{"id":8081,"date":"2025-10-10T10:08:17","date_gmt":"2025-10-10T01:08:17","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=8081"},"modified":"2025-10-10T10:16:19","modified_gmt":"2025-10-10T01:16:19","slug":"gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/","title":{"rendered":"GPT-QE : Transformer\u306b\u3088\u308b\u91cf\u5b50\u56de\u8def\u306e\u6700\u9069\u5316"},"content":{"rendered":"<div class=\"taxonomy-post_tag wp-block-post-terms\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/tag\/transformer\/\" rel=\"tag\">transformer<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/tag\/%e6%a9%9f%e6%a2%b0%e5%ad%a6%e7%bf%92\/\" rel=\"tag\">\u6a5f\u68b0\u5b66\u7fd2<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/tag\/%e9%87%8f%e5%ad%90%e5%8c%96%e5%ad%a6%e8%a8%88%e7%ae%97\/\" rel=\"tag\">\u91cf\u5b50\u5316\u5b66\u8a08\u7b97<\/a><\/div>\n\n\n<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\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%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\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%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\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%E8%83%8C%E6%99%AF\" >\u80cc\u666f<\/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\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#VQE_%E3%81%AE%E4%BB%95%E7%B5%84%E3%81%BF\" >VQE \u306e\u4ed5\u7d44\u307f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#VQE%E3%81%AE%E8%AA%B2%E9%A1%8C\" >VQE\u306e\u8ab2\u984c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%E6%89%8B%E6%B3%95\" >\u624b\u6cd5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#GQE\" >GQE<\/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\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#GPT-QE\" >GPT-QE<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#training\" >training<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#pre-training\" >pre-training<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%E5%AE%9F%E9%A8%93\" >\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-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%E5%90%84%E7%A8%AE%E8%A8%AD%E5%AE%9A\" >\u5404\u7a2e\u8a2d\u5b9a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#training-2\" >training<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#pre-training-2\" >pre-training<\/a><\/li><\/ul><\/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\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%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-16\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#Appendix\" >Appendix<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%E3%83%8F%E3%83%9F%E3%83%AB%E3%83%88%E3%83%8B%E3%82%A2%E3%83%B3%E3%81%8C%E3%83%91%E3%82%A6%E3%83%AA%E6%BC%94%E7%AE%97%E5%AD%90%E3%81%A7%E8%A1%A8%E3%81%9B%E3%82%8B%E7%90%86%E7%94%B1\" >\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u3067\u8868\u305b\u308b\u7406\u7531<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#UCCSD%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6\" >UCCSD\u306b\u3064\u3044\u3066<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%E5%9F%BA%E5%BA%95%E9%96%A2%E6%95%B0\" >\u57fa\u5e95\u95a2\u6570<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%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-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer%e3%81%ab%e3%82%88%e3%82%8b%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e3%81%ae%e6%9c%80%e9%81%a9%e5%8c%96\/#%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><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><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\n\n\n<ul class=\"wp-block-list\">\n<li>\u30bf\u30a4\u30c8\u30eb\uff1aThe generative quantum eigensolver (GQE) and its application for ground state search<\/li>\n\n\n\n<li>\u8457\u8005\uff1a<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Nakaji,+K\">Kouhei Nakaji<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Kristensen,+L+B\">Lasse Bj\u00f8rn Kristensen<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Campos-Gonzalez-Angulo,+J+A\">Jorge A. Campos-Gonzalez-Angulo<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Vakili,+M+G\">Mohammad Ghazi Vakili<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Huang,+H\">Haozhe Huang<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Bagherimehrab,+M\">Mohsen Bagherimehrab<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Gorgulla,+C\">Christoph Gorgulla<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Wong,+F\">FuTe Wong<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=McCaskey,+A\">Alex McCaskey<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Kim,+J\">Jin-Sung Kim<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Nguyen,+T\">Thien Nguyen<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Rao,+P\">Pooja Rao<\/a>,&nbsp;<a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Aspuru-Guzik,+A\">Alan Aspuru-Guzik<\/a><\/li>\n\n\n\n<li>\u66f8\u8a8c\u60c5\u5831(DOI)\uff1a<a href=\"https:\/\/doi.org\/10.48550\/arXiv.2401.09253\">https:\/\/doi.org\/10.48550\/arXiv.2401.09253<\/a><\/li>\n\n\n\n<li>\u51fa\u7248\u5e74\uff1a2024\/01 (Ver.1)\u3000<\/li>\n<\/ul>\n\n\n\n<p>\u203b \u672c\u8a18\u4e8b\u306f\u3001\u4e3b\u306b2024\u5e741\u6708\u306b\u516c\u958b\u3055\u308c\u305fVer.1\u306b\u57fa\u3065\u3044\u3066\u4f5c\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002arXiv\u306f2025\u5e749\u6708\u306bVer.2\u306b\u66f4\u65b0\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u308c\u306b\u4f75\u305b\u3066\u672c\u8a18\u4e8b\u3082\u66f4\u65b0\u3059\u308b\u4e88\u5b9a\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>VQE(Variational Quantum Eigensolver\/\u5909\u5206\u91cf\u5b50\u56fa\u6709\u5024\u30bd\u30eb\u30d0\u30fc)\u306f\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u5909\u5206\u539f\u7406\u3092\u7528\u3044\u3066\u57fa\u5e95\u72b6\u614b\u3092\u63a2\u7d22\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002VQE\u306fNISQ\u30c7\u30d0\u30a4\u30b9\u3067\u3082\u5b9f\u73fe\u53ef\u80fd\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u3001\u9577\u304d\u306b\u308f\u305f\u308a\u6ce8\u76ee\u3092\u6d74\u3073\u3066\u304d\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u30b9\u30b1\u30fc\u30e9\u30d3\u30ea\u30c6\u30a3\u3084\u91cf\u5b50\u8a08\u7b97\u8cc7\u6e90\u306e\u70b9\u3067\u6539\u5584\u306e\u4f59\u5730\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001\u53e4\u5178\u751f\u6210\u30e2\u30c7\u30eb\u3067\u3042\u308bTransformer \u3092\u7528\u3044\u3066\u91cf\u5b50\u56de\u8def\u3092\u6700\u9069\u5316\u3059\u308b\u65b0\u305f\u306a\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 GPT-QE\u3092\u63d0\u6848\u3057\u3066\u3044\u307e\u3059\u3002GPT-QE\u306f\u65e2\u5b58\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u305f\u4e8b\u524d\u5b66\u7fd2\u3068\u3001\u4e8b\u524d\u77e5\u8b58\u306a\u3057\u3067\u306e\u5b66\u7fd2\u306e\u53cc\u65b9\u306b\u3088\u308a\u3001\u91cf\u5b50\u8a08\u7b97\u30b3\u30b9\u30c8\u3092\u524a\u6e1b\u3057\u305f\u5b66\u7fd2\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u8ad6\u6587\u4e2d\u3067\u306f\u3001\u91cf\u5b50\u8a08\u7b97\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u7528\u3044\u3066GPT-QE\u306e\u5b9f\u8a3c\u5b9f\u9a13\u3092\u884c\u3044\u3001\u5206\u5b50\u306e\u57fa\u5e95\u72b6\u614b\u63a2\u7d22\u306b\u304a\u3051\u308bGPT-QE\u306e\u6709\u52b9\u6027\u3068\u4e8b\u524d\u5b66\u7fd2\u306b\u3088\u308b\u7cbe\u5ea6\u306e\u5411\u4e0a\u3092\u78ba\u8a8d\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF\"><\/span>\u80cc\u666f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u5f93\u6765\u306e\u57fa\u5e95\u72b6\u614b\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0VQE\u306e\u6982\u8981\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002VQE\u306f\u672c\u7814\u7a76\u3067\u63d0\u6848\u3059\u308bGPT-QE\u306e\u57fa\u3068\u306a\u3063\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3042\u308a\u3001GPT-QE\u306e\u91cd\u8981\u6027\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"VQE_%E3%81%AE%E4%BB%95%E7%B5%84%E3%81%BF\"><\/span>VQE \u306e\u4ed5\u7d44\u307f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>VQE(Variational Quantum Eigensolver\/\u5909\u5206\u91cf\u5b50\u56fa\u6709\u5024\u30bd\u30eb\u30d0\u30fc)\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 $\\hat H$\u306e\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc $E_0$\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u306e\u5206\u91ce\u3067\u306f\u3001\u5206\u5b50\u306e\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6c42\u3081\u308b\u305f\u3081\u306bVQE\u304c\u7528\u3044\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>VQE\u3067\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3(\u30a8\u30cd\u30eb\u30ae\u30fc)\u306e\u671f\u5f85\u5024 $E_N$\u3068\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc $E_0$\u306e\u9593\u306b\u6b21\u306e\u4e0d\u7b49\u5f0f\u304c\u6210\u7acb\u3059\u308b\u3053\u3068\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ E_N=\\bra{\\psi}\\hat H\\ket{\\psi}\\ge E_0 $$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001 $\\ket{\\psi}$\u304c\u57fa\u5e95\u72b6\u614b\u306e\u3068\u304d\u7b49\u53f7\u304c\u6210\u7acb\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u4ed8\u304d\u306e\u91cf\u5b50\u72b6\u614b $\\ket{\\psi(\\theta)}$\u3092\u7528\u610f\u3057\u3001\u305d\u308c\u3092$\\theta$\u306e\u66f4\u65b0\u306b\u3088\u308a\u57fa\u5e95\u72b6\u614b\u306b\u8fd1\u3065\u3051\u3066\u3044\u3051\u3070\u3001\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u8fd1\u4f3c\u7684\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u4ee5\u4e0b\u306e\u65b9\u6cd5\u3067\u5b9f\u88c5\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30d1\u30e9\u30e1\u30fc\u30bf\u4ed8\u304d\u306e\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50 $U(\\theta)$\u3092\u542b\u3080\u91cf\u5b50\u56de\u8def\u3092\u7528\u3044\u3066\u91cf\u5b50\u72b6\u614b $\\ket{\\psi(\\theta)}$\u3092\u7528\u610f\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $E_N(\\theta)$ \u306e\u52fe\u914d $\\frac{dE_N(\\theta)}{d\\theta}$\u3092\u6e2c\u5b9a\u3059\u308b<\/li>\n\n\n\n<li>\u52fe\u914d\u3092\u3082\u3068\u306b $\\theta$\u306e\u66f4\u65b0\u3092\u884c\u3046<\/li>\n\n\n\n<li>1-3\u3092\u6307\u5b9a\u56de\u6570\u5206\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"VQE%E3%81%AE%E8%AA%B2%E9%A1%8C\"><\/span>VQE\u306e\u8ab2\u984c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>VQE\u306f\u3001\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u304c\u4e0d\u5341\u5206\u306a\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u3042\u308bNISQ(Noisy Intermediate-Scale Quantum)\u30c7\u30d0\u30a4\u30b9\u3067\u3082\u5b9f\u884c\u53ef\u80fd\u306a\u512a\u308c\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u304c\u3001\u3044\u304f\u3064\u304b\u306e\u8ab2\u984c\u3092\u62b1\u3048\u3066\u3044\u307e\u3059\u3002\u307e\u305a\u3001\u91cf\u5b50\u8a08\u7b97\u8cc7\u6e90\u306e\u975e\u52b9\u7387\u6027\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002VQE\u3067\u306f $\\braket{\\hat H}$\u306e\u52fe\u914d\u306e\u6e2c\u5b9a\u306e\u305f\u3081\u306b\u5b9f\u969b\u306b\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u3092\u52d5\u304b\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u4e0d\u5b89\u5b9a\u306a\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u306e\u5b9f\u884c\u306f\u6700\u5c0f\u9650\u306b\u6291\u3048\u308b\u3053\u3068\u304c\u671b\u307e\u3057\u3044\u3067\u3059\u3002\u91cf\u5b50\u8a08\u7b97\u3092\u53e4\u5178\u8a08\u7b97\u3067\u52b9\u7387\u7684\u306b\u4ee3\u7528\u3059\u308b\u624b\u6cd5\u304c\u6c42\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u52a0\u3048\u3066\u3001\u5927\u898f\u6a21\u306a\u554f\u984c\u306b\u5bfe\u3057\u3066\u6027\u80fd\u3092\u767a\u63ee\u3067\u304d\u306a\u3044\u3001\u30b9\u30b1\u30fc\u30e9\u30d3\u30ea\u30c6\u30a3\u306e\u554f\u984c\u304c\u3042\u308a\u307e\u3059\u3002\u3042\u308b\u30b5\u30a4\u30ba\u3092\u8d85\u3048\u305f\u554f\u984c\u306b\u95a2\u3057\u3066\u3001\u53e4\u5178\u8a08\u7b97\u306b\u5bfe\u3059\u308b\u512a\u4f4d\u6027\u3092\u767a\u63ee\u3067\u304d\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%89%8B%E6%B3%95\"><\/span>\u624b\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u63d0\u6848\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u3001\u4e00\u822c\u306e\u53e4\u5178\u751f\u6210\u30e2\u30c7\u30eb\u3092\u7528\u3044\u308bGQE\u3068\u3001Transformer\u3092\u7528\u3044\u308bGPT-QE\u306e\u4e8c\u3064\u306b\u5206\u3051\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"GQE\"><\/span>GQE<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>GQE(Generative Quantum Eigensolver\/\u751f\u6210\u91cf\u5b50\u56fa\u6709\u5024\u30bd\u30eb\u30d0\u30fc)\u306f\u3001\u53e4\u5178\u751f\u6210\u30e2\u30c7\u30eb\u3092\u7528\u3044\u3066\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6c42\u3081\u308b\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u3053\u306e\u53e4\u5178\u751f\u6210\u30e2\u30c7\u30eb\u306f\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3057\u3001\u751f\u6210\u30e2\u30c7\u30eb\u5185\u90e8\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u8abf\u6574\u3059\u308b\u3053\u3068\u3067\u751f\u6210\u3055\u308c\u3084\u3059\u3044\u91cf\u5b50\u56de\u8def\u3092\u5909\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u57fa\u5e95\u72b6\u614b\u3092\u3064\u304f\u308b\u91cf\u5b50\u56de\u8def\u304c\u751f\u6210\u3055\u308c\u308b\u3088\u3046\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u767a\u898b\u3059\u308b\u3053\u3068\u304c\u3001\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u76ee\u6a19\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u5b9f\u969b\u306b\u306f\u4ee5\u4e0b\u306e\u624b\u9806\u3067\u5b66\u7fd2\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u53e4\u5178\u751f\u6210\u30e2\u30c7\u30eb\u3067\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b<\/li>\n\n\n\n<li>\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u4e0a\u3067\u91cf\u5b50\u56de\u8def\u3092\u5b9f\u884c\u3057\u3001\u91cf\u5b50\u72b6\u614b\u3092\u751f\u6210\u3059\u308b<\/li>\n\n\n\n<li>\u5f97\u3089\u308c\u305f\u91cf\u5b50\u72b6\u614b\u3092\u6e2c\u5b9a\u3057\u3001 $\\hat H$\u306e\u671f\u5f85\u5024 $E_N$\u3092\u6c42\u3081\u308b<\/li>\n\n\n\n<li>\u30b3\u30b9\u30c8\u95a2\u6570\u3092\u8a08\u7b97\u3057\u3001\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u3067\u53e4\u5178\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b<\/li>\n\n\n\n<li>1-4\u3092\u6307\u5b9a\u56de\u6570\u5206\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ol>\n\n\n\n<p>\u9069\u5207\u306a\u30b3\u30b9\u30c8\u95a2\u6570\u304c\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u308c\u3070\u3001\u751f\u6210\u30e2\u30c7\u30eb\u306e\u5b66\u7fd2\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u3088\u308a\u57fa\u5e95\u72b6\u614b\u306b\u8fd1\u3044\u91cf\u5b50\u72b6\u614b\u304c\u4f5c\u3089\u308c\u308b\u3053\u3068\u304c\u4e88\u60f3\u3055\u308c\u307e\u3059\u3002\u4ee5\u4e0a\u304cGQE\u306e\u6982\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<p>GQE\u3068VQE\u306e\u9055\u3044\u306f\u3001\u66f4\u65b0\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u53e4\u5178\u30e2\u30c7\u30eb\u5185\u306b\u3042\u308b\u304b\u3001\u91cf\u5b50\u56de\u8def\u5185\u306b\u3042\u308b\u304b\u3067\u6574\u7406\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5f93\u6765\u306eVQE\u304c\u30d1\u30e9\u30e1\u30fc\u30bf\u4ed8\u304d\u306e\u91cf\u5b50\u56de\u8def\u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u3066\u3044\u305f\u306e\u306b\u5bfe\u3057\u3001GQE\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u3042\u304f\u307e\u3067\u3082\u751f\u6210\u30e2\u30c7\u30eb\u5185\u306e\u3082\u306e\u3067\u3001\u91cf\u5b50\u56de\u8def\u81ea\u4f53\u306b\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u3064\u3044\u3066\u3044\u307e\u305b\u3093\u3002GQE\u3068VQE\u306e\u30a4\u30e1\u30fc\u30b8\u3092\u56f31\u306b\u793a\u3057\u307e\u3059\u3002VQE\u304c\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024$E$\u306e\u52fe\u914d\u3092\u7528\u3044\u3066\u91cf\u5b50\u56de\u8def\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u76f4\u63a5\u66f4\u65b0\u3057\u3066\u3044\u308b\u306e\u306b\u5bfe\u3057\u3001GQE\u3067\u306f\u30b3\u30b9\u30c8\u95a2\u6570 $C$(\u8a73\u3057\u304f\u306f\u5f8c\u8ff0\u3057\u307e\u3059)\u306e\u52fe\u914d\u3092\u7528\u3044\u3066\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b\u751f\u6210\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"690\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-2-1024x690.png\" alt=\"\" class=\"wp-image-8134\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-2-1024x690.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-2-300x202.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-2-768x517.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-2.png 1418w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f31. GQE\u3068VQE\u306e\u6bd4\u8f03\uff08Fig.1\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n<p>GQE\u306e\u5229\u70b9\u306f\u3001\u5358\u306b\u6df1\u5c64\u5b66\u7fd2\u306e\u77e5\u898b\u3092\u5fdc\u7528\u3067\u304d\u308b\u3068\u3044\u3046\u70b9\u3060\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002VQE\u3067\u91cf\u5b50\u8a08\u7b97\u3067\u5b9f\u884c\u3057\u3066\u3044\u305f\u52fe\u914d\u306e\u8a08\u7b97\u3092\u3001GQE\u3067\u306f\u53e4\u5178\u7684\u306a\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3068\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u3067\u4ee3\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001GQE\u3067\u306fVQE\u306b\u6bd4\u3079\u3066\u91cf\u5b50\u8a08\u7b97\u304c\u524a\u6e1b\u3055\u308c\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\u3002\u52a0\u3048\u3066\u3001\u5f93\u6765\u306f\u4eba\u9593\u304c\u884c\u3063\u3066\u3044\u305f\u91cf\u5b50\u56de\u8def\u306e\u8a2d\u8a08\u3092\u3001\u751f\u6210\u30e2\u30c7\u30eb\u304c\u81ea\u52d5\u3067\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u3044\u3046\u9577\u6240\u3082\u3042\u308a\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u4eba\u529b\u3067\u306f\u767a\u898b\u304c\u56f0\u96e3\u306a\u8907\u96d1\u306a\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3067\u304d\u308b\u53ef\u80fd\u6027\u3092\u79d8\u3081\u3066\u3044\u308b\u3068\u3044\u3046\u70b9\u3067\u3001GQE\u306f\u6709\u671b\u3060\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"GPT-QE\"><\/span>GPT-QE<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>GPT-QE(Generative Pre-trained