol{q}} \\exp \\left(-\\beta\\left(f_0(\\boldsymbol{q})-\\sum_k \\nu_k F_k(\\boldsymbol{q})\\right)\\right)} \\\\<br \/>\n&amp; =C_k- \\sum_{\\boldsymbol{q}} F_k(\\boldsymbol{q})\\frac{\\exp \\left(-\\beta\\left(f_0(\\boldsymbol{q})-\\sum_k \\nu_k F_k(\\boldsymbol{q})\\right)\\right)}{\\sum_{\\boldsymbol{q}} \\exp \\left(-\\beta\\left(f_0(\\boldsymbol{q})-\\sum_k \\nu_k F_k(\\boldsymbol{q})\\right)\\right)} \\\\<br \/>\n&amp; =C_k- \\sum_{\\boldsymbol{q}} F_k(\\boldsymbol{q})P(\\boldsymbol{q}) \\\\<br \/>\n&amp; =C_k- \\left \\langle F_k(\\boldsymbol{q})\\right\\rangle_q<br \/>\n\\end{aligned}<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u5f93\u3063\u3066\u3001\u52fe\u914d\u6cd5\u306f\u4ee5\u4e0b\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{equation}\\tag{18}<br \/>\n\\nu_k^{t+1}=\\nu_k^t+\\eta\\left(C_k-\\left\\langle F_k(\\boldsymbol{q})\\right\\rangle_q\\right)<br \/>\n\\end{equation}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$\\left\\langle F_k(\\boldsymbol{q})\\right\\rangle_q=\\sum_{\\boldsymbol{q}} F_k(\\boldsymbol{q})P(\\boldsymbol{q})$\u306f$F_k(\\boldsymbol{q})$\u306e\u671f\u5f85\u5024\u3067\u3042\u308a\u3001\u53b3\u5bc6\u306b\u8a08\u7b97\u3059\u308b\u306e\u306f\u5927\u5909\u3067\u3059\u3002\u305d\u3053\u3067\u3001D-Wave\u30de\u30b7\u30f3\u304b\u3089\u306e\u51fa\u529b\u304c\u30ae\u30d6\u30b9\u30fb\u30dc\u30eb\u30c4\u30de\u30f3\u5206\u5e03\u306b\u5f93\u3046\u3068\u3044\u3046\u7279\u5fb4\u3092\u5229\u7528\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u624b\u7d9a\u304d\u3067\u8fd1\u4f3c\u8a08\u7b97\u3092\u884c\u3044\u307e\u3057\u3087\u3046\u3002\u307e\u305a\u3001\u4f55\u3089\u304b\u306e$\\boldsymbol{\\nu}$\u3067\u56fa\u5b9a\u3057\u305f$H(\\boldsymbol{q}, \\boldsymbol{\\nu})$\u306b\u5bfe\u3057\u3066\u3001D-Wave\u30de\u30b7\u30f3\u304b\u3089$\\boldsymbol{q}$\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b5\u30f3\u30d7\u30eb\u306f\u30dc\u30eb\u30c4\u30de\u30f3\u5206\u5e03$P(\\boldsymbol{q})$\u306b\u5f93\u3046\u306e\u3067\u3001<br \/>\n$$<br \/>\nP(\\boldsymbol{q}) := \\boldsymbol{q}\u306e\u51fa\u73fe\u56de\u6570 \/  \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u56de\u6570<br \/>\n$$<br \/>\n\u3068\u3057\u3066\u8a08\u7b97\u51fa\u6765\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u671f\u5f85\u5024\u306e\u8fd1\u4f3c\u8a08\u7b97\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u307e\u3068\u3081\u308b\u3068\u3001\u5927\u95a2\u6cd5\u306e\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>Step1: \u5143\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u5909\u63db\u3059\u308b<br \/>\n$$<br \/>\nf(\\boldsymbol{q})=f_0(\\boldsymbol{q})+\\frac{1}{2} \\sum_i \\lambda_i\\left(F_i(\\boldsymbol{q})-C_i\\right)^2 \\quad\\to\\quad<br \/>\nH(\\boldsymbol{q}, \\boldsymbol{\\nu})=f_0(\\boldsymbol{q})-\\sum_i \\nu_i\\left(F_i(\\boldsymbol{q})-C_i\\right) \\\\<br \/>\n$$<\/li>\n<li>Step2: $\\boldsymbol{\\nu}$\u3092\u521d\u671f\u5316\u3059\u308b<\/li>\n<li>Step3: $\\boldsymbol{\\nu}$\u3092\u56fa\u5b9a\u3057\u3066\u3001D-Wave\u30de\u30b7\u30f3\u3067$\\boldsymbol{q}$\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b<\/li>\n<li>Step4: $\\left\\langle