{"id":6919,"date":"2024-02-09T10:00:03","date_gmt":"2024-02-09T01:00:03","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=6919"},"modified":"2025-09-30T13:12:41","modified_gmt":"2025-09-30T04:12:41","slug":"%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/","title":{"rendered":"\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3067\u4eba\u5de5\u7d20\u6750\u3092\u8a2d\u8a08\u3059\u308b \u201cFMQA\u201d"},"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 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href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%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\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E8%83%8C%E6%99%AF%E3%81%A8%E8%AA%B2%E9%A1%8C\" >\u80cc\u666f\u3068\u8ab2\u984c<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E3%83%A2%E3%83%87%E3%83%AB%E3%83%99%E3%83%BC%E3%82%B9%E6%88%A6%E7%95%A5\" >\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u6226\u7565<\/a><\/li><\/ul><\/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\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E6%89%8B%E6%B3%95_%E9%87%8F%E5%AD%90%E3%82%A2%E3%83%8B%E3%83%BC%E3%83%AA%E3%83%B3%E3%82%B0%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E3%83%96%E3%83%A9%E3%83%83%E3%82%AF%E3%83%9C%E3%83%83%E3%82%AF%E3%82%B9%E6%9C%80%E9%81%A9%E5%8C%96_FMQA\" >\u624b\u6cd5: \u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u7528\u3044\u305f\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316 (FMQA)<\/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\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E4%BB%A3%E7%90%86%E3%83%A2%E3%83%87%E3%83%AB\" >\u4ee3\u7406\u30e2\u30c7\u30eb<\/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\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E7%8D%B2%E5%BE%97%E9%96%A2%E6%95%B0\" >\u7372\u5f97\u95a2\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#FMQA%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\" >FMQA\u306e\u307e\u3068\u3081<\/a><\/li><\/ul><\/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\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E5%AE%9F%E9%A8%931_%E4%BA%88%E5%82%99%E5%AE%9F%E9%A8%93\" >\u5b9f\u9a131: \u4e88\u5099\u5b9f\u9a13<\/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\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#FM%E3%81%8C%E6%9D%90%E6%96%99%E6%8E%A2%E7%B4%A2%E3%81%AB%E5%88%A9%E7%94%A8%E3%81%A7%E3%81%8D%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AE%E7%A2%BA%E8%AA%8D\" >FM\u304c\u6750\u6599\u63a2\u7d22\u306b\u5229\u7528\u3067\u304d\u308b\u3053\u3068\u306e\u78ba\u8a8d<\/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\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#QA%E3%81%8C%E3%83%96%E3%83%A9%E3%83%83%E3%82%AF%E3%83%9C%E3%83%83%E3%82%AF%E3%82%B9%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%AE%E5%86%85%E9%83%A8%E3%82%BD%E3%83%AB%E3%83%90%E3%81%AB%E4%BD%BF%E3%81%88%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AE%E5%AE%9F%E8%A8%BC\" >QA\u304c\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u306e\u5185\u90e8\u30bd\u30eb\u30d0\u306b\u4f7f\u3048\u308b\u3053\u3068\u306e\u5b9f\u8a3c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E6%9C%80%E9%81%A9%E3%81%AA%E6%A7%8B%E9%80%A0%E3%81%AE%E6%8E%A2%E7%B4%A2\" >\u6700\u9069\u306a\u69cb\u9020\u306e\u63a2\u7d22<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E6%9C%AC%E5%AE%9F%E9%A8%93_%E6%9C%80%E9%81%A9%E6%A7%8B%E9%80%A0%E3%81%AE%E6%8E%A2%E7%B4%A2\" >\u672c\u5b9f\u9a13: \u6700\u9069\u69cb\u9020\u306e\u63a2\u7d22<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E3%81%BE%E3%81%A8%E3%82%81\" >\u307e\u3068\u3081<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%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-16\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/02\/09\/%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a7%e4%ba%ba%e5%b7%a5%e7%b4%a0%e6%9d%90%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%99%e3%82%8b-fmqa\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E4%BD%9C%E6%88%90%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u4f5c\u6210\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<!-- notionvc: 59bc2386-68e5-44e0-8aec-039bd14916b1 --><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb\uff1aDesigning metamaterials with quantum annealing and factorization machines<\/li>\n<li>\u8457\u8005\uff1aKoki Kitai, Jiang Guo, Shenghong Ju, Shu Tanaka, Koji Tsuda, Junichiro Shiomi, Ryo Tamura<\/li>\n<li>\u66f8\u8a8c\u60c5\u5831\uff1a<a href=\"https:\/\/doi.org\/10.1103\/PhysRevResearch.2.013319\">https:\/\/doi.org\/10.1103\/PhysRevResearch.2.013319<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<!-- notionvc: 38e11e67-b481-4bfa-95f3-ad1b2e1c0cce --><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>$\\def\\argmin#1{\\mathop{\\rm arg~min}\\nolimits #1}\\def\\R{\\mathbb R}\\def\\N{\\mathbb N}$\u8fd1\u5e74\u3001\u5149\u306e\u6ce2\u9577\u3088\u308a\u3082\u7d30\u304b\u306a\u30b9\u30b1\u30fc\u30eb\u3067\u7d20\u6750\u306e\u69cb\u9020\u3092\u5236\u5fa1\u3059\u308b\u6280\u8853\u304c\u767a\u5c55\u3057\u305f\u3053\u3068\u3067\u3001\u3053\u308c\u307e\u3067\u306e\u7d20\u6750\u306b\u306f\u306a\u3044\u7279\u6b8a\u306a\u6027\u8cea\u3092\u6301\u3063\u305f\u4eba\u5de5\u7d20\u6750\u304c\u8a2d\u8a08\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u304d\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u7d20\u6750\u306f\u300c\u30e1\u30bf\u30de\u30c6\u30ea\u30a2\u30eb\u300d\u3068\u547c\u3070\u308c\u3001\u6301\u7d9a\u53ef\u80fd\u306a\u793e\u4f1a\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5909\u63db\u3084\u74b0\u5883\u6d44\u5316\u3001\u533b\u7642\u306a\u3069\u306e\u5206\u91ce\u3067\u306e\u5fdc\u7528\u304c\u671f\u5f85\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u30e1\u30bf\u30de\u30c6\u30ea\u30a2\u30eb\u306e\u8a2d\u8a08\u306b\u304a\u3044\u3066\u306f\u3001\u6b21\u306e3\u3064\u306e\u8981\u7d20\u304c\u5927\u304d\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002<\/p>\n<ol>\n<li>\u5149\u306e\u6ce2\u9577\u3088\u308a\u3082\u7d30\u304b\u306a\u69cb\u9020\u3092\u5236\u5fa1\u3059\u308b\u6280\u8853<\/li>\n<li>\u7d30\u304b\u306a\u69cb\u9020\u30923\u6b21\u5143\u7684\u306b\u7a4d\u307f\u91cd\u306d\u308b\u6280\u8853<\/li>\n<li>\u76ee\u7684\u306e\u6027\u8cea\u3092\u6301\u3064\u7d20\u6750\u306e\u8a2d\u8a08\u56f3\u3092\u63a2\u3059\u6280\u8853\uff08\u81ea\u52d5\u6750\u6599\u767a\u898b\u6280\u8853\uff09<\/li>\n<\/ol>\n<p>\u672c\u7814\u7a76\u306f3\u756a\u76ee\u306e\u8981\u7d20\u306b\u6ce8\u76ee\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u554f\u984c\u3068\u306a\u308b\u306e\u304c\u3001\u300c\u76ee\u7684\u306e\u6027\u8cea\u300d\u3092\u3082\u3064\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u308b\u8a2d\u8a08\u56f3\u306e\u5019\u88dc\u304c\u3042\u307e\u308a\u306b\u3082\u591a\u3059\u304e\u308b\u3053\u3068\u3067\u3059\u3002\u8a2d\u8a08\u56f3\u306e\u5019\u88dc\u3092\u4e00\u3064\u4e00\u3064\u8671\u6f70\u3057\u306b\u8abf\u3079\u4e0a\u3052\u308b\u306e\u306f\u73fe\u5b9f\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u672c\u8ad6\u6587\u3067\u306f\u30e1\u30bf\u30de\u30c6\u30ea\u30a2\u30eb\u306e\u8a2d\u8a08\u56f3\u3092\u52b9\u7387\u7684\u306b\u63a2\u3059\u305f\u3081\u306e\u624b\u6cd5\u3068\u3057\u3066\u300c\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u300d\u6280\u8853\u3092\u7528\u3044\u307e\u3059\u3002\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u3067\u306