Transformer-QE)\u306fGQE\u306e\u4e00\u7a2e\u3067\u3042\u308a\u3001\u751f\u6210\u30e2\u30c7\u30eb\u306bTransformer\u3092\u63a1\u7528\u3057\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u3053\u308c\u306f\u3001Transformer\u306b\u3088\u308b\u6587\u66f8\u751f\u6210\u3092\u53c2\u8003\u306b\u8a2d\u8a08\u3055\u308c\u3066\u304a\u308a\u3001\u91cf\u5b50\u56de\u8def\u306e\u69cb\u6210\u8981\u7d20\u3067\u3042\u308b\u30c8\u30fc\u30af\u30f3\u3092\u3072\u3068\u3064\u305a\u3064\u9078\u629e\u3057\u3066\u3044\u304f\u3053\u3068\u3067\u91cf\u5b50\u56de\u8def\u5168\u4f53\u306e\u751f\u6210\u3092\u5b9f\u73fe\u3057\u307e\u3059\u3002\u307e\u305f\u3001GPT-QE\u306fTransformer\u3092\u5229\u7528\u3057\u3066\u3044\u308b\u305f\u3081\u4e8b\u524d\u5b66\u7fd2\u304c\u53ef\u80fd\u3067\u3042\u308a\u3001\u904e\u53bb\u306b\u5b9f\u884c\u3057\u305fGPT-QE\u306e\u7d50\u679c\u3092\u53e4\u5178\u8a08\u7b97\u306e\u307f\u3067\u5f15\u304d\u7d99\u3050\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u5b9f\u969b\u306e\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>GPT<\/strong>\u3068<strong>Sample<\/strong>\u3092\u7e70\u308a\u8fd4\u3057\u3001\u91cf\u5b50\u56de\u8def\u30921\u30c8\u30fc\u30af\u30f3\u305a\u3064\u751f\u6210\u3059\u308b\n<ul class=\"wp-block-list\">\n<li><strong>GPT<\/strong>\uff1a1\u3064\u524d\u306e\u30c8\u30fc\u30af\u30f3\u307e\u3067\u306e\u91cf\u5b50\u56de\u8def\u3092Transformer\u306b\u5165\u529b\u3057\u3001\u78ba\u7387\u5206\u5e03\u3092\u51fa\u529b<\/li>\n\n\n\n<li><strong>Sample<\/strong>\uff1a\u78ba\u7387\u5206\u5e03\u306b\u57fa\u3065\u304d\u6b21\u306e\u30c8\u30fc\u30af\u30f3\u306e\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u30921\u3064\u9078\u629e<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u4e0a\u3067\u5b9f\u969b\u306b\u91cf\u5b50\u56de\u8def\u3092\u5b9f\u884c\u3059\u308b<\/li>\n\n\n\n<li>\u751f\u6210\u3055\u308c\u305f\u72b6\u614b\u3068\u57fa\u5e95\u72b6\u614b\u306e\u8fd1\u3055\u3092\u30b3\u30b9\u30c8\u95a2\u6570\u3067\u8a55\u4fa1\u3059\u308b<\/li>\n\n\n\n<li>\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b<\/li>\n\n\n\n<li>1-4\u306e\u30b5\u30a4\u30af\u30eb\u3092\u6307\u5b9a\u56de\u6570\u5206\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u3053\u3067\u767b\u5834\u3057\u305f<strong>GPT<\/strong>\u3068<strong>Sample<\/strong>\u306f\u3001\u672c\u8ad6\u6587\u4e2d\u3067\u72ec\u81ea\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570\u3067\u3059\u3002\u4ee5\u4e0b\u3067\u8a73\u7d30\u306b\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">GPT<\/h4>\n\n\n\n<p><strong>GPT<\/strong>\u306f\u3001\u5404\u30c8\u30fc\u30af\u30f3\u306b\u304a\u3051\u308b\u78ba\u7387\u5206\u5e03(\u6b63\u78ba\u306b\u306f\u78ba\u7387\u306e\u5bfe\u6570)\u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570\u3067\u3059\u3002\u307e\u305a\u3001\u5165\u529b $\\vec j^{(k)}$\u3068\u51fa\u529b $W^{(k)}$\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5165\u529b\uff1a $\\vec j^{(k)}=\\{0,j_1,\\dots,j_{k-1}\\}$ $\\vec j^{(k)}$\u306f\u7b2c $(k-1)$\u30c8\u30fc\u30af\u30f3\u307e\u3067\u306e\u91cf\u5b50\u56de\u8def\u3092\u6574\u6570\u5024\u306e\u5217\u3067\u8868\u3057\u305f\u3082\u306e\u3067\u3059\u3002\u3042\u3089\u304b\u3058\u3081\u7528\u610f\u3057\u305f\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u3092\u6574\u6570\u5024 $1,\\dots,L$\u3067\u30e9\u30d9\u30eb\u4ed8\u3051\u3057\u3066\u304a\u304d\u3001\u5404\u30c8\u30fc\u30af\u30f3\u306e\u6f14\u7b97\u5b50\u3092\u6574\u6570\u5024\u3067\u8868\u3059\u3053\u3068\u3067\u7b2c $(k-1)$\u30c8\u30fc\u30af\u30f3\u307e\u3067\u306e\u91cf\u5b50\u56de\u8def\u3092\u6570\u5217 $\\vec j^{(k)}$\u3068\u3057\u3066\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\u3002 \u306a\u304a\u3001\u7528\u610f\u3057\u305f\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u306e\u96c6\u5408\u3092\u6f14\u7b97\u5b50\u30d7\u30fc\u30eb $\\mathcal{G}$\u3068\u547c\u3073\u307e\u3059\u3002 $\\mathcal{G}$\u306e\u4e2d\u8eab\u306f\u3001\u91cf\u5b50\u56de\u8def\u3092\u5341\u5206\u306b\u8868\u73fe\u3067\u304d\u308b\u3088\u3046\u306b\u8a2d\u8a08\u8005\u304c\u3042\u3089\u304b\u3058\u3081\u7528\u610f\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u672c\u8ad6\u6587\u4e2d\u306e\u5b9f\u9a13\u3067\u306f\u3001\u65e2\u5b58\u306e\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u306e\u624b\u6cd5\u3092\u53c2\u8003\u306b\u6f14\u7b97\u5b50\u30d7\u30fc\u30eb $\\mathcal G$\u3092\u69cb\u6210\u3057\u307e\u3059\u304c\u3001\u3053\u306e\u3068\u304d $\\mathcal G$\u306b\u542b\u307e\u308c\u308b\u6f14\u7b97\u5b50\u306b\u306f\u4f8b\u3048\u3070\u56f32\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\u4e00\u822c\u306b\u3001 $\\mathcal G$ \u306e\u5143\u306f\u8907\u6570\u306e\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u3082\u306e\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002 <\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"443\" height=\"271\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-3.png\" alt=\"\" class=\"wp-image-8135\" style=\"width:460px;height:auto\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-3.png 443w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-3-300x184.png 300w\" sizes=\"auto, (max-width: 443px) 100vw, 443px\" \/><figcaption class=\"wp-element-caption\">\u56f32. \u6f14\u7b97\u5b50\u306e\u4f8b\uff08Ver.1\u306eFig.5\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>\u51fa\u529b\uff1a $W^{(k)}=\\{\\vec w^{(1)},\\dots,\\vec w^{(k)}\\}$ $W^{(k)}$\u306f\u3001\u5404\u30c8\u30fc\u30af\u30f3\u306b\u304a\u3044\u3066\u5404\u6f14\u7b97\u5b50\u304c\u9078\u629e\u3055\u308c\u308b\u78ba\u7387\u3092\u96c6\u3081\u305f\u3082\u306e\u3067\u3059\u3002\u5404\u6210\u5206 $\\vec w^{(i)}=(w^{(i)}_1,\\dots,w^{(i)}_L)$\u306f $L$\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\u3001\u7b2c $k$\u30c8\u30fc\u30af\u30f3\u306b\u304a\u3051\u308b\u5404\u6f14\u7b97\u5b50\u306e\u78ba\u7387\u5206\u5e03\u3068\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 $W^{(k)}$\u5168\u4f53\u306f $L\\times k$ \u306e\u884c\u5217\u3068\u306a\u308a\u307e\u3059\u3002 \u300c$\\vec w^{(i)}$\u304c\u78ba\u7387\u5206\u5e03\u300d\u3068\u3044\u3046\u8868\u73fe\u306b\u3064\u3044\u3066\u3001\u3082\u3046\u5c11\u3057\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002<strong>GPT<\/strong>\u306b\u7d9a\u3044\u3066\u5b9f\u884c\u3059\u308b\u95a2\u6570<strong>Sample<\/strong>\u306f\u3001\u7b2c $k$\u30c8\u30fc\u30af\u30f3\u306e\u6f14\u7b97\u5b50\u3092\u78ba\u7387\u5206\u5e03\u306b\u5f93\u3063\u3066\u4e00\u3064\u9078\u629e\u3059\u308b\u95a2\u6570\u3067\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u7b2c $k$\u30c8\u30fc\u30af\u30f3\u306b $i$\u756a\u76ee\u306e\u6f14\u7b97\u5b50\u304c\u9078\u629e\u3055\u308c\u308b\u78ba\u7387\u306f $\\exp(-\\beta w_i^{(k)})$\u306b\u6bd4\u4f8b\u3057\u307e\u3059\u3002\uff08\u8a73\u7d30\u306f<strong>Sample<\/strong>\u306e\u9805\u3067\u8aac\u660e\u3057\u307e\u3059\u3002\uff09\u3059\u306a\u308f\u3061\u3001 $w$\u306f\u78ba\u7387\u5206\u5e03\u305d\u306e\u3082\u306e\u3068\u3044\u3046\u3088\u308a\u3001\u78ba\u7387\u5206\u5e03\u306e\u5bfe\u6570(\u306b\u6bd4\u4f8b\u3059\u308b\u91cf)\u3068\u89e3\u91c8\u3059\u308b\u306e\u304c\u9069\u5207\u3067\u3059\u3002\u539f\u8ad6\u6587\u306f\u3053\u306e$w$\u3092logit\u3068\u547c\u3093\u3067\u3044\u307e\u3059\u304c\u3001\u78ba\u7387\u5206\u5e03\u306e\u5bfe\u6570\u4ee5\u4e0a\u306e\u610f\u5473\u306f\u7279\u306b\u6301\u305f\u306a\u3044\u3068\u601d\u308f\u308c\u307e\u3059\u3002 \u306a\u304a\u3001\u7b2c $k$\u30c8\u30fc\u30af\u30f3\u306e\u751f\u6210\u6642\u306b $\\vec w^{(k)}$\u4ee5\u5916\u306e\u6210\u5206 $\\vec w^{(1)}, \\dots, \\vec w^{(k-1)}$\u306f\u5fc5\u8981\u3042\u308a\u307e\u305b\u3093\u3002\u7b2c $1$ ~ $(k-1)$\u30c8\u30fc\u30af\u30f3\u306e $w$\u3082\u751f\u6210\u3055\u308c\u307e\u3059\u304c\u3001<strong>Sample<\/strong>\u306e\u5165\u529b\u306b\u7528\u3044\u3089\u308c\u308b\u306e\u306f\u6700\u5f8c\u306e\u6210\u5206\u306e\u307f\u3067\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5165\u529b\u3068\u51fa\u529b\u306f\u3001Transformer\u3092\u30d9\u30fc\u30b9\u3068\u3057\u305f\u8907\u6570\u306e\u4e2d\u9593\u5c64\u306b\u3088\u3063\u3066\u7d50\u3070\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u306b<strong>GPT<\/strong>\u306e\u5177\u4f53\u7684\u306a\u30e2\u30c7\u30eb\u69cb\u9020\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Embedding\u5c64<ul><li>\u5165\u529b\uff1a$\\vec j^{(k)}=\\{0,j_1,\\dots,j_{k-1}\\}$<\/li><li>\u51fa\u529b\uff1a$L\\times k$ \u884c\u5217 ($L$\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3092 $k$\u500b\u4e26\u3079\u305f\u3082\u306e)<\/li><\/ul>\u5165\u529b\u30c7\u30fc\u30bf\u3092\u6a5f\u68b0\u304c\u5b66\u7fd2\u3057\u3084\u3059\u3044\u5f62\u306b\u5909\u5f62\u3059\u308b\u305f\u3081\u306e\u5c64\u3067\u3059\u3002 \u6570\u5217 $\\vec j^{(k)}$\u306e\u5404\u6210\u5206 $1,\\dots,L$ \u3092\u3001\u72ec\u7acb\u306a $L$\u6b21\u5143\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5909\u63db\u3057\u307e\u3059\u3002\uff08\u5909\u63db\u51e6\u7406\u306e\u5177\u4f53\u7684\u306a\u65b9\u6cd5\u306b\u3064\u3044\u3066\u306f\u3001\u660e\u78ba\u306a\u8a18\u8ff0\u304c\u898b\u3064\u304b\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002\uff09<\/li>\n\n\n\n<li>Attention\u5c64(\u8907\u6570)<ul><li>\u5165\u529b\uff1a$L\\times k$ \u884c\u5217<\/li><li>\u51fa\u529b\uff1a$L\\times k$ \u884c\u5217<\/li><\/ul>\u91cf\u5b50\u56de\u8def\u5185\u306e\u6f14\u7b97\u5b50\u540c\u58eb\u306e\u4f9d\u5b58\u95a2\u4fc2\u3084\u9806\u5e8f\u306e\u91cd\u8981\u6027\u3092\u5b66\u7fd2\u3057\u3001\u3069\u306e\u6f14\u7b97\u5b50\u3092\u6b21\u306b\u914d\u7f6e\u3059\u3079\u304d\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306e\u5c64\u3067\u3059\u3002 Attention\u5c64\u306f\u8907\u6570\u7528\u610f\u3055\u308c\u307e\u3059\u304c\u3001\u3044\u305a\u308c\u306e\u5c64\u3082\u5165\u529b\u3068\u51fa\u529b\u306e\u5f62\u3092\u5909\u5316\u3055\u305b\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001Embedding\u5c64\u306e\u51fa\u529b\u3067\u3042\u308b $L\\times k$ \u884c\u5217\u306e\u5f62\u304c\u6700\u5f8c\u306eAttention\u5c64\u306e\u51fa\u529b\u307e\u3067\u4fdd\u305f\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u51fa\u529b\u5c64<ul><li>\u5165\u529b\uff1a$L\\times k$ \u884c\u5217<\/li><li>\u51fa\u529b\uff1a$W^{(k)}=\\{\\vec w^{(1)},\\dots,\\vec w^{(k)}\\}$<\/li><\/ul>\u6b21\u306e<strong>Sample<\/strong>\u95a2\u6570\u306e\u5165\u529b\u3068\u306a\u308b $\\vec w^{(k)}$\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u5c64\u3067\u3059\u3002\u3053\u3053\u3067\u306f\u4fbf\u5b9c\u4e0a\u300c\u51fa\u529b\u5c64\u300d\u3068\u540d\u4ed8\u3051\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u306e\u5c64\u3082Attention\u5c64\u306e\u4e00\u3064\u3067\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4ee5\u4e0a\u304c<strong>GPT<\/strong>\u306e\u30e2\u30c7\u30eb\u69cb\u9020\u3067\u3059\u3002\u5b66\u7fd2\u3092\u884c\u3046\u3068\u304d\u306f\u3001\u5404Attention\u5c64\u306e\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec\\theta$\u3092\u66f4\u65b0\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u5b9f\u969b\u306b\u306f\u8907\u6570\u306eAttention\u6a5f\u69cb\u3092\u4e26\u5217\u3067\u52d5\u304b\u3059Multi-head Attention\u3092\u63a1\u7528\u3059\u308b\u3053\u3068\u304c\u591a\u304f\u3001\u305d\u306e\u5834\u5408\u30e2\u30c7\u30eb\u69cb\u9020\u306f\u3082\u3046\u5c11\u3057\u8907\u96d1\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u57fa\u672c\u7684\u306a\u4ed5\u7d44\u307f\u306f\u3053\u3053\u3067\u8aac\u660e\u3057\u305f\u3082\u306e\u3068\u540c\u3058\u3067\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Sample<\/h4>\n\n\n\n<p><strong>Sample<\/strong>\u306f\u3001<strong>GPT<\/strong>\u3067\u6c42\u3081\u305f\u78ba\u7387\u5206\u5e03\u3092\u3082\u3068\u306b\u6b21\u306e\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u30921\u3064\u78ba\u5b9a\u3055\u305b\u308b\u95a2\u6570\u3067\u3059\u3002\u5165\u529b\u3068\u51fa\u529b\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5165\u529b\uff1a $\\vec w^{(k)}=(w_1^{(k)},\\dots,w_L^{(k)})^T$ <br><strong>GPT<\/strong>\u306e\u51fa\u529b $W^{(k)}=\\{\\vec w^{(1)},\\dots,\\vec w^{(k)}\\}$\u306e\u3046\u3061\u3001 \u7b2c $k$ \u30c8\u30fc\u30af\u30f3\u306e\u78ba\u7387\u5206\u5e03\u3092\u8868\u3059$\\vec w^{(k)}$\u3092\u5165\u529b\u306b\u53d6\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u51fa\u529b\uff1a $j_k\\in\\{1,\\dots,L\\}$ <br>\u7b2c $k$ \u30c8\u30fc\u30af\u30f3\u306e\u6f14\u7b97\u5b50\u3092\u3001 $1,\\dots,k$ \u306e\u6574\u6570\u5024\u3067\u8868\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u305d\u3057\u3066\u3001\u7b2c $k$ \u30c8\u30fc\u30af\u30f3\u3067\u6f14\u7b97\u5b50 $i\\in\\{1,\\dots,L\\}$\u3092\u6307\u5b9a\u3059\u308b\u78ba\u7387\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ p=\\frac{\\exp(-\\beta w_i^{(k)})}{\\sum_l \\exp(-\\beta w_l^{(k)})} $$<\/p>\n\n\n\n<p>$i$\u756a\u76ee\u306e\u6f14\u7b97\u5b50\u3092\u6307\u5b9a\u3059\u308b\u78ba\u7387\u306f $\\exp(-\\beta w_i^{(k)})$\u306b\u6bd4\u4f8b\u3059\u308b\u305f\u3081\u3001 \u5bfe\u5fdc\u3059\u308b$w$\u306e\u5024\u304c\u5c0f\u3055\u3044\u6f14\u7b97\u5b50\u307b\u3069\u9078\u3070\u308c\u3084\u3059\u3044\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u5206\u6bcd\u306f\u898f\u683c\u5316\u5b9a\u6570\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u65b0\u3057\u304f\u5c0e\u5165\u3057\u305f $\\beta$\u306f\u9006\u6e29\u5ea6\u3068\u547c\u3070\u308c\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308a\u3001\u5206\u5e03\u306e\u92ed\u3055\u3092\u8868\u3057\u307e\u3059\u3002 \u4e0b\u56f3\u304b\u3089\u3082\u5206\u304b\u308b\u3088\u3046\u306b\u3001$\\beta$\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069\u3001\u5c0f\u3055\u3044 $w$\u304c\u3088\u308a\u96c6\u4e2d\u7684\u306b\u9078\u629e\u3055\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 $\\beta$\u306f\u30cf\u30a4\u30d1\u30fc\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308a\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u5ea6\u306b\u5916\u304b\u3089\u81ea\u7531\u306b\u5024\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u56f33\u306b\u3001\u5b9f\u969b\u306b10000\u500b\u306e\u30c7\u30fc\u30bf\u3092\u3053\u306e\u78ba\u7387\u5206\u5e03\u306b\u3057\u305f\u304c\u3063\u3066\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u305f\u7d50\u679c\u3092\u793a\u3057\u307e\u3059\u3002 $\\beta$ \u304c\u5927\u304d\u3044\u307b\u3069\u5206\u5e03\u304c\u92ed\u304f\u306a\u308a\u3001 \u5c0f\u3055\u3044 $w$ \u304c\u96c6\u4e2d\u7684\u306b\u9078\u629e\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u306a\u304a\u3001\u3053\u306e\u78ba\u7387\u5206\u5e03\u306f\u30ab\u30ce\u30cb\u30ab\u30eb\u5206\u5e03\u3092\u53c2\u8003\u306b\u4eba\u5de5\u7684\u306b\u8a2d\u8a08\u3055\u308c\u305f\u3082\u306e\u3067\u3042\u308a\u3001\u5c0e\u51fa\u3067\u304d\u308b\u3082\u306e\u3067\u306f\u306a\u3044\u70b9\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"275\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-4-1024x275.png\" alt=\"\" class=\"wp-image-8136\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-4-1024x275.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-4-300x80.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-4-768x206.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-4-1536x412.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-4.png 1790w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f33. \u9006\u6e29\u5ea6\u03b2\u3068\u78ba\u7387\u5206\u5e03\u306e\u95a2\u4fc2\uff08\u7b46\u8005\u4f5c\u6210\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u3053\u3053\u307e\u3067\u306e\u8a2d\u5b9a\u3092\u7528\u3044\u3066\u3001\u91cf\u5b50\u56de\u8def\u5168\u4f53\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u78ba\u7387\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3042\u308b\u91cf\u5b50\u56de\u8def $\\vec j=\\{j_1,\\dots,j_k\\}$\u304c\u751f\u6210\u3055\u308c\u308b\u78ba\u7387\u306f\u3001\u5404\u30c8\u30fc\u30af\u30f3\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u78ba\u7387\u306e\u7a4d\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081<\/p>\n\n\n\n<p>$$ \\prod_{k=1}^N \\exp(-\\beta w_{j_k}^{(k)})=\\exp\\Bigg(-\\beta\\sum_{k=1}^N w_{j_k}^{(k)}\\Bigg)=\\exp(-\\beta w_{\\mathrm{sum}}(\\vec{j}))$$<\/p>\n\n\n\n<p>\u306b\u6bd4\u4f8b\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u3042\u308b\u91cf\u5b50\u56de\u8def $\\vec j$\u306b\u5bfe\u3057\u3066\u3001\u5404\u30c8\u30fc\u30af\u30f3\u306e\u6f14\u7b97\u5b50\u306b\u5bfe\u5fdc\u3059\u308b $w$\u3092\u8db3\u3057\u5408\u308f\u305b\u305f\u91cf $w_\\mathrm{sum}$\u3092\u5b9a\u7fa9\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>$$ w_\\mathrm{sum}(\\vec j)=\\sum_{k=1}^Nw_{j_k}^{(k)} $$<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u91cf\u5b50\u56de\u8def $\\vec j$\u304c\u751f\u6210\u3055\u308c\u308b\u78ba\u7387\u306f<\/p>\n\n\n\n<p>$$ p_N(\\beta,\\vec{j})=\\frac{\\exp(-\\beta w_\\mathrm{sum}(\\vec{j}))}{\\sum_{\\vec{j}}\\exp(-\\beta w_\\mathrm{sum}(\\vec{j}))}=\\frac{\\exp(-\\beta w_\\mathrm{sum}(\\vec{j}))}{\\mathcal{Z}} $$<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5b9f\u969b\u306e\u6d41\u308c<\/h4>\n\n\n\n<p>\u4ee5\u4e0a\u3067\u8aac\u660e\u3057\u305f\u4e8c\u3064\u306e\u95a2\u6570 <strong>GPT<\/strong>\u3068<strong>Sample<\/strong>\u3092\u7e70\u308a\u8fd4\u3057\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u3001\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e00\u9023\u306e\u6d41\u308c\u3092\u5177\u4f53\u7684\u306b\u8ffd\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6700\u521d\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u5165\u529b\u5217 $\\{0\\}$\u3092\u7528\u3044\u3066\u7b2c$1$\u30c8\u30fc\u30af\u30f3 $j_1$\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p>$$ W^{(1)}=\\mathrm{GPT}(\\{0\\})\u3000\\to\u3000\\vec w^{(1)}=W_1^{(1)}\u3000\\to\u3000 j_1 = \\mathrm{Sample}(\\vec w^{(1)}) $$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e8c\u756a\u76ee\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u5165\u529b\u5217 $\\{0,j_1\\}$\u3092\u7528\u3044\u3066\u7b2c$2$\u30c8\u30fc\u30af\u30f3 $j_2$\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u307e\u3059\u3002 $$ W^{(2)}=\\mathrm{GPT}(\\{0,j_1\\})\u3000\\to\u3000\\vec w^{(2)}=W_2^{(2)}\u3000\\to\u3000 j_2 = \\mathrm{Sample}(\\vec w^{(2)}) $$<\/li>\n\n\n\n<li>$k$\u756a\u76ee\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001 $\\{0,j_1,\\dots,j_{k-1}\\}$\u3092\u7528\u3044\u3066\u7b2c $k$\u30c8\u30fc\u30af\u30f3 $j_k$\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u307e\u3059\u3002 $$ W^{(k)}=\\mathrm{GPT}(\\{0,j_1,\\dots,j_{k-1}\\})\u3000\\to\u3000\\vec w^{(k)}=W_k^{(k)}\\to\u3000 j_k = \\mathrm{Sample}(\\vec