F_k(\\boldsymbol{q})\\right\\rangle_q$\u3092\u8a08\u7b97\u3057\u3066\u3001\u52fe\u914d\u6cd5\u3067$\\boldsymbol{\\nu}$\u3092\u66f4\u65b0\u3059\u308b<\/li>\n<li>Step5: $\\boldsymbol{\\nu}$\u304c\u53ce\u675f\u3059\u308b\u307e\u3067\u3001Step3,4\u3092\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ul>\n<p>\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u5b9f\u9a13\u7d50\u679c\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u8ad6\u6587\u3067\u306f6\u3064\u306e\u6700\u9069\u5316\u554f\u984c\u306b\u53d6\u308a\u7d44\u3093\u3067\u3044\u307e\u3059\u304c\u3001\u672c\u8a18\u4e8b\u3067\u306f2\u3064\u306e\u307f\u53d6\u308a\u4e0a\u3052\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E9%A8%93\"><\/span>\u5b9f\u9a13<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u300cN\u500b\u306e\u4e71\u6570\u304b\u3089K\u500b\u9078\u3073\u3001\u305d\u306e\u548c\u3092\u6700\u5c0f\u306b\u3059\u308b\u554f\u984c\u300d\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002\u3053\u306e\u554f\u984c\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u5909\u63db\u5f8c\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$\\tag{19}<br \/>\nf(\\boldsymbol{q})=\\sum_{i=1}^N h_i q_i+\\frac{\\lambda}{2}\\left(\\sum_{i=1}^N q_i-K\\right)^2 \\quad\\to\\quad H(\\boldsymbol{q}, \\nu)=\\sum_{i=1}^N h_i q_i-\\nu\\left(\\sum_{i=1}^N q_i-K\\right)<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$N=2000, K=5, \\nu^{t=0}=0$\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u7d50\u679c\u306f\u56f35\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<div style=\"width: 1648px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/media.springernature.com\/full\/springer-static\/image\/art%3A10.1038%2Fs41598-020-60022-5\/MediaObjects\/41598_2020_60022_Fig1_HTML.png?as=webp\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/media.springernature.com\/full\/springer-static\/image\/art%3A10.1038%2Fs41598-020-60022-5\/MediaObjects\/41598_2020_60022_Fig1_HTML.png?as=webp\" width=\"1638\" height=\"226\" alt=\"\" \/><\/a><p class=\"wp-caption-text\">\u56f35: \u5b9f\u9a13\u7d50\u679c,[\u5f15\u7528]https:\/\/www.nature.com\/articles\/s41598-020-60022-5<\/p><\/div>\n<p>\u5de6\u56f3\u306f\u3001step\u6bce\u306e\u6b8b\u5dee\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u53f3\u56f3\u306f\u3001step\u6bce\u306e$\\nu$\u306e\u5024\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u30023step\u76ee\u3067\u3001$\\nu$\u304c\u53ce\u675f\u3057\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u6b21\u306b\u3001\u300c\u6570\u5206\u5272\u554f\u984c\u300d\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002\u3053\u306e\u554f\u984c\u306f\u3001\u30b3\u30b9\u30c8\u9805\u304c2\u6b21\u3068\u306a\u308b\u554f\u984c\u3067\u3059\u3002\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u5909\u63db\u5f8c\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$\\tag{20}<br \/>\nf(\\boldsymbol{q})=\\frac{1}{2}\\left(\\sum_{i=1}^N n_{i}q_{i}\\right)^2 \\quad\\to\\quad H(\\boldsymbol{q}, \\nu)=\\nu\\sum_{i=1}^N n_{i}q_{i}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001$N=2000$\u3068\u8a2d\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002\u7d50\u679c\u306f\u56f36\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<div