f\u3001\u3059\u3067\u306b\u6027\u80fd\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u7d20\u6750\u306e\u8a2d\u8a08\u56f3\u3092\u3082\u3068\u306b\u3001\u3088\u308a\u300c\u512a\u308c\u305f\u300d\u8a2d\u8a08\u56f3\u3092\u63a2\u3059\u305f\u3081\u306e\u6700\u9069\u5316\u554f\u984c\u3092\u4f5c\u6210\u3057\u3001\u305d\u308c\u3092\u89e3\u304f\u3053\u3068\u3067\u6700\u9069\u306a\u8a2d\u8a08\u56f3\u3092\u63a2\u3057\u307e\u3059\u3002\u672c\u7814\u7a76\u3067\u306f\u3001\u3053\u306e\u6700\u9069\u5316\u554f\u984c\u3092\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u7528\u3044\u3066\u89e3\u304f\u8a66\u307f\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u304c\u81ea\u52d5\u6750\u6599\u767a\u898b\u6280\u8853\u306b\u5fdc\u7528\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u306b\u3001\u7279\u5b9a\u306e\u6ce2\u9577\u3067\u71b1\u306e\u653e\u5c04\u30fb\u5438\u53ce\u304c\u884c\u308f\u308c\u308b\uff08\u6ce2\u9577\u9078\u629e\u578b\uff09\u30e9\u30b8\u30a8\u30fc\u30bf\u30fc\u306b\u9069\u3057\u305f\u7d20\u6750\u306e\u8a2d\u8a08\u56f3\u3092\u63a2\u7d22\u3057\u307e\u3059\u3002\u6570\u5024\u5b9f\u9a13\u306e\u7d50\u679c\u3001\u4eba\u9593\u304c\u8a2d\u8a08\u3057\u305f\u5f93\u6765\u306e\u7d20\u6750\u306b\u6bd4\u3079\u3066\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u7528\u3044\u305f\u81ea\u52d5\u6750\u6599\u767a\u898b\u3067\u4f5c\u6210\u3057\u305f\u7d20\u6750\u306e\u65b9\u304c\u3001\u3088\u308a\u9ad8\u3044\u6027\u80fd\u3092\u793a\u3059\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u3053\u306e\u3053\u3068\u304b\u3089\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u306f\u81ea\u52d5\u6750\u6599\u767a\u898b\u6280\u8853\u306b\u5fdc\u7528\u3067\u304d\u308b (\u304b\u3082\u3057\u308c\u306a\u3044) \u3053\u3068\u304c\u793a\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<p><!-- notionvc: cefd1b69-94e1-4daa-b4f0-b3db83119b63 --><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF%E3%81%A8%E8%AA%B2%E9%A1%8C\"><\/span>\u80cc\u666f\u3068\u8ab2\u984c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u3088\u3046\u306b\u3001\u5236\u7d04\u6761\u4ef6 $g(\\bm x) \\leq 0$ \u306e\u4e0b\u3067\u3001\u30b3\u30b9\u30c8\u95a2\u6570 $f(\\bm x)$ \u3092\u6700\u3082\u5c0f\u3055\u304f\u3059\u308b\u3088\u3046\u306a\u7d44\u5408\u305b $\\bm x$ \u3092\u6c42\u3081\u308b\u554f\u984c\u3092\u300c\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u300d\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n&amp;\\mathop{\\rm minimize}\\limits_{\\bm x \\in \\{0, 1\\}^N} &amp;&amp; f(\\bm x) \\\\<br \/>\n&amp;\\mathop{\\rm subject\\ to} &amp;&amp; g(\\bm x) \\leq 0 \\\\<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u306f\u3001\u30b3\u30b9\u30c8\u95a2\u6570 $f(\\bm x)$ \u306e\u8a55\u4fa1\uff08$f$ \u306b\u5177\u4f53\u7684\u306a\u5024 $\\bm x$ \u3092\u5165\u529b\u3057\u3066\u51fa\u529b\u3092\u8a08\u7b97\u3059\u308b\u64cd\u4f5c\uff09\u306b\u6642\u9593\u304c\u304b\u304b\u3089\u306a\u3044\u554f\u984c\u3068\u3001$f(\\bm x)$ \u306e\u8a55\u4fa1\u306b\u6642\u9593\u304c\u304b\u304b\u308b\u554f\u984c\u306b\u5927\u5225\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u307e\u3063\u305f\u304f\u7570\u306a\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u53d6\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u8a55\u4fa1\u306b\u6642\u9593\u304c\u304b\u304b\u3089\u306a\u3044\u554f\u984c\u306e\u5834\u5408\u3001\u307e\u305a\u306f\u305d\u306e\u554f\u984c\u304c\u3001<strong>\u6700\u5927\u72ec\u7acb\u96c6\u5408\u554f\u984c<\/strong>\u3001<strong>\u5de1\u56de\u30bb\u30fc\u30eb\u30b9\u30de\u30f3\u554f\u984c<\/strong>\u3001<strong>\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c<\/strong>\u306a\u3069\u306e\u6709\u540d\u306a\u554f\u984c\u306e\u5f62\u3067\u5b9a\u5f0f\u5316\u3067\u304d\u308b\u304b\u3092\u8003\u3048\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6709\u540d\u306a\u554f\u984c\u306f\u7814\u7a76\u306e\u6b74\u53f2\u304c\u9577\u304f\u3001<strong>\u53b3\u5bc6\u89e3\u6cd5<\/strong>\uff08\u6642\u9593\u306f\u304b\u304b\u308b\u304c\u53b3\u5bc6\u306a\u89e3\u3092\u5f97\u308b\u4fdd\u8a3c\u306e\u3042\u308b\u89e3\u6cd5\uff09\u3084<strong>\u8fd1\u4f3c\u89e3\u6cd5<\/strong>\uff08\u6bd4\u8f03\u7684\u9ad8\u901f\u304b\u3064\u3001\u5f97\u3089\u308c\u305f\u89e3\u304c\u53b3\u5bc6\u89e3\u304b\u3089\u3069\u308c\u307b\u3069\u201c\u96e2\u308c\u3066\u3044\u308b\u201d\u304b\u304c\u4fdd\u8a3c\u3055\u308c\u3066\u3044\u308b\u89e3\u6cd5\uff09\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\u3053\u308c\u3089\u306b\u5bfe\u3059\u308b<strong>\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9<\/strong>\uff08\u53b3\u5bc6\u306a\u89e3\u3092\u5f97\u308b\u4fdd\u8a3c\u306f\u306a\u3044\u304c\u3001\u7d4c\u9a13\u7684\u306b\u826f\u3044\u89e3\u3092\u5f97\u3089\u308c\u308b\u3068\u77e5\u3089\u308c\u3066\u3044\u308b\u624b\u6cd5\u306e\u7dcf\u79f0\uff09\u3082\u7814\u7a76\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u306e\u4e00\u74b0\u3068\u3057\u3066\u4ee5\u4e0b\u306b\u793a\u3059QUBO (Quadratic Unconstrained Binary Optimization) \u306e\u5f62\u5f0f\u3067\u306e\u5b9a\u5f0f\u5316\u3082\u8003\u6848\u3055\u308c\u3066\u3044\u307e\u3059 [Lucas 2014; Glover et al. 2018]\u3002<\/p>\n<p>$$<br \/>\n\\mathop{\\rm minimize}\\limits_{\\bm x \\in \\{0, 1\\}^N}<br \/>\n\\quad<br \/>\n\\bm x^\\top \\bm Q \\bm x<br \/>\n$$<\/p>\n<p>\u6709\u540d\u306a\u89e3\u6cd5\u306b\u5e30\u7740\u3067\u304d\u306a\u3044\u5834\u5408\u306b\u306f\u3001\u907a\u4f1d\u7684\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3084\u30b7\u30df\u30e5\u30ec\u30fc\u30c6\u30c3\u30c9\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u306a\u3069\u3068\u3044\u3063\u305f\u53e4\u5178\u7684\u306a\u300c\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u300d\u3092\u7528\u3044\u308b\u304b\u3001\u305d\u306e\u554f\u984c\u306b\u9069\u3057\u305f\u65b0\u305f\u306a\u89e3\u6cd5\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<p>\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u306f\u901a\u5e38\u3001\u4f55\u5ea6\u3082 $f(\\bm x)$ \u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u6700\u9069\u89e3\u3092\u63a2\u7d22\u3059\u308b\u305f\u3081\u3001\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u8a55\u4fa1\u306b\u6642\u9593\u304c\u304b\u304b\u3089\u306a\u3044\uff08$f(\\bm x)$ \u306e\u8a08\u7b97\u304c\u4e00\u77ac\u3067\u7d42\u308f\u308b\uff09\u5834\u5408\u306b\u6709\u52b9\u3067\u3059\u3002\u3068\u3053\u308d\u304c\u3001<strong>\u73fe\u5b9f\u4e16\u754c\u3067\u306e\u5b9f\u9a13\u306e\u7d50\u679c\u5f97\u3089\u308c\u308b\u5024\u3092\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u5024\u3068\u3059\u308b\u3082\u306e<\/strong> \u3084\u3001<strong>\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u7d50\u679c\u5f97\u3089\u308c\u308b\u5024\u3092\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u5024\u3068\u3059\u308b\u3082\u306e<\/strong> \u306a\u3069\u3001$f(\\bm x)$ \u3092\u8a55\u4fa1\u3059\u308b\u306e\u306b\u6642\u9593\u304c\u304b\u304b\u308b\u554f\u984c\u3082\u4e16\u306e\u4e2d\u306b\u306f\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u8a55\u4fa1\u306b\u6642\u9593\u304c\u304b\u304b\u308b\uff081\u5206\u30822\u5206\u3082\u304b\u304b\u308b\uff09\u554f\u984c\u306b\u5bfe\u3057\u3066\u53e4\u5178\u7684\u306a\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u3092\u7528\u3044\u308b\u306e\u306f\u73fe\u5b9f\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u5225\u306e\u89d2\u5ea6\u3067\u306e\u6226\u7565\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E3%83%A2%E3%83%87%E3%83%AB%E3%83%99%E3%83%BC%E3%82%B9%E6%88%A6%E7%95%A5\"><\/span>\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u6226\u7565<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001$f(\\bm