style=\"width: 1648px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/media.springernature.com\/full\/springer-static\/image\/art%3A10.1038%2Fs41598-020-60022-5\/MediaObjects\/41598_2020_60022_Fig2_HTML.png?as=webp\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/media.springernature.com\/full\/springer-static\/image\/art%3A10.1038%2Fs41598-020-60022-5\/MediaObjects\/41598_2020_60022_Fig2_HTML.png?as=webp\" width=\"1638\" height=\"212\" class=\"size-full\" \/><\/a><p class=\"wp-caption-text\">\u56f36: \u6570\u5206\u5272\u554f\u984c\u306e\u7d50\u679c,[\u5f15\u7528]https:\/\/www.nature.com\/articles\/s41598-020-60022-5<\/p><\/div>\n<p>\u7d50\u679c\u306e\u898b\u65b9\u306f\u3001\u56f35\u3068\u540c\u69d8\u3067\u3059\u3002\u3053\u3061\u3089\u306b\u95a2\u3057\u3066\u3082\u3001\u7d0412step\u3067\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u306e\u554f\u984c\u30b5\u30a4\u30ba\u306e\u5834\u5408\u3001\u901a\u5e38\u306fD-Wave 2000Q\u3067\u89e3\u304f\u3053\u3068\u306f\u51fa\u6765\u307e\u305b\u3093\u3002\u4e00\u65b9\u3067\u3001\u5927\u95a2\u6cd5\u306f\u3001$\\boldsymbol{\\nu}$\u3082\u63a2\u7d22\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u304f\u306a\u308b\u3082\u306e\u306e\u3001\u6271\u3048\u308b\u554f\u984c\u30b5\u30a4\u30ba\u304c\u98db\u8e8d\u7684\u306b\u5411\u4e0a\u3057\u307e\u3059\u3002\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u304c\u9650\u3089\u308c\u3066\u3044\u308b\u73fe\u72b6\u306b\u304a\u3044\u3066\u3001\u3053\u306e\u3088\u3046\u306a\u624b\u6cd5\u306f\u975e\u5e38\u306b\u91cd\u8981\u306a\u610f\u5473\u3092\u6301\u3064\u3068\u3044\u3048\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5b9f\u9a13\u7d50\u679c\u3092\u898b\u308b\u3068\u3001$\\boldsymbol{\\nu}$\u306f\u632f\u52d5\u3059\u308b\u3053\u3068\u306a\u304f\u53ce\u675f\u3057\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u52fe\u914d\u6cd5\u306e\u5b66\u7fd2\u7387$\\eta$\u306e\u5024\u3092\u9069\u5207\u306b\u8a2d\u5b9a\u3057\u306a\u3044\u3068\u3001\u4e0a\u624b\u304f\u53ce\u675f\u3057\u306a\u3044\u3068\u3044\u3046\u7d50\u679c\u3082\u3042\u308a\u307e\u3059[1]\u3002\u3053\u308c\u306f\u3001$\\boldsymbol{q}$\u3068$\\boldsymbol{\\nu}$\u306e\u5b66\u7fd2\u901f\u5ea6\u306e\u9055\u3044\u304c\u95a2\u4fc2\u3057\u3066\u3044\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u8003\u3048\u307e\u3057\u305f\u3002 \u3064\u307e\u308a\u3001$\\boldsymbol{q}$\u306b\u95a2\u3057\u3066\u306f1step\u3067\u978d\u70b9\u306b\u5230\u9054\u3059\u308b\u3082\u306e\u306e\u3001$\\boldsymbol{\\nu}$\u306b\u95a2\u3057\u3066\u306f\u52fe\u914d\u6cd5\u3067\u3086\u3063\u304f\u308a\u3068\u978d\u70b9\u3092\u76ee\u6307\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001$\\eta$\u306e\u5024\u306b\u3088\u3063\u3066\u306f$\\boldsymbol{\\nu}$\u304c\u632f\u52d5\u3057\u3066\u3057\u307e\u3046\u5834\u5408\u304c\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>[1]\u00a0<a