x)$ \u3092\u8a08\u7b97\u3059\u308b\u306e\u306b\u6642\u9593\u304c\u304b\u304b\u308b\u554f\u984c\u3092\u300c\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u554f\u984c\u300d\u3068\u547c\u3076\u3053\u3068\u306b\u3057\u307e\u3059\u3002\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u554f\u984c\u306b\u5bfe\u3057\u3066\u306f\u300c\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u5024\u306e\u8a08\u7b97\u56de\u6570\u3092\u6e1b\u3089\u3059\u300d\u3053\u3068\u304c\u57fa\u672c\u7684\u306a\u65b9\u91dd\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3088\u304f\u7528\u3044\u3089\u308c\u308b\u306e\u304c\u300c\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u300d\u306a\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u6226\u7565\u3067\u3059\u3002<\/p>\n<p>\u30e2\u30c7\u30eb\u30d9\u30fc\u30b9\u306a\u624b\u6cd5\u3067\u306f\u3001\u30b3\u30b9\u30c8\u95a2\u6570 $f(\\bm x)$ \u3092\u76f4\u63a5\u6700\u9069\u5316\u3059\u308b\u306e\u3092\u8ae6\u3081\u3001\u4ee3\u308f\u308a\u306b\u300c\u4ee3\u7406\u30e2\u30c7\u30eb\u300d\u3068\u547c\u3070\u308c\u308b\u30e2\u30c7\u30eb\u3067\u8fd1\u4f3c\u3057\u306a\u304c\u3089\u3001\u4ee5\u4e0b\u306e\u624b\u9806\u3067\u9593\u63a5\u7684\u306b\u6700\u9069\u5316\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li><strong>Model-based Optimization<\/strong>\n<ol>\n<li>$t = b, b+1, \\dots, B$ \u306e\u3042\u3044\u3060\u7e70\u308a\u8fd4\u3059:<\/li>\n<li>$\\quad$ \u30c7\u30fc\u30bf $\\mathcal D=\\{\\bm x^{(i)}, y^{(i)}\\}_{i=1}^t$ \u306b\u4ee3\u7406\u30e2\u30c7\u30eb $\\hat f$ \u3092\u30d5\u30a3\u30c3\u30c8\u3055\u305b\u308b<\/li>\n<li>$\\quad$ \u4ee3\u7406\u30e2\u30c7\u30eb $\\hat f$ \u3092\u7528\u3044\u3066\u7372\u5f97\u95a2\u6570 $\\alpha(\\bm x)$\u3092\u4f5c\u6210<\/li>\n<li>$\\quad$ \u7372\u5f97\u95a2\u6570 $\\alpha(\\bm x)$ \u3092\u6700\u5c0f\u5316\u3059\u308b\u5165\u529b\u5024 $\\bm x^{(t+1)} = \\argmin_{\\bm x} \\alpha(\\bm x)$ \u3092\u63a2\u7d22<\/li>\n<li>$\\quad$ \u30b3\u30b9\u30c8\u95a2\u6570\u306e\u5024 $y^{(t+1)} = f(\\bm x^{(t+1)})$ \u3092\u8a55\u4fa1 <strong>(\u3053\u306e\u8a08\u7b97\u306f\u6642\u9593\u304c\u304b\u304b\u308b\u3068\u60f3\u5b9a)<\/strong><\/li>\n<li>$\\quad$ \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\mathcal D$ \u306b $(\\bm x^{(t+1)}, y^{(t+1)})$ \u3092\u8ffd\u52a0<\/li>\n<li>\u5f97\u3089\u308c\u305f\u6700\u9069\u306a\u5165\u529b\u5024 $\\bm x^\\ast = \\argmin_{\\bm x, y \\in \\mathcal D} y$ \u3092\u51fa\u529b<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u3001$b$ \u306f\u521d\u671f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\mathcal D=\\{\\bm x^{(i)}, y^{(i)}\\}_{i=1}^b$ \u306e\u30c7\u30fc\u30bf\u6570\u3001$B$ \u306f\u7d42\u671f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\mathcal D=\\{\\bm x^{(i)}, y^{(i)}\\}_{i=1}^B$ \u306e\u30c7\u30fc\u30bf\u6570\u3067\u3059\u3002$B$ \u306f\u300c\u4e88\u7b97 (budget)\u300d\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n<p>\u7d44\u5408\u305b\u69cb\u9020\u3092\u3082\u3064\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u554f\u984c\u306b\u3053\u306e\u3088\u3046\u306a\u6226\u7565\u3092\u7528\u3044\u308b\u969b\u306b\u554f\u984c\u3068\u306a\u308b\u306e\u304c\u3001\u7372\u5f97\u95a2\u6570\u306e\u6700\u9069\u5316\u554f\u984c<\/p>\n<p>$$<br \/>\n\\mathop{\\rm minimize}\\limits_{\\bm x \\in \\{0, 1\\}^N} \\quad \\alpha(\\bm x)<br \/>\n$$<\/p>\n<p>\u306b\u53b3\u5bc6\u89e3\u6cd5\u3092\u7528\u3044\u308b\u306e\u304c\u73fe\u5b9f\u7684\u3067\u306f\u306a\u304f\u306a\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u9069\u5207\u306a\u8fd1\u4f3c\u89e3\u6cd5\u3084\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u3067\u89e3\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u884c\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u672c\u8ad6\u6587\u3067\u306f\u3001\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u306e1\u7a2e\u3067\u3042\u308b\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0 (Quantum Annealing; QA) \u306b\u3088\u3063\u3066\u89e3\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b\u65b9\u6cd5\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E6%89%8B%E6%B3%95_%E9%87%8F%E5%AD%90%E3%82%A2%E3%83%8B%E3%83%BC%E3%83%AA%E3%83%B3%E3%82%B0%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E3%83%96%E3%83%A9%E3%83%83%E3%82%AF%E3%83%9C%E3%83%83%E3%82%AF%E3%82%B9%E6%9C%80%E9%81%A9%E5%8C%96_FMQA\"><\/span>\u624b\u6cd5: \u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u7528\u3044\u305f\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316 (FMQA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001\u7372\u5f97\u95a2\u6570 $\\alpha(\\bm x)$ \u3092\u4ee5\u4e0b\u306e QUBO \u306e\u5f62\u3067\u8a18\u8ff0\u3057\u3001D-Wave\u793e (2020\u5e74\u5f53\u6642) \u306e\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3067\u3042\u308b D-Wave 2000Q \u3092\u7528\u3044\u3066\u89e3\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n&amp;\\mathop{\\rm minimize}\\limits_{\\bm x \\in \\{0, 1\\}^N}<br \/>\n&amp;&amp; \\alpha(\\bm x) = \\sum_{i, j = 1}^N Q_{ij} x_i x_j<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067 $\\bm x \\in \\{0, 1\\}^N$ \u306f $N$ \u6b21\u5143\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3001\u5404\u8981\u7d20\u306f $0$ \u307e\u305f\u306f $1$ \u306e\u5024\u3092\u3068\u308a\u307e\u3059\u3002$\\bm Q = [Q_{ij}] \\in \\R^{N \\times N}$ \u306f $N$ \u884c $N$ \u5217\u306e\u884c\u5217\u3067\u3001\u5404\u8981\u7d20\u306f\u5b9f\u6570\u5024\u3092\u3068\u308a\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E4%BB%A3%E7%90%86%E3%83%A2%E3%83%87%E3%83%AB\"><\/span>\u4ee3\u7406\u30e2\u30c7\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001\u4ee3\u7406\u30e2\u30c7\u30eb\u306e\u5b66\u7fd2\u306b\u4f7f\u7528\u3067\u304d\u308b\u30c7\u30fc\u30bf\u6570\u3092\u5897\u3084\u3059\u305f\u3081\u306b\u306f\u3001\u8a55\u4fa1\u306b\u6642\u9593\u306e\u304b\u304b\u308b\u76ee\u7684\u95a2\u6570 $f$ \u3092\u3042\u308b $\\bm x$ \u3067\u8a55\u4fa1\u3057\u3066\u3001$(\\bm x, y=f(\\bm x))$ \u306e\u30da\u30a2\u3092\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u8a2d\u5b9a\u3067\u306f\u3001\u3067\u304d\u308b\u3060\u3051\u5c11\u6570\u306e\u30c7\u30fc\u30bf\u6570\u3092\u5143\u306b\u3001\u76ee\u7684\u95a2\u6570\u3092\u3046\u307e\u304f\u8fd1\u4f3c\u3067\u304d\u308b\u3088\u3046\u306a\u4ee3\u7406\u30e2\u30c7\u30eb\u304c\u671b\u307e\u3057\u3044\u3067\u3059\u3002<\/p>\n<p><strong>Factorization Machines (FM):<\/strong> \u4ee5\u4e0a\u306e\u3088\u3046\u306a\u8981\u671b\u3092\u6e80\u305f\u3059\u30e2\u30c7\u30eb\u3068\u3057\u3066\u3001\u672c\u8ad6\u6587\u3067\u306f\u300cFactorization Machines (FM)\u300d[Rendle 2010] \u3068\u3044\u3046\u30e2\u30c7\u30eb\u306b\u7740\u76ee\u3057\u307e\u3059\u3002FM \u306f\u4ee5\u4e0b\u306e\u5f62\u5f0f\u3067\u66f8\u304b\u308c\u308b\u56de\u5e30\u30e2\u30c7\u30eb\u3067\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\nf_\\mathrm{FM}(\\bm x ; b, \\bm w, \\bm V)<br \/>\n&amp;= b + \\sum_{i=1}^N w_i x_i + \\sum_{i,j: i \\lt j} \\bm v_i^\\top \\bm v_j x_i x_j \\\\<br \/>\n&amp;= b + \\sum_{i=1}^N w_i x_i + \\sum_{i=1}^{N-1} \\sum_{j=i+1}^N \\sum_{k=1}^K v_{ik} v_{jk} x_i x_j<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>$b \\in \\R, \\bm w \\in \\R^N, \\bm V \\in \\R^{N \\times K}$ \u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3001$K \\in \\N$ \u306f\u30cf\u30a4\u30d1\u30fc\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3059\u3002<\/p>\n<p>FM \u306f\u3001\u76f8\u4e92\u4f5c\u7528\u9805 $x_i x_j$ \u306e\u4fc2\u6570\u304c\u300c\u96a0\u308c\u30d9\u30af\u30c8\u30eb\u300d\u3068\u547c\u3070\u308c\u308b\u30d9\u30af\u30c8\u30eb $\\bm v_i$ \u3068 $\\bm v_j$ \u306e\u5185\u7a4d $\\bm v_i^\\top \\bm v_j$ \u3067\u66f8\u304b\u308c\u3066\u3044\u308b\u306e\u304c\u7279\u5fb4\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30e2\u30c7\u30eb\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u500b\u6570\u306f<\/p>\n<p>$$<br \/>\np = \\underbrace{1}_{b} + \\underbrace{N}_{w} + \\underbrace{ KN }_{\\bm v} =\\mathcal{O}(KN)<br \/>\n$$<\/p>\n<p>\u306b\u6291\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001FM\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u6570\u306e\u5897\u5927\u304c\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u3067\u3042\u308b\u3068\u3044\u3046\u5f37\u307f\u3092\u6301\u3063\u3066\u3044\u308b\u306e\u304c\u7279\u5fb4\u3067\u3059\u3002<\/p>\n<blockquote><p>\u4e00\u65b9\u3001\u6bd4\u8f03\u306e\u305f\u3081\u306b\u3001\u4f8b\u3048\u3070\u6b21\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b2\u6b21\u591a\u9805\u5f0f<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\nf_{\\mathrm{poly}2}(\\bm x ; b, \\bm w, \\bm W)<br \/>\n&amp;= b + \\sum_{i=1}^N w_i x_i + \\sum_{i,j: i \\lt j} w_{ij} x_i x_j<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>\u3092\u898b\u3066\u307f\u308b\u3068\u3001\u30e2\u30c7\u30eb\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u500b\u6570\u306f<\/p>\n<p>$$<br \/>\np = \\underbrace{1}_{b} + \\underbrace{N}_{w} + \\underbrace{ \\frac{1}{2} N (N-1) }_{\\bm v} =\\mathcal{O}(N^2)<br \/>\n$$<\/p>\n<p>\u3068\u306a\u308a\u3001\u5909\u6570\u306e\u500b\u6570 $N$ \u306e\u5e73\u65b9\u306e\u30aa\u30fc\u30c0\u30fc\u3067\u5897\u52a0\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p><\/blockquote>\n<p><strong>\u672c\u8ad6\u6587\u3067\u306eFM<\/strong>: \u672c\u8ad6\u6587\u3067\u306f\u5b9a\u6570\u9805 $b$ \u306f\u7121\u8996\u3057\u3001\u3055\u3089\u306b\u76f8\u4e92\u4f5c\u7528\u9805\u306b\u304a\u3044\u3066 $i \\lt j$ \u3067\u548c\u3092\u53d6\u308b\u90e8\u5206\u3092\u3001\u3059\u3079\u3066\u306e $i$ \u3068 $j$ \u3067\u548c\u3092\u53d6\u308b\u3088\u3046\u306b\u5909\u66f4\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u306e\u5909\u66f4\u306b\u3088\u3063\u3066\u30e2\u30c7\u30eb\u306e\u6027\u8cea\u304c\u6839\u672c\u7684\u306b\u5909\u308f\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>$$ \\begin{aligned} \\hat f_\\mathrm{FM}(\\bm x ; \\bm w, \\bm V) &amp;= \\sum_{i=1}^N w_i x_i + \\sum_{i=1}^{N} \\sum_{j=1}^N \\sum_{k=1}^K v_{ik} v_{jk} x_i x_j \\end{aligned} $$<\/p>\n<p>\u3053\u306eFM\u306e1\u56de\u306e\u8a08\u7b97\u91cf\u306f\u3001\u6570\u5f0f\u901a\u308a\u306b\u8a08\u7b97\u3057\u305f\u5834\u5408\u306b\u306f $\\mathcal O(KN^2)$ \u3067\u3059\u304c\u3001\u76f8\u4e92\u4f5c\u7528\u9805\u306b\u5bfe\u3057\u6b21\u306e\u3088\u3046\u306a\u5909\u5f62\u3092\u884c\u3046\u3053\u3068\u3067 $\\mathcal O(KN)$ \u306b\u524a\u6e1b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\sum_{i=1}^{N} \\sum_{j=1}^N \\sum_{k=1}^K v_{ik} v_{jk} x_i x_j<br \/>\n&amp;= \\sum_{k=1}^K \\left( \\sum_{i=1}^{N} \\sum_{j=1}^N v_{ik} v_{jk} x_i x_j \\right) \\\\<br \/>\n&amp;= \\sum_{k=1}^K \\left( \\sum_{i=1}^{N} v_{ik} x_i \\sum_{j=1}^N v_{jk} x_j \\right) \\\\<br \/>\n&amp;= \\sum_{k=1}^K \\left( \\sum_{i=1}^{N} v_{ik} x_i \\right)^2<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>\u307e\u305f\u3001\u5404 $x_i$ \u304c $0$ \u307e\u305f\u306f $1$ \u306e\u5024\u3092\u53d6\u308b\u3068\u6307\u5b9a\u3057\u305f\u5834\u5408\u3001$x_i^2 = x_i$ \u304c\u5e38\u306b\u6210\u308a\u7acb\u3064\u306e\u3067\u3001\u3053\u306e\u30e2\u30c7\u30eb\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304d\u76f4\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\n\\begin{aligned}<br \/>\n\\hat f_\\mathrm{FM}(\\bm x ; \\bm w, \\bm V)<br \/>\n&amp;= \\bm x^\\top \\left( \\mathop{\\rm diag}[\\bm w] + \\bm V^\\top \\bm V \\right) \\bm x<br \/>\n\\end{aligned}<br \/>\n$$<\/p>\n<p>\u305f\u3060\u3057<\/p>\n<p>$$<br \/>\n\\bm V<br \/>\n= [\\bm v_1, \\bm v_2, \\dots, \\bm v_N]<br \/>\n=\\begin{bmatrix}<br \/>\nv_{11} &amp; v_{21} &amp; \\cdots &amp; v_{N1} \\\\<br \/>\nv_{12} &amp; v_{22} &amp; \\cdots &amp; v_{N2} \\\\<br \/>\n\\vdots &amp; \\vdots &amp; \\ddots &amp; \\vdots \\\\<br \/>\nv_{1K} &amp; v_{2K} &amp; \\cdots &amp; v_{NK}<br \/>\n\\end{bmatrix}<br \/>\n\\in \\R^{K \\times N}<br \/>\n$$<\/p>\n<p>\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3053\u306e\u30e2\u30c7\u30eb\u306f\u3001QUBO\u5f62\u5f0f\u306e\u76ee\u7684\u95a2\u6570<\/p>\n<p>$$ f(\\bm x) = \\bm x^\\top \\bm Q \\bm x $$<\/p>\n<p>\u306b\u304a\u3051\u308b\u884c\u5217 $\\bm Q$ \u3092\u30e9\u30f3\u30af $K$ \u3067\u4f4e\u30e9\u30f3\u30af\u8fd1\u4f3c\u3057\u3066\u3044\u308b\u3068\u307f\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3053\u306e\u30e2\u30c7\u30eb\u3092\u3001\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\mathcal D$ \u3092\u7528\u3044\u3066\u52fe\u914d\u6cd5\u3067\u8a13\u7df4\u3057\u307e\u3059\u3002\u4ee5\u4e0a\u306e\u3088\u3046\u306a FM \u3092\u4ee3\u7406\u30e2\u30c7\u30eb\u306b\u4f7f\u7528\u3057\u3001QA \u3067\u89e3\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u884c\u3046\u3053\u3068\u304b\u3089\u3001\u672c\u624b\u6cd5\u306f <strong>FMQA<\/strong> \u3068\u540d\u4ed8\u3051\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E7%8D%B2%E5%BE%97%E9%96%A2%E6%95%B0\"><\/span>\u7372\u5f97\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div id=\"attachment_6923\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6923\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/Untitled-300x298.png\" alt=\"FMQA\u306e\u7372\u5f97\u95a2\u6570\u306e\u6a21\u5f0f\u56f3\u3002\u8ad6\u6587\u3092\u5143\u306b\u8a18\u4e8b\u4f5c\u6210\u8005\u304c\u4f5c\u6210\u3002\" width=\"300\" height=\"298\" class=\"wp-image-6923 size-medium\" \/><p id=\"caption-attachment-6923\" class=\"wp-caption-text\">FMQA\u306e\u7372\u5f97\u95a2\u6570\u306e\u6a21\u5f0f\u56f3\u3002\u8ad6\u6587\u3092\u5143\u306b\u8a18\u4e8b\u4f5c\u6210\u8005\u304c\u4f5c\u6210\u3002<\/p><\/div>\n<p>FMQA \u3067\u7528\u3044\u308b\u7372\u5f97\u95a2\u6570\u306f\u4ee3\u7406\u30e2\u30c7\u30eb\u3068\u540c\u4e00\u306e\u3082\u306e\u3067\u3059\u3002\u305f\u3060\u3057\u3001D-Wave 2000Q \u3067\u89e3\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b\u305f\u3081\u306b\u3001FM \u3092 QUBO \u306e\u5f62\u306b\u66f8\u304d\u76f4\u3057\u307e\u3059\u3002<\/p>\n<p>$$ \\begin{aligned} f_\\mathrm{FM}(\\bm x ; \\bm w, \\bm V) &amp;= \\sum_{i=1}^N w_i x_i + \\sum_{i=1}^{N} \\sum_{j=1}^N \\sum_{k=1}^K v_{ik} v_{jk} x_i x_j \\\\ &amp;= \\sum_{i=1}^{N} \\sum_{j=1}^N Q_{ij} x_i x_j \\\\ &amp;= \\alpha(\\bm x) \\end{aligned} $$<\/p>\n<p>\u305f\u3060\u3057<\/p>\n<p>$$ \\begin{aligned} Q_{ij} &amp;= \\left\\{\\begin{aligned} &amp; \\sum_{k=1}^K (v_{ik})^2 + w_i &amp;&amp; (i=j) \\\\ &amp; \\sum_{k=1}^K v_{ik} v_{jk} &amp;&amp; (i \\ne j) \\end{aligned}\\right. \\end{aligned} $$<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u4f5c\u6210\u3055\u308c\u305f QUBO \u3092 <code>dwave.embedding.chimera.find_clique_embedding<\/code> \u30e1\u30bd\u30c3\u30c9 [<a href=\"https:\/\/docs.ocean.dwavesys.com\/projects\/system\/en\/stable\/reference\/generated\/dwave.embedding.chimera.find_clique_embedding.html\">document<\/a>] \u3092\u7528\u3044\u3066\u30ad\u30e1\u30e9\u30b0\u30e9\u30d5\u4e0a\u306b\u57cb\u3081\u8fbc\u307f\u3001D-Wave 2000Q \u306b\u9001\u4fe1\u3057\u307e\u3059\u3002D-Wave 2000Q \u306e\u5236\u7d04\u4e0a\u3001\u3053\u306e\u65b9\u5f0f\u3067\u57cb\u3081\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u308b\u5168\u7d50\u5408\u30b0\u30e9\u30d5\u306e\u9802\u70b9\u6570\u306f63\u9802\u70b9\u306b\u9650\u5b9a\u3055\u308c\u308b\u305f\u3081\u3001\u6700\u5927\u554f\u984c\u30b5\u30a4\u30ba\u3082 $N=63$ \u306b\u9650\u5b9a\u3055\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"FMQA%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>FMQA\u306e\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4ee5\u4e0a\u3092\u307e\u3068\u3081\u308b\u3068\u3001FMQA\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li><strong>FMQA: Black-box optimization using FM and QA<\/strong>\n<ol>\n<li>$t = b, b+1, \\dots, B$ \u306e\u3042\u3044\u3060\u7e70\u308a\u8fd4\u3059:<\/li>\n<li>\u00a0 \u00a0 \u00a0 FM\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u3001\u30c7\u30fc\u30bf $\\mathcal D=\\{\\bm x^{(i)}, y^{(i)}\\}_{i=1}^t$ \u3092\u7528\u3044\u3066\u52fe\u914d\u6cd5\u3067\u8a13\u7df4\u3059\u308b<\/li>\n<li>\u00a0 \u00a0 \u00a0 FM \u3092\u6700\u5c0f\u5316\u3059\u308b\u5165\u529b\u5024 $\\bm x^{(t+1)} = \\argmin_{\\bm x} \\hat f_{\\mathrm{FM}}(\\bm x)$ \u3092\u63a2\u7d22<\/li>\n<li>\u00a0 \u00a0 \u00a0 \u30b3\u30b9\u30c8\u95a2\u6570\u306e\u5024 $y^{(t+1)} = f(\\bm x^{(t+1)})$ \u3092\u8a55\u4fa1 <strong>(\u3053\u306e\u8a08\u7b97\u306f\u6642\u9593\u304c\u304b\u304b\u308b\u3068\u60f3\u5b9a)<\/strong><\/li>\n<li>\u00a0 \u00a0 \u00a0 \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\mathcal D$ \u306b $(\\bm x^{(t+1)}, y^{(t+1)})$ \u3092\u8ffd\u52a0<\/li>\n<li>\u5f97\u3089\u308c\u305f\u6700\u9069\u306a\u5165\u529b\u5024 $\\bm x^\\ast = \\argmin_{\\bm x, y \\in \\mathcal D} y$ \u3092\u51fa\u529b<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E9%A8%931_%E4%BA%88%E5%82%99%E5%AE%9F%E9%A8%93\"><\/span>\u5b9f\u9a131: \u4e88\u5099\u5b9f\u9a13<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"attachment_6940\" style=\"width: 373px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6940\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/FMQA_preliminary-300x161.png\" alt=\"\u672c\u5b9f\u9a13\u306e\u5168\u4f53\u56f3\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\" width=\"363\" height=\"195\" class=\" wp-image-6940\" \/><p id=\"caption-attachment-6940\" class=\"wp-caption-text\">\u672c\u5b9f\u9a13\u306e\u5168\u4f53\u56f3\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002<\/p><\/div>\n<p>\u3053\u3053\u304b\u3089\u306f\u8ad6\u6587\u5185\u306e\u5b9f\u9a13\u7d50\u679c\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u5b9f\u9a13\u8a2d\u5b9a\u3084\u5909\u6570\u306e\u8a2d\u5b9a\u65b9\u6cd5\u306a\u3069\u306f\u5225\u306e\u8a18\u4e8b\u3067\u8aac\u660e\u3059\u308b\u4e88\u5b9a\u3067\u3059\u3002\u3053\u3053\u3067\u306e\u7d50\u679c\u3092\u898b\u308b\u305f\u3081\u306b\u62bc\u3055\u3048\u3066\u304a\u304f\u3079\u304d\u70b9\u306f\u4ee5\u4e0b\u306e4\u70b9\u3067\u3059\u3002<\/p>\n<ol>\n<li>FOM (Figure of Merit) \u3068\u547c\u3070\u308c\u308b\u6750\u6599\u306e \u201c\u3088\u3055\u201d \u306e\u6700\u5927\u5316\u3092\u76ee\u7684\u3068\u3059\u308b<\/li>\n<li>FOM\u306f\u8a2d\u8a08\u3055\u308c\u305f\u7d20\u6750\u3068\u3001\u7279\u5b9a\u306e\u6ce2\u9577\u9818\u57df\u3067\u306e\u9ed2\u4f53\u3068\u306e \u201c\u8fd1\u3055\u201d \u3068 \u201c\u9060\u3055\u201d \u3092\u6e2c\u308b\u3082\u306e\u3067\u3001\u7406\u8ad6\u4e0a\u306e\u6700\u5c0f\u5024\u306f $-1$\u3001\u6700\u5927\u5024\u306f $1$ \u3067\u3042\u308b (\u305f\u3060\u3057 $\\mathrm{FOM} = 1$ \u304c\u5b9f\u73fe\u3067\u304d\u308b\u3068\u306f\u9650\u3089\u306a\u3044)<br \/>\n\u3088\u308a\u5177\u4f53\u7684\u306b\u306f\u3001\u653e\u5c04\u5f37\u5ea6 (\u96fb\u78c1\u653e\u5c04\u306e\u5f37\u3055\u3001\u9ed2\u4f53\u306e\u3068\u304d\u306b\u6700\u5927\u3068\u306a\u308b) \u304c\u3001\u6ce2\u9577\u57df $8-13~\\mathrm{\\mu m}$ \u9818\u57df\u3067\u9ed2\u4f53\u306b\u8fd1\u304f\u3001\u305d\u308c\u4ee5\u5916\u306e\u9818\u57df\u3067\u307b\u307c $0$ \u306b\u306a\u308b\u3088\u3046\u306b\u8a2d\u8a08<\/li>\n<li>\u5909\u6570\u306e\u500b\u6570 $N$ \u306f\u3001\u6750\u6599\u306e \u201c\u6a2a\u5411\u304d\u201d \u306e\u30b0\u30ea\u30c3\u30c9\u6570 $C$ \u3068\u3001\u201c\u7e26\u5411\u304d\u201d \u306e\u30b0\u30ea\u30c3\u30c9\u6570 $L$ \u3092\u7528\u3044\u3066 $N = L\\times(C+1)$ \u3067\u8868\u3055\u308c\u308b<\/li>\n<li>\u6750\u6599\u306f \u201c\u6a2a\u5411\u304d\u201d \u306b\u7e70\u308a\u8fd4\u3055\u308c\u308b\u30fb\u30fb\u30fb\u3064\u307e\u308a\u3001$C=8$ \u3067\u306f $C=4$ \u306e\u3082\u306e\u3068\u540c\u4e00\u306e\u69cb\u9020\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3082\u53ef\u80fd<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"FM%E3%81%8C%E6%9D%90%E6%96%99%E6%8E%A2%E7%B4%A2%E3%81%AB%E5%88%A9%E7%94%A8%E3%81%A7%E3%81%8D%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AE%E7%A2%BA%E8%AA%8D\"><\/span>FM\u304c\u6750\u6599\u63a2\u7d22\u306b\u5229\u7528\u3067\u304d\u308b\u3053\u3068\u306e\u78ba\u8a8d<!-- notionvc: 80203dec-6676-42cf-b187-ea42d39cc5a5 --><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div id=\"attachment_6937\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6937\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/Untitled-1-300x244.png\" alt=\"FM\u3001\u30ac\u30a6\u30b9\u904e\u7a0b\u3001\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u306e3\u624b\u6cd5\u306e\u6bd4\u8f03\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\u521d\u671f\u30c7\u30fc\u30bf\u306e\u500b\u6570\u306f50\u500b\u3002\u521d\u671f\u30c7\u30fc\u30bf\u3092\u5909\u5316\u3055\u305b\u306a\u304c\u308916\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5b9f\u884c\u3057\u305f\u5e73\u5747\u306e\u307f\u3092\u8a18\u8f09\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\" width=\"300\" height=\"244\" class=\"wp-image-6937 size-medium\" \/><p id=\"caption-attachment-6937\" class=\"wp-caption-text\">FM\u3001\u30ac\u30a6\u30b9\u904e\u7a0b\u3001\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u306e3\u624b\u6cd5\u306e\u6bd4\u8f03\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\u521d\u671f\u30c7\u30fc\u30bf\u306e\u500b\u6570\u306f50\u500b\u3002\u521d\u671f\u30c7\u30fc\u30bf\u3092\u5909\u5316\u3055\u305b\u306a\u304c\u308916\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5b9f\u884c\u3057\u305f\u5e73\u5747\u306e\u307f\u3092\u8a18\u8f09\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002<\/p><\/div>\n<p>\u307e\u305a\u3001\u672c\u8ad6\u6587\u3067\u7528\u3044\u305f\u4ee3\u7406\u30e2\u30c7\u30eb\u3067\u3042\u308b FM \u304c\u81ea\u52d5\u6750\u6599\u63a2\u7d22\u306e\u305f\u3081\u306e\u30e2\u30c7\u30eb\u3068\u3057\u3066\u6709\u7528\u3067\u3042\u308b\u3053\u3068\u3092\u5b9f\u8a3c\u3059\u308b\u305f\u3081\u306b\u3001\u521d\u671f\u30c7\u30fc\u30bf\u3068\u3057\u3066 50 \u70b9\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u4e0e\u3048\u305f\u3042\u3068\u3001FM\u3001\u30ac\u30a6\u30b9\u904e\u7a0b (Gaussian process)\u3001\u304a\u3088\u3073\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1 (random search) \u3067\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u3092\u884c\u3044\u3001\u7d50\u679c\u3092\u6bd4\u8f03\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u5b9f\u9a13\u3067\u306f\u554f\u984c\u306e\u5909\u6570\u3092 $16$ \u3068\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u7406\u8ad6\u4e0a\u5b58\u5728\u3059\u308b\u8a2d\u8a08\u56f3\u306f $2^{16} = 65,536$ \u901a\u308a\u3067\u3059\u3002\u3053\u306e\u7a0b\u5ea6\u306e\u500b\u6570\u3067\u3042\u308c\u3070\u3001\u4ee3\u7406\u30e2\u30c7\u30eb $\\hat f$ \u306b\u5bfe\u3057\u3066\u5168\u63a2\u7d22\u3092\u884c\u3063\u3066\u3082\u3001\u73fe\u5728\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u3082\u73fe\u5b9f\u7684\u306a\u6642\u9593\u3067\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4eca\u56de\u306e\u5b9f\u9a13\u3067\u306f\u3001\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3057\u305f\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u6700\u5927\u5316 (\u3042\u308b\u3044\u306f\u6700\u5c0f\u5316) \u3059\u308b\u5165\u529b $\\bm x$ \u3092\u5168\u63a2\u7d22\u306b\u3088\u308a\u767a\u898b\u3057\u3066\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u52a0\u3048\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u7d50\u679c\u3001\u7e70\u308a\u8fd4\u3057\u56de\u6570\u306e\u4e0a\u9650\u306b\u9054\u3057\u305f\u6642\u70b9\u3067\u3001FOM\u306e\u5927\u304d\u3044\u9806\u306bFM\u3001\u30ac\u30a6\u30b9\u904e\u7a0b\u3001\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u3068\u4e26\u3073\u307e\u3057\u305f\u3002\u4e2d\u3067\u3082 FM \u3092\u7528\u3044\u305f\u5834\u5408\u306b\u306f\u3001300\u30b9\u30c6\u30c3\u30d7\u4ee5\u5185\u306b\u5b9f\u969b\u306b\u6700\u3082\u826f\u3044\u8a2d\u8a08\u56f3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u306f\u3001FM \u304c\u6750\u6599\u63a2\u7d22\u306e\u554f\u984c\u306b\u304a\u3044\u3066\u6709\u7528\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"QA%E3%81%8C%E3%83%96%E3%83%A9%E3%83%83%E3%82%AF%E3%83%9C%E3%83%83%E3%82%AF%E3%82%B9%E6%9C%80%E9%81%A9%E5%8C%96%E3%81%AE%E5%86%85%E9%83%A8%E3%82%BD%E3%83%AB%E3%83%90%E3%81%AB%E4%BD%BF%E3%81%88%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AE%E5%AE%9F%E8%A8%BC\"><\/span>QA\u304c\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u306e\u5185\u90e8\u30bd\u30eb\u30d0\u306b\u4f7f\u3048\u308b\u3053\u3068\u306e\u5b9f\u8a3c<!-- notionvc: 9ac8f123-9efd-43bb-a872-270a077b4352 --><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div id=\"attachment_6938\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6938\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/FMQA_2-300x237.png\" alt=\"FMQA\u3068\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u306e\u6bd4\u8f03\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\u521d\u671f\u30c7\u30fc\u30bf\u306e\u500b\u6570\u306f50\u500b\u3002\u521d\u671f\u30c7\u30fc\u30bf\u3092\u5909\u5316\u3055\u305b\u306a\u304c\u308916\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5b9f\u884c\u3057\u305f\u5e73\u5747\u306e\u307f\u3092\u8a18\u8f09\u3002\" width=\"300\" height=\"237\" class=\"wp-image-6938 size-medium\" \/><p id=\"caption-attachment-6938\" class=\"wp-caption-text\">FMQA\u3068\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u306e\u6bd4\u8f03\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\u521d\u671f\u30c7\u30fc\u30bf\u306e\u500b\u6570\u306f50\u500b\u3002\u521d\u671f\u30c7\u30fc\u30bf\u3092\u5909\u5316\u3055\u305b\u306a\u304c\u308916\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5b9f\u884c\u3057\u305f\u5e73\u5747\u306e\u307f\u3092\u8a18\u8f09\u3002<\/p><\/div>\n<p>FM\u304c\u6750\u6599\u63a2\u7d22\u306b\u6709\u52b9\u3067\u3042\u308b\u3053\u3068\u306f\u5206\u304b\u308a\u307e\u3057\u305f\u3002\u7d9a\u3044\u3066\u3001\u3088\u308a\u9ad8\u6b21\u5143\u306e\u8a2d\u5b9a\u306e\u5834\u5408\u306b\u3001QA\u3092\u7528\u3044\u3066\u3082\u826f\u3044\u6027\u80fd\u3092\u51fa\u305b\u308b\u304b\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002FMQA\u304c\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u3092\u4e0a\u56de\u308b\u7d50\u679c\u3092\u51fa\u3059\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u3067\u3001\u5c11\u306a\u304f\u3068\u3082\u7121\u60c5\u5831\u3067\u306e\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u3092\u884c\u3046\u3088\u3046\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306f\u306a\u3044\u3068\u8a00\u3048\u308b\u306f\u305a\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u3053\u3053\u3067\u306f\u5168\u63a2\u7d22\u306b\u3088\u308b\u6700\u9069\u5316\u306f\u975e\u73fe\u5b9f\u7684\u3068\u306a\u308b\u3088\u3046\u306a\u3001\u7406\u8ad6\u4e0a\u5b58\u5728\u3059\u308b\u8a2d\u8a08\u56f3\u304c $2^{24} = 16,777,216$ \u901a\u308a\u306e\u8a2d\u5b9a\u3092\u7528\u3044\u3066\u3001FMQA\u3092\u7528\u3044\u305f\u3082\u306e\u3068\u3001\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u3092\u7528\u3044\u305f\u3082\u306e\u3067\u6bd4\u8f03\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u7d50\u679c\u3001\u3053\u306e\u554f\u984c\u8a2d\u5b9a\u3067\u306f FMQA \u304c\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u3092\u4e0a\u56de\u3063\u3066\u3044\u308b\u305f\u3081\u3001FMQA \u306f\u5b8c\u5168\u306b\u30e9\u30f3\u30c0\u30e0\u306b\u63a2\u7d22\u3059\u308b\u3088\u308a\u3082\u8ce2\u3044\u624b\u6cd5\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u5c11\u306a\u304f\u3068\u3082 QA \u304c\u539f\u56e0\u3067\u30e9\u30f3\u30c0\u30e0\u30b5\u30fc\u30c1\u3088\u308a\u3082\u6027\u80fd\u304c\u4f4e\u4e0b\u3059\u308b\u3068\u3044\u3046\u3088\u3046\u306a\u4e8b\u614b\u306b\u306f\u306a\u3063\u3066\u3044\u306a\u3044\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E6%9C%80%E9%81%A9%E3%81%AA%E6%A7%8B%E9%80%A0%E3%81%AE%E6%8E%A2%E7%B4%A2\"><\/span>\u6700\u9069\u306a\u69cb\u9020\u306e\u63a2\u7d22<!-- notionvc: 6540d53e-9b34-498d-86d2-32e39f864c14 --><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div id=\"attachment_6939\" style=\"width: 353px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6939\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/FMQA_3-230x300.png\" alt=\"\u6700\u5927FOM\u3092\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u305f\u8a2d\u8a08\u56f3\u306e\u500b\u6570\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u793a\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002(a) $C=3$ \u306b\u56fa\u5b9a\u3057\u3001$L$ \u3092\u5909\u5316\u3055\u305b\u3066\u6750\u6599\u63a2\u7d22\u3092\u884c\u3063\u305f\u7d50\u679c\u3001(b) $L=5$ \u306b\u56fa\u5b9a\u3057\u3001$C$ \u3092\u5909\u5316\u3055\u305b\u3066\u6750\u6599\u63a2\u7d22\u3092\u884c\u3063\u305f\u7d50\u679c\u3002\" width=\"343\" height=\"447\" class=\" wp-image-6939\" \/><p id=\"caption-attachment-6939\" class=\"wp-caption-text\">\u6700\u5927FOM\u3092\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u305f\u8a2d\u8a08\u56f3\u306e\u500b\u6570\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u793a\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002(a) $C=3$ \u306b\u56fa\u5b9a\u3057\u3001$L$ \u3092\u5909\u5316\u3055\u305b\u3066\u6750\u6599\u63a2\u7d22\u3092\u884c\u3063\u305f\u7d50\u679c\u3001(c) $L=5$ \u306b\u56fa\u5b9a\u3057\u3001$C$ \u3092\u5909\u5316\u3055\u305b\u3066\u6750\u6599\u63a2\u7d22\u3092\u884c\u3063\u305f\u7d50\u679c\u3002<\/p><\/div>\n<p>\u3053\u3053\u307e\u3067\u3067 FMQA \u304c\u6750\u6599\u63a2\u7d22\u306b\u304a\u3044\u3066\u6709\u7528\u306a\u624b\u6cd5\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u306e\u3067\u3001D-Wave 2000Q \u304c\u53d6\u308a\u6271\u3044\u53ef\u80fd\u306a\u7bc4\u56f2\u3067 $L$ \u3068 $C$ \u3092\u5909\u5316\u3055\u305b\u306a\u304c\u3089\u6750\u6599\u63a2\u7d22\u3092\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u3001\u5c0f\u898f\u6a21\u306a\u7bc4\u56f2\u3067\u306e\u6700\u9069FOM\u306e\u63a2\u7d22\u3092\u884c\u3044\u307e\u3059\u3002\u56f3 (a) \u3067\u306f $L$\u3001\u3059\u306a\u308f\u3061\u5c64\u306e\u6570\u3092\u5909\u5316\u3055\u305b\u306a\u304c\u3089\u5b9f\u9a13\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u56f3 (c) \u3067\u306f $C$ \u3059\u306a\u308f\u3061\u8a2d\u8a08\u56f3\u306e\u5468\u671f\u3092\u5909\u5316\u3055\u305b\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u3001$(L,C) = (5,4)$ \u306e\u5834\u5408\u3068 $(L,C) = (5,8)$ \u306e\u5834\u5408\u3092\u6bd4\u8f03\u3059\u308b\u3068\u3001$(L,C) = (5,4)$ \u306e\u307b\u3046\u304cFOM\u304c\u5927\u304d\u304f\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u3082\u3057\u3082\u4e21\u65b9\u306e\u5b9f\u9a13\u306b\u304a\u3044\u3066\u53b3\u5bc6\u306b\u6700\u3082\u826f\u3044\u69cb\u9020\u304c\u5f97\u3089\u308c\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3059\u308b\u306a\u3089\u3070\u3001\u3053\u308c\u306f\u4e0d\u81ea\u7136\u3067\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u8a2d\u8a08\u3055\u308c\u305f\u7d20\u6750\u306e\u69cb\u9020\u306f $x$ \u65b9\u5411\u306b\u7e70\u308a\u8fd4\u3059\u3068\u4eee\u5b9a\u3057\u3066\u3044\u308b\u305f\u3081\u3001$(L,C) = (5,4)$ \u3067\u826f\u3044\u69cb\u9020\u304c\u5f97\u3089\u308c\u3066\u3044\u308b\u306a\u3089\u3070\u3001\u305d\u308c\u3092\u5358\u306b $x$ \u65b9\u5411\u306b2\u56de\u7e70\u308a\u8fd4\u3057\u3066\u5f97\u3089\u308c\u308b $(L,C) = (5,8)$ \u306e\u69cb\u9020\u306f\u3001\u540c\u3058\u304f\u3089\u3044\u826f\u3044\u69cb\u9020\u3068\u8a55\u4fa1\u3055\u308c\u308b\u306f\u305a\u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/FMQA_3-1-300x194.png\" alt=\"\" width=\"300\" height=\"194\" class=\"size-medium wp-image-6941 aligncenter\" \/><\/p>\n<p>\u306b\u3082\u95a2\u308f\u3089\u305a\u3001\u540c\u3058\u304f\u3089\u3044\u826f\u3044\u89e3\u304c\u5f97\u3089\u308c\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u5358\u306b $x$ \u65b9\u5411\u306b2\u56de\u7e70\u308a\u8fd4\u3057\u305f\u3060\u3051\u306e\u69cb\u9020\u304c\u767a\u898b\u3067\u304d\u3066\u3044\u306a\u3044\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5b9f\u969b\u306b\u306f\u3001\u73fe\u5728\u306e\u6761\u4ef6 (\u6700\u5927\u30672000\u30b9\u30c6\u30c3\u30d7) \u306b\u304a\u3044\u3066\u306f\u3001\u6700\u3082\u826f\u3044\u69cb\u9020\u306f\u767a\u898b\u3067\u304d\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u5b9f\u969b\u3001\u30b0\u30e9\u30d5 (c) \u3067 $(L,C) = (5,4)$ (\u9752) \u3068 $(L,C) = (5,8)$ (\u30aa\u30ec\u30f3\u30b8) \u306e\u66f2\u7dda\u3092\u3088\u304f\u898b\u3066\u307f\u308b\u3068\u3001\u524d\u8005\u306e\u5834\u5408\u306f 1000 \u30b9\u30c6\u30c3\u30d7\u7a0b\u5ea6\u3067FOM\u304c\u3042\u308b\u7a0b\u5ea6\u53ce\u675f\u3057\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u5f8c\u8005\u306e\u5834\u5408\u306f2000\u30b9\u30c6\u30c3\u30d7\u6642\u70b9\u3067\u306f\u82e5\u5e72\u53f3\u80a9\u4e0a\u304c\u308a\u3067\u3042\u308b\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002\u78ba\u304b\u306b\u30012000\u30b9\u30c6\u30c3\u30d7\u7a0b\u5ea6\u3067\u306f\u6700\u3082\u826f\u3044\u69cb\u9020\u3092\u767a\u898b\u3067\u304d\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u4e3b\u5f35\u306f\u6210\u7acb\u3057\u305d\u3046\u3067\u3059\u3002<\/p>\n<p>\u4ee5\u4e0a\u306e\u3053\u3068\u306f\u3001\u3088\u308a\u5927\u898f\u6a21\u306a\u8a2d\u5b9a\u3067\u6700\u9069\u69cb\u9020\u3092\u63a2\u7d22\u3059\u308b\u306b\u306f\u3001\u3088\u308a\u63a2\u7d22\u30b9\u30c6\u30c3\u30d7\u6570\u3092\u5897\u3084\u3057\u305f\u308a\u3001\u3088\u308a\u52b9\u679c\u7684\u306aFM\u306e\u8a13\u7df4\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E5%AE%9F%E9%A8%93_%E6%9C%80%E9%81%A9%E6%A7%8B%E9%80%A0%E3%81%AE%E6%8E%A2%E7%B4%A2\"><\/span>\u672c\u5b9f\u9a13: \u6700\u9069\u69cb\u9020\u306e\u63a2\u7d22<!-- notionvc: 61d153a0-ea82-4523-9533-674535caea56 --><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"attachment_6942\" style=\"width: 382px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6942\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/11\/FMQA_4-226x300.jpg\" alt=\"\u5404 $(L,C)$ \u306e\u7d44\u306b\u5bfe\u3057\u3001\u6750\u6599\u63a2\u7d22\u306b\u3088\u308a\u767a\u898b\u3055\u308c\u305f\u8a2d\u8a08\u56f3\u3092\u53ef\u8996\u5316\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\u5404\u884c\u306f $L$ \u3092\u3001\u5404\u5217\u306f $C$ \u3092\u8868\u3059\u3002\" width=\"372\" height=\"494\" class=\" wp-image-6942\" \/><p id=\"caption-attachment-6942\" class=\"wp-caption-text\">\u5404 $(L,C)$ \u306e\u7d44\u306b\u5bfe\u3057\u3001\u6750\u6599\u63a2\u7d22\u306b\u3088\u308a\u767a\u898b\u3055\u308c\u305f\u8a2d\u8a08\u56f3\u3092\u53ef\u8996\u5316\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\u5404\u884c\u306f $L$ \u3092\u3001\u5404\u5217\u306f $C$ \u3092\u8868\u3059\u3002<\/p><\/div>\n<p>\u3053\u306e\u56f3\u306f\u3001\u69d8\u3005\u306a $(L, C)$ \u306e\u7d44\u306b\u5bfe\u3057\u3001FMQA\u3067\u63a2\u7d22\u3092\u884c\u3063\u3066\u5f97\u3089\u308c\u305f\u6700\u9069\u69cb\u9020\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u5185\u3001\u8d64\u306e\u7834\u7dda\u3067\u56f2\u307e\u308c\u305f $(L,C) = (5,6)$ \u306f\u3001FOM\u304c\u6700\u3082\u5927\u304d\u304f\u306a\u3063\u305f\u3082\u306e\u3067\u3059\u3002\u3053\u306e\u3068\u304d $\\mathrm{FOM} = 0.724$ \u3067\u3001\u672c\u8ad6\u6587\u306b\u3088\u308c\u3070\u3001\u3053\u306e\u5024\u306f\u5f93\u6765\u306e\u4eba\u9593\u304c\u624b\u63a2\u308a\u3067\u8a2d\u8a08\u3057\u3066\u5f97\u3089\u308c\u305fFOM\u3088\u308a\u3082\u5927\u304d\u306a\u5024\u3067\u3059\u3002\u3053\u306e\u3053\u3068\u304b\u3089\u3001FMQA\u306f\u4eba\u9593\u3088\u308a\u3082\u512a\u308c\u305f\u6027\u80fd\u3092\u3082\u3064\u6750\u6599\u63a2\u7d22\u6a5f\u3067\u3042\u308b\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n<p>\u3068\u3053\u308d\u3067\u3001\u4e0a\u56f3\u306b\u304a\u3044\u3066\u7070\u8272\u306e\u90e8\u5206\u306f\u3001\u201cPMMA\u201d (\u30dd\u30ea\u30e1\u30bf\u30af\u30ea\u30eb\u9178\u30e1\u30c1\u30eb\u3001\u30a2\u30af\u30ea\u30eb\u30ac\u30e9\u30b9\u3068\u547c\u3070\u308c\u308b\u900f\u660e\u306a\u30d7\u30e9\u30b9\u30c1\u30c3\u30af\u3067\u3001\u30a2\u30af\u30ea\u30eb\u677f\u3084\u773c\u93e1\u306e\u30ec\u30f3\u30ba\u306a\u3069\u5e45\u5e83\u304f\u7528\u3044\u3089\u308c\u308b) \u304c\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002$L=5$ \u3092\u8d85\u3048\u308b\u591a\u5c64\u69cb\u9020\u306b\u304a\u3044\u3066\u5b9f\u9a13\u306e\u7bc4\u56f2\u5185\u3067\u5f97\u3089\u308c\u305f\u6700\u9069\u69cb\u9020\u3092\u898b\u308b\u3068\u3001PMMA\u3060\u3051\u3067\u69cb\u6210\u3055\u308c\u305f\u5c64\u304c\u591a\u304f\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u5927\u898f\u6a21\u306a\u30e1\u30bf\u30de\u30c6\u30ea\u30a2\u30eb\u306e\u8a2d\u8a08\u306b\u304a\u3044\u3066\u306f\u3001\u96fb\u78c1\u6ce2\u3092\u307b\u3068\u3093\u3069\u900f\u904e\u3059\u308b\u7b87\u6240\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u4f55\u3089\u304b\u306e\u91cd\u8981\u306a\u5f79\u5272\u3092\u62c5\u3063\u3066\u3044\u308b\u306e\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n<div id=\"attachment_6944\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-6944\" src=\"\/T-Wave\/wp-content\/uploads\/2023\/12\/FMQA_5-300x300.png\" alt=\"$L=5$\u3001$C=6$ \u3067\u6700\u3082FOM\u304c\u9ad8\u3044\u8a2d\u8a08\u69cb\u9020\u306b\u3064\u3044\u3066\u3001RCWA\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u305f\u653e\u5c04\u5f37\u5ea6\uff08\u8d64\u7dda\uff09\u3001\u9ed2\u4f53\u653e\u5c04\u5f37\u5ea6\uff08\u9752\u7dda\uff09\u3001\u304a\u3088\u3073 $C=1$ \u3068\u3057\u3066\u540c\u69d8\u306e\u63a2\u7d22\u3092\u884c\u3063\u305f\u5834\u5408\uff08\u7070\u8272\u306e\u7dda\uff09\u306e\u653e\u5c04\u5f37\u5ea6\u3092\u6ce2\u9577\u306e\u95a2\u6570\u3068\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002\" width=\"300\" height=\"300\" class=\"size-medium wp-image-6944\" \/><p id=\"caption-attachment-6944\" class=\"wp-caption-text\">$L=5$\u3001$C=6$ \u3067\u6700\u3082FOM\u304c\u9ad8\u3044\u8a2d\u8a08\u69cb\u9020\u306b\u3064\u3044\u3066\u3001RCWA (\u53b3\u5bc6\u7d50\u5408\u6ce2\u89e3\u6790\u3001<span>\u5468\u671f\u7684\u306a\u69cb\u9020\u3092\u6271\u3046\u305f\u3081\u306b<\/span><span>\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u7528\u3044\u3066\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u6c42\u3081\u308b\u624b\u6cd5<\/span>) \u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u305f\u653e\u5c04\u5f37\u5ea6\uff08\u8d64\u7dda\uff09\u3001\u9ed2\u4f53\u653e\u5c04\u5f37\u5ea6\uff08\u9752\u7dda\uff09\u3001\u304a\u3088\u3073 $C=1$ \u3068\u3057\u3066\u540c\u69d8\u306e\u63a2\u7d22\u3092\u884c\u3063\u305f\u5834\u5408\uff08\u7070\u8272\u306e\u7dda\uff09\u306e\u653e\u5c04\u5f37\u5ea6\u3092\u6ce2\u9577\u306e\u95a2\u6570\u3068\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3002\u5143\u8ad6\u6587\u3088\u308a\u5f15\u7528\u3002<\/p><\/div>\n<p>\u3053\u306e\u56f3\u306f\u3001FOM\u304c\u6700\u5927\u3068\u306a\u3063\u305f $(L, C) = (5, 6)$ \u306b\u304a\u3051\u308b\u6700\u9069\u69cb\u9020\u306e\u653e\u5c04\u5f37\u5ea6\u3092\u56f3\u793a\u3057\u305f\u3082\u306e\u3067\u3059\u3002\u6ce2\u9577\u57df $8-13~\\mathrm{\\mu m}$ \u9818\u57df\u3067\u306f\u9ed2\u4f53\u306b\u8fd1\u304f\u3001\u305d\u308c\u4ee5\u5916\u306e\u9818\u57df\u3067\u306f\u653e\u5c04\u5f37\u5ea6\u304c\u307b\u307c $0$ \u306b\u306a\u308b\u3088\u3046\u306b\u8a2d\u8a08\u3067\u304d\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<!-- notionvc: fac9aa1b-795f-4b36-88e0-3bf4e0d9acd6 --><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u307e\u3068\u3081<!-- notionvc: 7d415e4b-ff60-4602-af4d-74f7136649f5 --><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u306e\u8ad6\u6587\u3067\u306f\u3001\u6975\u3081\u3066\u591a\u304f\u306e\u5019\u88dc\u306e\u4e2d\u304b\u3089\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u3088\u3063\u3066\u6700\u9069\u306a\u8a2d\u8a08\u56f3\u3092\u63a2\u7d22\u3059\u308b\u300c\u6750\u6599\u63a2\u7d22\u300d\u306b\u3001Factorization Machines \u3068\u3044\u3046\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u30de\u30b7\u30f3\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u65b0\u305f\u306a\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u624b\u6cd5\u3001\u300cFMQA\u300d\u304c\u63d0\u6848\u3055\u308c\u307e\u3057\u305f\u3002FMQA\u3092\u71b1\u6ce2\u9577\u9078\u629e\u578b\u30e1\u30bf\u30de\u30c6\u30ea\u30a2\u30eb\u306e\u8a2d\u8a08\u306b\u7528\u3044\u305f\u3068\u3053\u308d\u3001\u6700\u5927FOM\u3068\u3057\u3066 0.724 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class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<!-- notionvc: a013c2fb-36f7-4646-8f94-6fcd88576321 --><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6750\u6599\u79d1\u5b66\u306b\u95a2\u3059\u308b\u8ad6\u6587\u306e\u305f\u3081\u304b\u3001\u5c02\u9580\u7528\u8a9e\u304c\u8aac\u660e\u7121\u3057\u306b\u767b\u5834\u3059\u308b\u306e\u3067\u8aad\u3080\u306e\u306b\u5927\u5909\u82e6\u52b4\u3057\u307e\u3057\u305f\u304c\u3001\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u306e\u624b\u6cd5\u3068\u3057\u3066\u304b\u306a\u308a\u8208\u5473\u3092\u3082\u3063\u3066\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002FM\u306f\u52fe\u914d\u6cd5\u306b\u3088\u308b\u8a13\u7df4\u304c\u53ef\u80fd\u3067\u3042\u308a\u3001\u5927\u898f\u6a21\u306a\u554f\u984c\u306b\u5bfe\u3057\u3066\u3082\u4e26\u5217\u51e6\u7406\u306a\u3069\u3092\u99c6\u4f7f\u3057\u3066\u4ee3\u7406\u30e2\u30c7\u30eb\u306e\u8a13\u7df4\u304c\u3067\u304d\u308b\u306e\u304c1\u3064\u306e\u30e1\u30ea\u30c3\u30c8\u3067\u306f\u306a\u3044\u304b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\u3057\u304b\u3057\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3067\u306f\u306a\u304f\u30b7\u30df\u30e5\u30ec\u30fc\u30c6\u30c3\u30c9\u30fb\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3084\u305d\u306e\u4ed6\u306e\u30e1\u30bf\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u3092\u7528\u3044\u305f\u5834\u5408\u306b\u3064\u3044\u3066\u306e\u6027\u80fd\u8a55\u4fa1\u306f\u3042\u307e\u308a\u3057\u3063\u304b\u308a\u3068\u884c\u308f\u308c\u3066\u3044\u306a\u304b\u3063\u305f\u308a\u3001\u6bd4\u8f03\u5bfe\u8c61\u306e\u300c\u30ac\u30a6\u30b9\u904e\u7a0b\u300d\u3068\u3044\u3046\u6642\u306b\u30ab\u30fc\u30cd\u30eb\u95a2\u6570\u3068\u3057\u3066\u4f55\u3092\u7528\u3044\u305f\u306e\u304b\u3001\u30cf\u30a4\u30d1\u30fc\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3069\u3046\u3057\u305f\u306e\u304b\u306a\u3069\u306e\u60c5\u5831\u304c\u6b20\u843d\u3057\u3066\u3044\u308b\u306a\u3069\u3001\u6700\u9069\u5316\u624b\u6cd5\u3068\u3057\u3066\u306f\u8abf\u3079\u3089\u308c\u308b\u70b9\u304c\u591a\u304f\u3042\u308b\u3088\u3046\u306b\u601d\u3044\u307e\u3059\u3002\u4ed6\u306e\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u306e\u624b\u6cd5\u3068\u306e\u6bd4\u8f03\u3082\u8996\u91ce\u306b\u5165\u308c\u306a\u304c\u3089\u8abf\u67fb\u3092\u884c\u3063\u3066\u3044\u304f\u3068\u3001FMQA\u306e\u7279\u6027\u306b\u3064\u3044\u3066\u3082\u3063\u3068\u308f\u304b\u308b\u3053\u3068\u304c\u3042\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n<p>\u4eca\u5f8c\u306f\u3055\u3089\u306b\u3001\u3053\u306e\u624b\u6cd5\u304c\u3069\u306e\u3088\u3046\u306a\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u6700\u9069\u5316\u624b\u6cd5\u306b\u5bfe\u3057\u3066\u512a\u308c\u305f\u6027\u80fd\u3092\u767a\u63ee\u3059\u308b\u306e\u304b\u3001\u307e\u305f\u91cf\u5b50\u30a2\u30cb\u30fc\u30e9\u4ee5\u5916\u306e\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30af\u30b9\u3092\u5fdc\u7528\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u306a\u3069\u306b\u3064\u3044\u3066\u8abf\u3079\u308b\u3068\u3001\u3088\u308a\u53ef\u80fd\u6027\u304c\u5e83\u304c\u3063\u3066\u3044\u304f\u306e\u3067\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E4%BD%9C%E6%88%90%E8%80%85\"><\/span>\u672c\u8a18\u4e8b\u306e\u4f5c\u6210\u8005<!-- notionvc: e1a7359c-8d64-49c8-a179-cee7386c74c5 --><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u68ee\u7530\u572d\u7950<!-- notionvc: b95b0d83-ea8f-4062-ae2b-eab23c98190e --><\/p>\n<p><!-- notionvc: 9da6adc8-5046-4dd5-8bff-ed8e14204288 --><\/p>\n<p><!-- notionvc: e5a13838-1775-44d0-b978-e74b157caba3 --><\/p>\n<p><!-- notionvc: ebc5617b-7a7b-4de9-ab28-45afffaa88d2 --><\/p>\n<p><!-- notionvc: 69b4e169-446a-4680-b7ed-0d06ffabed4e --><\/p>\n<p><!-- notionvc: 737a0ec8-5d0b-40ce-b9f8-a50f817c3a7a --><\/p>\n<p><!-- notionvc: 89d98da0-afee-4212-b6df-a3d3a2ec865c --><\/p>\n<p><!-- notionvc: 518f3d5e-7e05-4d20-a764-255914c99412 --><\/p>\n<p><!-- notionvc: 5f45baf5-2860-4854-bd20-9e0a56777d08 --><\/p>\n<p><!-- notionvc: 9df6e0b9-8dd2-42c2-8b9b-616c8e41e2bd --><\/p>\n<p><!-- notionvc: 46035680-7044-4167-b186-16ab88f13421 --><\/p>\n<p><!-- notionvc: 346db1f0-5d9d-4f38-a377-9079eb57d3f9 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