href=\"https:\/\/github-nakasho.github.io\/mo\/ohzeki\">https:\/\/github-nakasho.github.io\/mo\/ohzeki<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\"><\/span>\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u9e7f\u5185\u601c\u592e<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u73fe\u72b6\u306eD-Wave\u30de\u30b7\u30f3\u3067\u306f\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u4e0a\u306b\u89e3\u304d\u305f\u3044\u554f\u984c\u306e\u30b0\u30e9\u30d5\u3092\u57cb\u3081\u8fbc\u3080\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u30b0\u30e9\u30d5\u304c\u5bc6\u306b\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u306f\u5c11\u306a\u304f\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u554f\u984c\u3092QUBO\u5f62\u5f0f\u3067\u8868\u73fe\u3059\u308b\u969b\u3001\u5236\u7d04\u3092\u7f70\u91d1\u9805\u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u7f70\u91d1\u9805\u306f2\u6b21\u9805\u3067\u3042\u308b\u305f\u3081\u5fc5\u7136\u7684\u306b\u30b0\u30e9\u30d5\u306f\u5bc6\u306b\u306a\u3063\u3066\u3057\u307e\u3044\u3001\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u3092\u5c11\u306a\u304f\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u672c\u8ad6\u6587\u3067\u306f\u3001\u3053\u306e\u3088\u3046\u306aD-Wave\u30de\u30b7\u30f3\u3092\u4f7f\u7528\u3059\u308b\u969b\u306b\u751f\u3058\u3066\u3057\u307e\u3046\u5236\u9650\u3092\u89e3\u6d88\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[11,122],"class_list":["post-6571","post","type-post","status-publish","format-standard","hentry","category-review","tag-d-wave-2000q","tag-122"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>D-Wave\u30de\u30b7\u30f3\u306e\u9650\u754c\u3092\u8d85\u3048\u308b&quot;\u5927\u95a2\u6cd5&quot; - T-QARD Harbor<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/09\/13\/d-wave\u30de\u30b7\u30f3\u306e\u9650\u754c\u3092\u8d85\u3048\u308b\u5927\u95a2\u6cd5\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"D-Wave\u30de\u30b7\u30f3\u306e\u9650\u754c\u3092\u8d85\u3048\u308b&quot;\u5927\u95a2\u6cd5&quot; - T-QARD Harbor\" \/>\n<meta property=\"og:description\" content=\"\u73fe\u72b6\u306eD-Wave\u30de\u30b7\u30f3\u3067\u306f\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u4e0a\u306b\u89e3\u304d\u305f\u3044\u554f\u984c\u306e\u30b0\u30e9\u30d5\u3092\u57cb\u3081\u8fbc\u3080\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u30b0\u30e9\u30d5\u304c\u5bc6\u306b\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u306f\u5c11\u306a\u304f\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u554f\u984c\u3092QUBO\u5f62\u5f0f\u3067\u8868\u73fe\u3059\u308b\u969b\u3001\u5236\u7d04\u3092\u7f70\u91d1\u9805\u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u7f70\u91d1\u9805\u306f2\u6b21\u9805\u3067\u3042\u308b\u305f\u3081\u5fc5\u7136\u7684\u306b\u30b0\u30e9\u30d5\u306f\u5bc6\u306b\u306a\u3063\u3066\u3057\u307e\u3044\u3001\u4f7f\u7528\u3067\u304d\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u3092\u5c11\u306a\u304f\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u672c\u8ad6\u6587\u3067\u306f\u3001\u3053\u306e\u3088\u3046\u306aD-Wave\u30de\u30b7\u30f3\u3092\u4f7f\u7528\u3059\u308b\u969b\u306b\u751f\u3058\u3066\u3057\u307e\u3046\u5236\u9650\u3092\u89e3\u6d88\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\" 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