w^{(k)}) $$<\/li>\n\n\n\n<li>\u3042\u3089\u304b\u3058\u3081\u6307\u5b9a\u3057\u305f\u91cf\u5b50\u56de\u8def\u306e\u9577\u3055\u306b\u5230\u9054\u3057\u305f\u3089\u3001\u30eb\u30fc\u30d7\u3092\u505c\u6b62\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"training\"><\/span>training<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p><strong>GPT<\/strong>\u3068<strong>Sample<\/strong>\u3092\u7e70\u308a\u8fd4\u3057\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u3001\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u4eca\u5ea6\u306f\u751f\u6210\u3055\u308c\u305f\u91cf\u5b50\u56de\u8def\u3092\u8a55\u4fa1\u3057\u3001\u3088\u308a\u826f\u3044\u56de\u8def\u304c\u751f\u6210\u3055\u308c\u308b\u3088\u3046\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u66f4\u65b0\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u66f4\u65b0\u65b9\u6cd5\u306b\u306f\u3001\u5b9f\u969b\u306b\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u3092\u52d5\u304b\u3057\u3066\u884c\u3046training\u3068\u3001\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3067\u4ee3\u7528\u3059\u308bpre-training\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u7bc0\u3067\u306f\u524d\u8005\u306etraining\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>training\u5168\u4f53\u306e\u6d41\u308c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u53e4\u5178\u751f\u6210\u30e2\u30c7\u30eb\u3067\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b<\/li>\n\n\n\n<li>\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u4e0a\u3067\u91cf\u5b50\u56de\u8def\u3092\u5b9f\u884c\u3057\u3001\u91cf\u5b50\u72b6\u614b\u3092\u751f\u6210\u3059\u308b<\/li>\n\n\n\n<li>\u5f97\u3089\u308c\u305f\u91cf\u5b50\u72b6\u614b\u3092\u6e2c\u5b9a\u3057\u3001 $\\hat H$\u306e\u671f\u5f85\u5024$E_N$\u3092\u6c42\u3081\u308b<\/li>\n\n\n\n<li>\u30b3\u30b9\u30c8\u95a2\u6570\u3092\u8a08\u7b97\u3057\u3001\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u3067\u53e4\u5178\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b<\/li>\n\n\n\n<li>1-4\u3092\u6307\u5b9a\u56de\u6570\u5206\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ol>\n\n\n\n<p>\u524d\u7bc0\u3067\u306f1. \u3092\u8aac\u660e\u3057\u305f\u306e\u3067\u3001\u4ee5\u4e0b\u3067\u306f2\u304b\u30895\u306e\u5177\u4f53\u7684\u306a\u624b\u9806\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u91cf\u5b50\u72b6\u614b\u306e\u751f\u6210\u3068\u671f\u5f85\u5024\u306e\u6e2c\u5b9a<\/h4>\n\n\n\n<p>training\u3067\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024\u3092\u5b9f\u969b\u306e\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u3092\u7528\u3044\u3066\u6e2c\u5b9a\u3057\u307e\u3059\u3002\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3055\u308c\u305f\u91cf\u5b50\u56de\u8def $\\vec j$ \u3092\u5b9f\u969b\u306b\u751f\u6210\u3057\u305f\u3082\u306e\u3092 $U_N(\\vec j)$\u3068\u8868\u3059\u3053\u3068\u306b\u3059\u308b\u3068\u3001\u521d\u671f\u72b6\u614b $\\rho_0$\u306f<\/p>\n\n\n\n<p>$$ \\rho_0\\to U_N(\\vec j)\\rho_0 U_N(\\vec j)^\\dagger $$<\/p>\n\n\n\n<p>\u306e\u3088\u3046\u306b\u5909\u5316\u3057\u307e\u3059\u3002\u5909\u5316\u5f8c\u306e\u72b6\u614b\u306b\u3064\u3044\u3066\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 $\\hat H$\u306e\u6e2c\u5b9a\u3092\u7e70\u308a\u8fd4\u3057\u884c\u3046\u3053\u3068\u3067\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $E_N$\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u521d\u671f\u72b6\u614b\u306f\u56fa\u5b9a\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u3042\u3089\u304b\u3058\u3081\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u4f4e\u3044\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u308b\u72b6\u614b\u3092\u521d\u671f\u72b6\u614b\u306b\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u3001\u6700\u7d42\u7684\u306b\u5f97\u3089\u308c\u308b\u671f\u5f85\u5024\u304c\u3088\u308a\u4f4e\u304f\u306a\u308a\u3084\u3059\u304f\u308b\u3053\u3068\u304c\u4e88\u60f3\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u672c\u8ad6\u6587\u4e2d\u3067\u884c\u308f\u308c\u308b\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u3067\u306f\u3001Hartree-Fock\u6cd5\u3092\u8a08\u7b97\u3057\u3066\u5f97\u3089\u308c\u308bHartree-Fock\u72b6\u614b\u304c\u521d\u671f\u72b6\u614b\u306b\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u30b3\u30b9\u30c8\u95a2\u6570<\/h4>\n\n\n\n<p>\u6e2c\u5b9a\u3057\u305f\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $E_N$\u3092\u3082\u3068\u306b\u3001\u30b3\u30b9\u30c8\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u7d50\u8ad6\u304b\u3089\u8ff0\u3079\u308b\u3068\u3001\u30b3\u30b9\u30c8\u95a2\u6570 $C$\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ C\\Big(\\{w_\\mathrm{sum}(\\vec j_m)\\}_{m=1}^M,\\{E_N(\\vec j_m)_{m=1}^M\\}\\Big)=\\frac{1}{M}\\sum_{m=1}^M\\bigg[\\exp\\big(-w_\\mathrm{sum}(\\vec j_m)\\big)-\\exp\\big(-E_N(\\vec j_m)\\big)\\bigg]^2 $$<\/p>\n\n\n\n<p>\u30b3\u30b9\u30c8\u95a2\u6570 $C$ \u306f\u3001 $M$\u500b\u306e\u91cf\u5b50\u56de\u8def\u305d\u308c\u305e\u308c\u306b\u304a\u3051\u308b $w_\\mathrm{sum}$\u3068 $E_N$\u3092\u5f15\u6570\u306b\u6301\u3064\u95a2\u6570\u3068\u306a\u308a\u307e\u3059\u3002$w_\\mathrm{sum}$ \u306f Transformer\u306e\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec\\theta$ \u306b\u4f9d\u5b58\u3059\u308b\u306e\u3067\u3001 $C$ \u306f\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec\\theta$ \u306b\u3082\u4f9d\u5b58\u3057\u307e\u3059\u3002\u5f0f\u4e2d\u306e $\\exp\\big(-w_\\mathrm{sum}(\\vec j_m)\\big)-\\exp\\big(-E_N(\\vec j_m)\\big)$\u306e\u90e8\u5206\u306f\u3001 $w_\\mathrm{sum}$\u3068 $E_N$\u306e\u8fd1\u3055\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002(\u305d\u308c\u305e\u308c\u306e\u6307\u6570\u3092\u3068\u3063\u305f\u5f62\u3067\u5b9a\u7fa9\u3059\u308b\u7406\u7531\u306b\u3064\u3044\u3066\u306f\u3001\u660e\u78ba\u306a\u8a18\u8ff0\u304c\u898b\u3064\u304b\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002)<\/p>\n\n\n\n<p>\u3053\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u5b9a\u7fa9\u304c\u63a1\u7528\u3055\u308c\u305f\u7406\u7531\u3092\u4ee5\u4e0b\u3067\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u306f\u3001\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c\u304c\u5b9f\u73fe\u3059\u3079\u304d\u5024\u304b\u3089\u3069\u308c\u3060\u3051\u96e2\u308c\u3066\u3044\u308b\u304b\u3092\u8868\u3059\u95a2\u6570\u3067\u3059\u3002\u30e2\u30c7\u30eb\u306e\u5b66\u7fd2\u306f\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u5024\u3092\u5c0f\u3055\u304f\u3059\u308b\u65b9\u5411\u306b\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b\u3053\u3068\u3067\u5b9f\u73fe\u3055\u308c\u307e\u3059\u3002GPT-QE\u306b\u304a\u3051\u308b\u30b3\u30b9\u30c8\u95a2\u6570\u306f\u3001\u751f\u6210\u3057\u305f\u91cf\u5b50\u72b6\u614b\u304c\u3069\u308c\u3060\u3051\u57fa\u5e95\u72b6\u614b\u306b\u8fd1\u3044\u304b\u3092\u8868\u3059\u95a2\u6570\u3067\u3042\u308a\u3001Transformer\u5185\u90e8\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u3069\u306e\u3088\u3046\u306b\u66f4\u65b0\u3059\u308b\u304b\u3092\u6c7a\u5b9a\u3065\u3051\u308b\u91cf\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u524d\u7bc0\u3067\u8aac\u660e\u3057\u305f\u901a\u308a\u3001\u3042\u308b\u91cf\u5b50\u56de\u8def $\\vec j$ \u304c\u751f\u6210\u3055\u308c\u308b\u78ba\u7387\u306f<\/p>\n\n\n\n<p>$$ p_N(\\beta,\\vec j)=\\frac{\\exp(-\\beta w_\\mathrm{sum}(\\vec j))}{\\mathcal{Z}} $$<\/p>\n\n\n\n<p>\u3067\u8868\u305b\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u5b66\u7fd2\u3092\u59cb\u3081\u308b\u524d\u306eTransformer\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u307f\u307e\u3059\u3002Transformer\u5185\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u30e9\u30f3\u30c0\u30e0\u3067\u3042\u308b\u305f\u3081\u3001<strong>GPT<\/strong>\u306e\u51fa\u529b $W^{(k)}=\\{\\vec w^{(1)},\\dots,\\vec w^{(k)}\\}$\u3082\u5404\u6210\u5206\u304c\u30e9\u30f3\u30c0\u30e0\u306a\u5024\u3092\u53d6\u308a\u307e\u3059\u3002\u3086\u3048\u306b $p_N(\\beta,\\vec j)$\u306f\u30e9\u30f3\u30c0\u30e0\u306a\u78ba\u7387\u5206\u5e03\u3068\u306a\u308a\u3001\u76ee\u7684\u3067\u3042\u308b $E_N$\u304c\u4f4e\u3044\u56de\u8def $\\vec j$ \u306e\u751f\u6210\u78ba\u7387\u304c\u9ad8\u304f\u306a\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>\u4e00\u65b9\u3001\u4eee\u306b\u4efb\u610f\u306e $\\vec j$\u306b\u3064\u3044\u3066 $w_\\mathrm{sum}(\\vec j)=E_N(\\vec j)$\u304c\u6210\u7acb\u3059\u308b\u306a\u3089\u3070\u3001\u78ba\u7387\u5206\u5e03\u306f<\/p>\n\n\n\n<p>$$ p_N(\\beta,\\vec j)=\\frac{\\exp(-\\beta E_N(\\vec j))}{\\mathcal{Z}} $$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5f0f\u306f\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024\u304c\u4f4e\u3044\u91cf\u5b50\u56de\u8def\u307b\u3069\u751f\u6210\u3055\u308c\u3084\u3059\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u7406\u60f3\u7684\u306a\u78ba\u7387\u5206\u5e03\u306e\u4e00\u3064\u3067\u3042\u308a\u3001 $\\beta$\u3092\u5927\u304d\u304f\u3057\u3066\u5206\u5e03\u3092\u6025\u5cfb\u306b\u3059\u308c\u3070\u975e\u5e38\u306b\u9ad8\u3044\u78ba\u7387\u3067\u6700\u4f4e\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3082\u5206\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306f\u30e9\u30f3\u30c0\u30e0\u306a $w_\\mathrm{sum}(\\vec j)$\u3092\u3001\u7406\u60f3\u7684\u306a\u72b6\u6cc1\u3067\u3042\u308b $w_\\mathrm{sum}(\\vec j)=E_N(\\vec j)$\u306b\u8fd1\u3065\u3051\u3066\u3044\u304f\u3053\u3068\u304c\u3001Transformer\u3092\u5b66\u7fd2\u3059\u308b\u3046\u3048\u3067\u306e\u57fa\u672c\u7684\u306a\u65b9\u91dd\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u306e\u8003\u5bdf\u304b\u3089\u3001\u4e8c\u3064\u306e\u5206\u5e03 $w_\\mathrm{sum}(\\vec j)$\u3068 $E_N(\\vec j)$\u306e\u8fd1\u3055\u3092\u8868\u3059\u95a2\u6570\u3092\u3001\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308c\u3070\u3088\u3044\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u5b9f\u969b\u306b\u306f\u8003\u3048\u5f97\u308b\u5168\u3066\u306e\u91cf\u5b50\u56de\u8def $\\vec j$\u306b\u3064\u3044\u3066\u5024\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u305d\u3053\u3067\u3001<strong>GPT<\/strong>\u3067\u51fa\u529b\u3055\u308c\u305f $M$\u500b\u306e\u91cf\u5b50\u56de\u8def $\\vec j$ \u306e\u5834\u5408\u306e\u307f\u306b\u3064\u3044\u3066\u8a08\u7b97\u3057\u3001\u305d\u306e\u5e73\u5747\u3092\u53d6\u308b\u3053\u3068\u3067\u30b3\u30b9\u30c8\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u66f4\u65b0<\/h4>\n\n\n\n<p>\u30b3\u30b9\u30c8\u95a2\u6570\u3092\u8a08\u7b97\u3057\u305f\u5f8c\u306f\u3001<strong>GPT<\/strong>\u5185\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u306b\u3088\u308a\u66f4\u65b0\u3057\u307e\u3059\u3002\u30b3\u30b9\u30c8\u95a2\u6570\u306f\u3001\u300c $w_\\mathrm{sum}(\\vec j)$\u306e\u5206\u5e03\u3068 $E_N(\\vec j)$\u306e\u5206\u5e03\u306e\u8fd1\u3055\u300d\u3092\u8868\u3059\u95a2\u6570\u3067\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u30d1\u30e9\u30e1\u30fc\u30bf $w$\u3092\u30b3\u30b9\u30c8\u95a2\u6570 $C$\u304c\u5c0f\u3055\u304f\u306a\u308b\u65b9\u5411\u306b\u8abf\u6574\u3059\u308b\u3053\u3068\u3067\u3001\u6b21\u306e\u30b5\u30a4\u30af\u30eb\u3067\u5f97\u3089\u308c\u308b\u671f\u5f85\u5024\u3092\u3088\u308a\u5c0f\u3055\u304f\u3059\u308b\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u7528\u3044\u308b\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u306f\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u3092\u4f7f\u308f\u305a\u306b\u5b9f\u884c\u53ef\u80fd\u306a\u53e4\u5178\u8a08\u7b97\u306a\u306e\u3067\u3001\u91cf\u5b50\u30ea\u30bd\u30fc\u30b9\u306e\u524a\u6e1b\u306b\u7e4b\u304c\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u52a0\u3048\u3066\u3001<strong>Sample<\/strong>\u95a2\u6570\u5185\u306e\u30d1\u30e9\u30e1\u30fc\u30bf $\\beta$ \u3082\u66f4\u65b0\u3057\u307e\u3059\u3002\u5148\u8ff0\u306e\u901a\u308a\u3001<strong>Sample<\/strong>\u95a2\u6570\u306b\u3088\u308a\u91cf\u5b50\u56de\u8def $\\vec j$\u304c\u9078\u629e\u3055\u308c\u308b\u78ba\u7387\u306f\u3001$\\mathcal{Z}$\u3092\u898f\u683c\u5316\u5b9a\u6570\u3068\u3057\u3066<\/p>\n\n\n\n<p>$$ p_N(\\beta,\\vec{j})=\\frac{\\exp(-\\beta w_\\mathrm{sum}(\\vec{j}))}{\\sum_{\\vec{j}}\\exp(-\\beta w_\\mathrm{sum}(\\vec{j}))}=\\frac{\\exp(-\\beta w_\\mathrm{sum}(\\vec{j}))}{\\mathcal{Z}} $$<\/p>\n\n\n\n<p>\u306b\u5f93\u3044\u307e\u3059\u3002\u5f0f\u3092\u898b\u308b\u3068\u3001$\\beta$\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069 $w_\\mathrm{sum}(\\vec j)$\u304c\u5c0f\u3055\u3044 $\\vec j$\u304c\u9078\u3070\u308c\u3084\u3059\u304f\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u6975\u7aef\u306a\u5834\u5408\u3092\u898b\u308b\u3068\u3001 $\\beta\\to\\infty$\u306e\u3068\u304d\u306f $w_\\mathrm{sum}(\\vec j)$\u304c\u6700\u5c0f\u3068\u306a\u308b $\\vec j$\u3060\u3051\u304c\u9078\u3070\u308c\u308b\u3053\u3068\u3082\u5206\u304b\u308a\u307e\u3059\u3002 \u5b66\u7fd2\u521d\u671f\u306e\u6bb5\u968e\u3067\u306f$w_\\mathrm{sum}(\\vec j)$\u306f\u307e\u3060\u30e9\u30f3\u30c0\u30e0\u306a\u306e\u3067\u3001$\\beta$\u3092\u5927\u304d\u304f\u3057\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u304c\u3001 $w_\\mathrm{sum}(\\vec j)$\u3068 $E_N(\\vec j)$\u304c\u8fd1\u3065\u304f\u306b\u3064\u308c $\\beta$\u3092\u5927\u304d\u304f\u3057\u3066\u3044\u304f\u3053\u3068\u306f\u3001\u6700\u5c0f\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u63a2\u7d22\u3059\u308b\u3046\u3048\u3067\u6709\u52b9\u306a\u6226\u7565\u3068\u306a\u308b\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u307e\u3059\u3002\u30d1\u30e9\u30e1\u30fc\u30bf$w$\u304c\u30b3\u30b9\u30c8\u95a2\u6570 $C$\u306b\u57fa\u3065\u3044\u3066\u81ea\u52d5\u3067\u66f4\u65b0\u3055\u308c\u308b\u4e00\u65b9\u3001\u30d1\u30e9\u30e1\u30fc\u30bf $\\beta$\u306f\u4eba\u9593\u304c\u624b\u52d5\u3067\u8abf\u6574\u3059\u308b\u30cf\u30a4\u30d1\u30fc\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3069\u306e\u3088\u3046\u306a\u52a0\u6e1b\u3067 $\\beta$\u3092\u5927\u304d\u304f\u3057\u3066\u3044\u304f\u304b\u306f\u81ea\u7531\u306b\u6c7a\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u5f8c\u8ff0\u3059\u308b\u672c\u8ad6\u6587\u4e2d\u306e\u5b9f\u9a13\u3067\u306f\u6bce\u56de\u306e\u30b5\u30a4\u30af\u30eb\u3067 $\\beta$\u3092\u4e00\u5b9a\u306e\u5024\u305a\u3064\u5897\u3084\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4e8c\u3064\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u66f4\u65b0\u3092\u884c\u3063\u305f\u5f8c\u306f\u3001\u307e\u305f<strong>GPT<\/strong>\u3068<strong>Sample<\/strong>\u3067\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u306b\u623b\u308a\u307e\u3059\u3002\u91cf\u5b50\u56de\u8def\u306e\u751f\u6210\u2192\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u66f4\u65b0\u306e\u30b5\u30a4\u30af\u30eb\u3092\u6307\u5b9a\u56de\u6570\u3060\u3051\u5b9f\u884c\u3057\u305f\u3089\u3001\u6700\u5f8c\u306e\u30b5\u30a4\u30af\u30eb\u306e\u91cf\u5b50\u56de\u8def\u3092\u51fa\u529b\u7d50\u679c\u3068\u3057\u3066GPT-QE\u3092\u7d42\u4e86\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306ftraining\u306e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8\u3067\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"662\" height=\"871\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-5.png\" alt=\"\" class=\"wp-image-8137\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-5.png 662w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-5-228x300.png 228w\" sizes=\"auto, (max-width: 662px) 100vw, 662px\" \/><figcaption class=\"wp-element-caption\">\u56f34. training\u306e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8\uff08\u7b46\u8005\u4f5c\u6210\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pre-training\"><\/span>pre-training<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>pre-training\u306f\u3001\u3042\u3089\u304b\u3058\u3081\u7528\u610f\u3057\u305f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3067\u5b66\u7fd2\u3092\u884c\u3046\u65b9\u6cd5\u3067\u3059\u3002\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\mathcal D$ \u306f\u3001\u91cf\u5b50\u56de\u8def $\\vec j$\u3068\u5bfe\u5fdc\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $E_N$\u304b\u3089\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\mathcal D=\\{\\vec j_m,E_N(\\vec j)\\} $$<\/p>\n\n\n\n<p>training\u3067\u306f\u5b9f\u969b\u306b\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u3092\u7528\u3044\u305f\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $E_N$\u306e\u6e2c\u5b9a\u304c\u5fc5\u8981\u3068\u306a\u308b\u306e\u306b\u5bfe\u3057\u3001pre-training\u3067\u306f\u904e\u53bb\u306etraining\u306e\u7d50\u679c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u53e4\u5178\u8a08\u7b97\u306e\u307f\u3067\u5b66\u7fd2\u3092\u5b8c\u7d50\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u7684\u306a\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\{\\vec j_m, E_N(\\vec j_m)\\}$\u3092\u8aad\u307f\u8fbc\u3080<\/li>\n\n\n\n<li>$\\vec j$ \u3092<strong>GPT<\/strong>\u306b\u5165\u529b\u3057\u3001 $w_\\mathrm{sum}(\\vec j_m)$\u3092\u8a08\u7b97\u3059\u308b<\/li>\n\n\n\n<li>\u30b3\u30b9\u30c8\u95a2\u6570 $C$\u3092\u8a08\u7b97\u3059\u308b<\/li>\n\n\n\n<li>\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b<\/li>\n\n\n\n<li>1-4\u3092\u5168\u30c7\u30fc\u30bf\u306e\u5b66\u7fd2\u304c\u5b8c\u4e86\u3059\u308b\u307e\u3067\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ol>\n\n\n\n<p>\u30b3\u30b9\u30c8\u95a2\u6570 $C(w_\\mathrm{sum}(\\vec j), E_N(\\vec j))$\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u60c5\u5831\u306f $w_\\mathrm{sum}(\\vec j)$\u3068 $E_N(\\vec j)$\u3067\u3042\u308a\u3001 $w_\\mathrm{sum}(\\vec j)$\u306f<strong>GPT<\/strong>\u306b\u3088\u3063\u3066\u3001 $E_N(\\vec j)$\u306f<strong>Sample<\/strong>\u3068\u5b9f\u969b\u306b\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u3092\u7528\u3044\u305f\u6e2c\u5b9a\u306b\u3088\u3063\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001pre-training\u3067\u8aad\u307f\u8fbc\u3080\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u306f\u65e2\u306b\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $E_N(\\vec j)$\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u305f\u3081\u3001<strong>Sample<\/strong>\u3068\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u3092\u7528\u3044\u305f\u6e2c\u5b9a\u306f\u7701\u7565\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4e0b\u306b\u793a\u3059pre-training\u306e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8\u3092training\u306e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8\u3068\u6bd4\u8f03\u3059\u308b\u3068\u3001pre-training\u3067\u306f<strong>Sample<\/strong>\u3068\u91cf\u5b50\u6e2c\u5b9a\u304c\u7701\u7565\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"833\" height=\"887\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-6.png\" alt=\"\" class=\"wp-image-8138\" style=\"width:497px;height:auto\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-6.png 833w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-6-282x300.png 282w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-6-768x818.png 768w\" sizes=\"auto, (max-width: 833px) 100vw, 833px\" \/><figcaption class=\"wp-element-caption\">\u56f35. pre-training\u306e\u30d5\u30ed\u30fc\u30c1\u30e3\u30fc\u30c8\uff08\u7b46\u8005\u4f5c\u6210\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">\u5177\u4f53\u7684\u306a\u65b9\u6cd5<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Model-to-model transfer scenario <\/strong><br>\u5168\u304f\u540c\u3058\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u5bfe\u3057\u3066\u904e\u53bb\u306b\u30c7\u30fc\u30bf\u3092\u96c6\u3081\u3066\u3044\u305f\u5834\u5408\u306f\u3001 $\\vec j, E_N(\\vec j)$ \u3092\u305d\u306e\u307e\u307e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3068\u3057\u3066\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u3001\u4f8b\u3048\u3070\u30e2\u30c7\u30eb\u3092\u6539\u5584\u3057\u305f\u3044\u5834\u5408\u306b\u7528\u3044\u3089\u308c\u307e\u3059\u3002\u30e2\u30c7\u30eb GPT-A \u3092\u7528\u3044\u3066\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 $\\hat H$ \u306b\u5bfe\u3059\u308b\u5b66\u7fd2\u3092\u884c\u3063\u305f\u3082\u306e\u306e\u3001\u3088\u308a\u512a\u308c\u305f\u30e2\u30c7\u30eb GPT-B \u3092\u4f7f\u3044\u305f\u304f\u306a\u3063\u305f\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u540c\u4e00\u3067\u3042\u308c\u3070\u3001GPT-A\u3067\u5f97\u3089\u308c\u305f $\\vec j, E_N(\\vec j)$\u3092\u305d\u306e\u307e\u307eGPT-B\u306epre-training\u306b\u7528\u3044\u3066\u5b66\u7fd2\u3092\u5f15\u304d\u7d99\u3050\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30e2\u30c7\u30eb\u3092\u5909\u3048\u305a\u3001GPT-A\u3067\u3055\u3089\u306b\u5b66\u7fd2\u3092\u884c\u3044\u305f\u304f\u306a\u3063\u305f\u3068\u304d\u306b\u3082\u3053\u306e\u65b9\u6cd5\u304c\u6d3b\u7528\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>Config-to-config transfer scenario <\/strong><br>\u904e\u53bb\u306b\u5165\u624b\u3057\u305f $\\vec j, E_N(\\vec j)$ \u3092pre-training\u306b\u305d\u306e\u307e\u307e\u5229\u7528\u3067\u304d\u308b\u306e\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u540c\u4e00\u3067\u3042\u308b\u5834\u5408\u306b\u9650\u3089\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3042\u308b\u5de5\u592b\u3092\u52a0\u3048\u308b\u3053\u3068\u3067\u3001\u7570\u306a\u308b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304b\u3089\u5165\u624b\u3057\u305f\u30c7\u30fc\u30bf\u3092\u4e8b\u524d\u5b66\u7fd2\u306b\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002Config-to-config transfer scenario\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u69cb\u9020\u306f\u540c\u3058\u3067\u3042\u308a\u3001\u5404\u9805\u306e\u4fc2\u6570\u3060\u3051\u304c\u7570\u306a\u308b\u5834\u5408\u306b\u7528\u3044\u3089\u308c\u308b\u65b9\u6cd5\u3067\u3059\u3002 \u3053\u3053\u3067\u306f\u5206\u304b\u308a\u3084\u3059\u3055\u306e\u305f\u3081\u3001\u4e00\u3064\u306e\u5177\u4f53\u4f8b\u3068\u3057\u3066\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u306e\u4e00\u7a2e\u3067\u3042\u308b\u5206\u5b50\u306e\u57fa\u5e95\u72b6\u614b\u63a2\u7d22\u3092\u53d6\u308a\u4e0a\u3052\u307e\u3059\u3002\u307e\u305a\u3001\u5206\u5b50\u306b\u304a\u3051\u308b1\u96fb\u5b50\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u3001 $$ \\hat H=\\sum_a^{N_H}h_a\\hat P_a $$ \u306e\u3088\u3046\u306b\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d $\\hat P_a$ \u306e\u7dda\u5f62\u7d50\u5408\u3067\u8868\u305b\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u3053\u306e\u5206\u5b50\u306e\u539f\u5b50\u9593\u8ddd\u96e2\u3084\u7d50\u5408\u89d2\u3092\u5909\u66f4\u3057\u305f\u3068\u304d\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u69cb\u9020\u3092\u4fdd\u3063\u305f\u307e\u307e\u4fc2\u6570 $h_a$\u3060\u3051\u3092\u5909\u3048\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u539f\u5b50\u306e\u914d\u7f6e\u306e\u60c5\u5831\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u96c6\u5408 $\\vec \\Delta$ \u3068\u8868\u3059\u3053\u3068\u306b\u3059\u308c\u3070\u3001 $$ \\hat H(\\vec\\Delta)=\\sum_a^{N_H}h_a(\\vec\\Delta)\\hat P_a $$ \u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002Config-to-config transfer scenario\u3067\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 $\\hat H(\\vec\\Delta)$\u3067\u5f97\u305f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u3001\u4fc2\u6570\u304c\u5909\u5316\u3057\u305f\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 $\\hat H(\\vec\\Delta&#8217;)$ \u306epre-training\u306b\u7528\u3044\u308b\u65b9\u6cd5\u3092\u63d0\u6848\u3057\u307e\u3059\u3002 \u4e00\u3064\u76ee\u306e\u65b9\u6cd5\u306fcoefficient re-weighting\u3067\u3059\u3002\u307e\u305a\u3001\u91cf\u5b50\u56de\u8def $\\vec j$ \u306b\u5bfe\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u671f\u5f85\u5024 $E_N(\\vec\\Delta,\\vec j)$\u306f <br>$$ <br>\\begin{align}<br>E_N(\\vec\\Delta,\\vec j)<br>&amp;=\\mathrm{Tr}(\\hat H(\\vec \\Delta)U_N(\\vec j)\\rho_0U_N(\\vec j)^\\dagger)\\\\ <br>&amp;=\\mathrm{Tr}\\bigg(\\sum_a^{N_H}h_a(\\vec\\Delta)\\hat P_aU_N(\\vec j)\\rho_0U_N(\\vec j)^\\dagger\\bigg)\\\\ <br>&amp;=\\sum_a^{N_H}h_a(\\vec\\Delta)\\mathrm{Tr}(\\hat P_aU_N(\\vec j)\\rho_0U_N(\\vec j)^\\dagger) <br>\\end{align}<br>$$ <br>\u3068\u8868\u305b\u307e\u3059\u3002\u3053\u3053\u3067\u3001 $q_a(\\vec j)$\u3092 <br>$$ q_a(\\vec j)=\\mathrm{Tr}(\\hat P_aU_N(\\vec j)\\rho_0U_N(\\vec j)^\\dagger) $$ <br>\u3068\u5b9a\u7fa9\u3059\u308b\u3068\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024\u306f <br>$$ E_N(\\vec\\Delta,\\vec j)=\\sum_a^{N_H}h_a(\\vec\\Delta)q_a(\\vec j) $$ <br>\u3068\u66f8\u3051\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002 $q_a(\\vec j)$\u306f\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec\\Delta$\u306b\u3088\u3089\u306a\u3044\u91cf\u306a\u306e\u3067\u3001\u524d\u3082\u3063\u3066 $\\hat H(\\vec\\Delta)$\u306etraining\u3067 $q_a(\\vec j)$\u3092\u6c42\u3081\u3066\u304a\u3051\u3070\u3001\u65b0\u3057\u3044\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec\\Delta&#8217;$\u306b\u5bfe\u3059\u308b\u4fc2\u6570 $h_a(\\vec \\Delta&#8217;)$\u3068\u7d50\u5408\u3059\u308b\u3053\u3068\u3067 $E_N(\\vec\\Delta&#8217;)$\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001 $\\vec\\Delta&#8217;$\u306b\u5bfe\u5fdc\u3059\u308b\u91cf\u5b50\u6e2c\u5b9a\u3092\u5b9f\u969b\u306b\u884c\u308f\u306a\u304f\u3066\u3082\u3001\u9593\u63a5\u7684\u306b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8 $\\{\\vec j,E_N(\\vec\\Delta&#8217;,\\vec j)\\}$\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u3082\u3046\u4e00\u3064\u306e\u65b9\u6cd5\u306f\u3001<strong>GPT<\/strong>\u306e\u62e1\u5f35\u3067\u3059\u3002\u5f93\u6765\u306e<strong>GPT<\/strong>\u306f\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u306e\u5217 $\\{j_1,\\dots,j_k\\}$\u3092\u5165\u529b\u306b\u53d6\u308a\u307e\u3059\u304c\u3001\u65b0\u305f\u306b\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec\\Delta$\u3092\u5165\u529b\u306b\u52a0\u3048\u308b\u3053\u3068\u3067\u3001 $\\vec\\Delta$\u3082\u542b\u3081\u305f\u5b66\u7fd2\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306f <br>$$ \\mathcal D=\\{\\mathcal D_r\\}_{r=1}^R,\\quad \\mathcal D_r=\\{\\vec\\Delta_r, \\vec j_{m_r}, E_N(\\vec\\Delta_r,\\vec j_{m_r})\\}_{m_r=1}^{M_r} $$ <br>\u306e\u3088\u3046\u306b\u7528\u610f\u3057\u307e\u3059\u3002<\/li>\n\n\n\n<li><strong>Molecule-to-molecule transfer scenario <\/strong><br>\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u69cb\u9020\u81ea\u4f53\u304c\u7570\u306a\u308b\u5834\u5408\u3001\u3059\u306a\u308f\u3061\u7570\u306a\u308b\u5206\u5b50\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u306f\u30e2\u30c7\u30eb\u306b\u5927\u304d\u306a\u62e1\u5f35\u3092\u52a0\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u8ab2\u984c\u304c\u591a\u304f\u5177\u4f53\u7684\u306a\u65b9\u6cd5\u306f\u8003\u6848\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E9%A8%93\"><\/span>\u5b9f\u9a13<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>4\u3064\u306e\u5206\u5b50(H\u2082\u3001LiH\u3001BeH\u2082\u3001N\u2082)\u306e\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u63a2\u7d22\u306bGPT-QE\u3092\u9069\u7528\u3057\u3001\u5b9f\u969b\u306btraining\u3068pre-training\u304c\u6709\u52b9\u3067\u3042\u308b\u3053\u3068\u3092\u691c\u8a3c\u3057\u307e\u3059\u3002\u3053\u306e\u5b9f\u9a13\u3067\u306f\u5b9f\u969b\u306e\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u306f\u7528\u3044\u305a\u3001\u4ee3\u308f\u308a\u306b\u53e4\u5178\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306b\u3088\u308b\u91cf\u5b50\u8a08\u7b97\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%90%84%E7%A8%AE%E8%A8%AD%E5%AE%9A\"><\/span>\u5404\u7a2e\u8a2d\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u8a2d\u5b9a<\/h4>\n\n\n\n<p>\u5206\u5b50\u5168\u4f53\u306e\u96fb\u5b50\u7cfb\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 $\\hat H$ \u306f\u3001\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d $\\hat P$ \u306e\u7dda\u5f62\u7d50\u5408\u3067<\/p>\n\n\n\n<p>$$ \\hat H(\\vec \\Delta)=\\sum_lh_l(\\vec\\Delta)\\hat P_l $$<\/p>\n\n\n\n<p>\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30d1\u30e9\u30e1\u30fc\u30bf $\\vec\\Delta$ \u306f\u539f\u5b50\u306e\u914d\u7f6e\u3092\u8868\u73fe\u3059\u308b\u5024\u3067\u3042\u308a\u3001\u4f8b\u3048\u3070\u539f\u5b50\u9593\u306e\u8ddd\u96e2\u304c\u7528\u3044\u3089\u308c\u307e\u3059\u3002\u539f\u5b50\u9593\u8ddd\u96e2\u304c\u7570\u306a\u308b\u540c\u4e00\u306e\u5206\u5b50\u3067\u3042\u308c\u3070\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u4fc2\u6570\u306e\u307f\u304c\u5909\u5316\u3057\u307e\u3059\u3002\u306a\u304a\u3001\u4f7f\u7528\u3059\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u3084\u6f14\u7b97\u5b50 $\\hat P$\u306e\u7a2e\u985e\u3001\u4fc2\u6570 $h$ \u306e\u5024\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u306f\u5177\u4f53\u7684\u306a\u6ce2\u52d5\u95a2\u6570\u306e\u5f62\u304c\u5fc5\u8981\u3067\u3059\u3002\u3053\u306e\u5b9f\u9a13\u3067\u306fsto-3g\u3068\u547c\u3070\u308c\u308b\u57fa\u5e95\u95a2\u6570\u3067\u6ce2\u52d5\u95a2\u6570\u3092\u8fd1\u4f3c\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6f14\u7b97\u5b50\u306e\u8a2d\u5b9a<\/h4>\n\n\n\n<p>\u6f14\u7b97\u5b50\u30d7\u30fc\u30eb $\\mathcal G$ \u306f\u3001\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50 $\\exp(-i\\hat Pt)$\u306e\u96c6\u5408\u3068\u3057\u3066\u69cb\u6210\u3057\u307e\u3059\u3002 $\\hat P$ \u306f\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u3067\u3001 $t$ \u306f $\\pm2^k\/160\\,(k=1,2,3,4)$\u306e\u3044\u305a\u308c\u304b\u306e\u5024\u3092\u53d6\u308b\u5b9f\u6570\u3067\u3059\u3002\u3053\u306e\u6f14\u7b97\u5b50\u306f\u3001\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u306e\u4ee3\u8868\u7684\u306a\u624b\u6cd5\u3067\u3042\u308bUCCSD(\u30e6\u30cb\u30bf\u30ea\u7d50\u5408\u30af\u30e9\u30b9\u30bf\u5358\u4e00\u30fb\u4e8c\u91cd\u52b1\u8d77)\u3092\u3082\u3068\u306b\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002UCCSD\u3067\u306f\u3001\u96fb\u5b50\u306e\u52b1\u8d77\u3092\u8868\u3059\u6f14\u7b97\u5b50 $\\hat T$ \u3092\u7528\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u5f0f\u306b\u57fa\u3065\u304d\u521d\u671f\u72b6\u614b $\\ket{\\psi_\\mathrm{HF}}$\u304b\u3089\u91cf\u5b50\u72b6\u614b $\\ket{\\psi_\\mathrm{CC}}$\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ \\ket{\\psi_\\mathrm{CC}}=e^{\\hat T-\\hat T^\\dagger}\\ket{\\psi_\\mathrm{HF}} $$<\/p>\n\n\n\n<p>$\\ket{\\psi_\\mathrm{CC}}$\u304c\u57fa\u5e95\u72b6\u614b\u306b\u8fd1\u3065\u304f\u3088\u3046\u306b\u3001\u6f14\u7b97\u5b50 $\\hat T$ \u5185\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6700\u9069\u5316\u3059\u308b\u3053\u3068\u3067\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6c42\u3081\u307e\u3059\u3002\u3053\u306e\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50 $e^{\\hat T-\\hat T^\\dagger}$\u306f\u3001Trotter\u5206\u89e3\u3084Jordan-Wigner\u5909\u63db\u306b\u3088\u3063\u3066\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d $\\hat P$ \u306e\u7dda\u5f62\u7d50\u5408\u3067\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ e^{\\hat T-\\hat T^\\dagger}\\simeq\\prod _k \\exp(-i\\hat P_k t_k) $$<\/p>\n\n\n\n<p>\u5206\u89e3\u5f8c\u306e\u5f62 $\\exp(-i\\hat Pt)$\u306f\u7c21\u5358\u306a\u91cf\u5b50\u56de\u8def\u3067\u8868\u305b\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u304a\u308a\u3001\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4e0a\u3067\u5b9f\u969b\u306b\u5b9f\u884c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f36\u306b\u305d\u306e\u4e00\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"687\" height=\"283\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-7.png\" alt=\"\" class=\"wp-image-8146\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-7.png 687w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-7-300x124.png 300w\" sizes=\"auto, (max-width: 687px) 100vw, 687px\" \/><figcaption class=\"wp-element-caption\">\u56f36. \u91cf\u5b50\u30b2\u30fc\u30c8exp(-iPt)\u306e\u4e00\u4f8b\uff08Ver.1\u306eFig.5\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u4eca\u56de\u306e\u5b9f\u9a13\u3067\u306f\u3001UCCSD\u306b\u767b\u5834\u3059\u308b\u6f14\u7b97\u5b50 $\\exp(-i\\hat Pt)$\u3092\u7528\u3044\u3066GPT-QE\u3092\u5b9f\u884c\u3057\u307e\u3059\u304c\u3001\u52d5\u4f5c\u539f\u7406\u81ea\u4f53\u306fUCCSD\u3068\u306f\u7570\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\u3002UCCSD\u3067\u306f\u6f14\u7b97\u5b50 $\\hat T$ \u306e\u6700\u9069\u5316\u3092\u884c\u3046\u4e00\u65b9\u3001\u4eca\u56de\u306e\u5b9f\u9a13\u3067\u306f<strong>GPT<\/strong>\u95a2\u6570\u5185\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5909\u66f4\u3059\u308b\u3068\u3044\u3046\u9055\u3044\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u74b0\u5883<\/h4>\n\n\n\n<p>\u4eca\u56de\u306e\u5b9f\u9a13\u3067\u306f\u3001\u5b9f\u969b\u306e\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u4f7f\u7528\u305b\u305a\u3001\u4ee3\u308f\u308a\u306b CUDA Quantum \u30e9\u30a4\u30d6\u30e9\u30ea\u306b\u3088\u308b\u91cf\u5b50\u8a08\u7b97\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u884c\u3044\u307e\u3059\u3002\u8a08\u7b97\u74b0\u5883\u306e\u8a73\u7d30\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8a08\u7b97\u6a5f\u30b7\u30b9\u30c6\u30e0\uff1a<a href=\"https:\/\/www.nersc.gov\/what-we-do\/computing-for-science\/perlmutter\">Perlmutter<\/a>\n<ul class=\"wp-block-list\">\n<li>\u7c73\u56fd\u306eNERSC(\u56fd\u7acb\u30a8\u30cd\u30eb\u30ae\u30fc\u7814\u7a76\u79d1\u5b66\u8a08\u7b97\u30bb\u30f3\u30bf\u30fc)\u306b\u8a2d\u7f6e\u3055\u308c\u305f\u30b9\u30fc\u30d1\u30fc\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>GPU\uff1aNVIDIA A100<\/li>\n\n\n\n<li>\u91cf\u5b50\u8a08\u7b97\u30b7\u30df\u30e5\u30ec\u30fc\u30bf\u30fc\uff1a<a href=\"https:\/\/github.com\/NVIDIA\/cuda-quantum\">CUDA Quantum<\/a><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u305d\u306e\u4ed6<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Transformer\u30e2\u30c7\u30eb\u306fGPT-2\u3068\u540c\u3058\u8a2d\u5b9a\u304c\u63a1\u7528\u3055\u308c\u3066\u304a\u308a\u300112\u679a\u306eattention\u5c64\u300112\u500b\u306eattention head\u3001768\u6b21\u5143\u306eembedding\u5c64\u304b\u3089\u306a\u308a\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u521d\u671f\u72b6\u614b $\\rho_0$ \u306fHartree-Fock\u72b6\u614b\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002Hartree-Fock\u72b6\u614b\u306fHartree-Fock\u6cd5\u306b\u3088\u308a\u5f97\u3089\u308c\u308b\u72b6\u614b\u3067\u3042\u308a\u3001\u7cbe\u5ea6\u306f\u4f4e\u3044\u3082\u306e\u306e\u57fa\u5e95\u72b6\u614b\u306b\u8fd1\u3044\u72b6\u614b\u3092\u4f4e\u30b3\u30b9\u30c8\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002Hartre-Fock\u72b6\u614b\u304b\u3089\u8a08\u7b97\u3092\u958b\u59cb\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u65e9\u304fGPT-QE\u306b\u3088\u308b\u57fa\u5e95\u72b6\u614b\u3092\u6c42\u3081\u3089\u308c\u308b\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u307e\u3059\u3002<\/li>\n\n\n\n<li>\u8a08\u7b97\u306e\u5b89\u5b9a\u6027\u3092\u4e0a\u3052\u308b\u305f\u3081\u3001\u30b3\u30b9\u30c8\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u969b\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $E_N(\\vec j)$ \u306e\u4ee3\u308f\u308a\u306b\u30aa\u30d5\u30bb\u30c3\u30c8\u3092\u8ffd\u52a0\u3057\u305f $E_N(\\vec j)+E_\\mathrm{offset}$\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002$E_\\mathrm{offset}$\u306e\u5024\u306f\u5206\u5b50\u3054\u3068\u306b\u7570\u306a\u308a\u3001H\u2082\u3001LiH\u3001BeH\u2082\u3001N\u2082\u306b\u5bfe\u3057\u305d\u308c\u305e\u308c 0, 7, 14, 106 Hartree\u3068\u3057\u3066\u3044\u307e\u3059(1 Hartree = 27.211 eV)\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"training-2\"><\/span>training<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>H\u2082\u3001LiH\u3001BeH\u2082\u3001N\u2082\u305d\u308c\u305e\u308c\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u57fa\u5e95\u72b6\u614b\u63a2\u7d22\u3092\u3001training\u3092\u7528\u3044\u3066\u5b9f\u884c\u3057\u307e\u3059\u3002\u8a73\u7d30\u306a\u6761\u4ef6\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>H\u2082\n<ul class=\"wp-block-list\">\n<li>\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\uff1a4<\/li>\n\n\n\n<li>\u30b9\u30c6\u30c3\u30d7\u6570\uff1a50<\/li>\n\n\n\n<li>1\u30b9\u30c6\u30c3\u30d7\u5f53\u305f\u308a\u306e\u30b5\u30f3\u30d7\u30eb\u6570(\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba)\uff1a25<\/li>\n\n\n\n<li>\u91cf\u5b50\u56de\u8def\u306e\u9577\u3055(\u30c8\u30fc\u30af\u30f3\u6570)\uff1a10<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>LiH\u3001BeH\u2082\u3001N\u2082\n<ul class=\"wp-block-list\">\n<li>\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\uff1a\u9806\u306b\u300110, 12, 12<\/li>\n\n\n\n<li>\u30b9\u30c6\u30c3\u30d7\u6570\uff1a500<\/li>\n\n\n\n<li>1\u30b9\u30c6\u30c3\u30d7\u5f53\u305f\u308a\u306e\u30b5\u30f3\u30d7\u30eb\u6570(\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba)\uff1a50<\/li>\n\n\n\n<li>\u91cf\u5b50\u56de\u8def\u306e\u9577\u3055(\u30c8\u30fc\u30af\u30f3\u6570)\uff1a40<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u9006\u6e29\u5ea6\u03b2\u306f\u521d\u671f\u5024\u304c5\u3001\u5404\u30b9\u30c6\u30c3\u30d7\u3054\u3068\u306b0.1\u5897\u52a0\u3055\u305b\u308b<\/li>\n\n\n\n<li>\u5404\u5206\u5b50\u306b\u3064\u3044\u30663\u56deGPT-QE\u3092\u8a66\u884c\u3057\u305f\u3046\u3061\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u6700\u5c0f\u306a\u3082\u306e\u3092\u8a18\u9332<\/li>\n<\/ul>\n\n\n\n<p>\u5b9f\u884c\u7d50\u679c\u3092\u56f37\u3001\u56f38\u306b\u793a\u3057\u307e\u3059\u3002\u4e8c\u3064\u306e\u56f3\u306b\u306f\u3001\u6a2a\u8ef8\u306b\u539f\u5b50\u9593\u306e\u7d50\u5408\u9577\u3001\u7e26\u8ef8\u306b\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002GPT-QE\u306b\u3088\u308b\u7d50\u679c\u306f\u7dd1\u8272\u306e\u70b9\u3067\u793a\u3055\u308c\u3066\u304a\u308a\u3001\u9ed2\u7dda\u3067\u793a\u3055\u308c\u305f\u53b3\u5bc6\u89e3\u3001\u70b9\u7dda\u3067\u793a\u3055\u308c\u305fHartree-Fock\u72b6\u614b(\u521d\u671f\u72b6\u614b)\u3068\u6bd4\u8f03\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u56f38\u3067\u306f\u3001\u5b66\u7fd2\u3092\u884c\u308f\u305a\u30e9\u30f3\u30c0\u30e0\u306b\u6f14\u7b97\u5b50\u3092\u9078\u629e\u3057\u305f\u3060\u3051\u306e\u5834\u5408(benchmark)\u3082\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u56f3\u304b\u3089\u8aad\u307f\u53d6\u308c\u308b\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5168\u3066\u306e\u5206\u5b50\u306b\u304a\u3044\u3066\u3001Hartree-Fock\u72b6\u614b\u3088\u308a\u3082\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u4f4e\u3044\u72b6\u614b\u306e\u63a2\u7d22\u306b\u6210\u529f\u3057\u305f\u3002<\/li>\n\n\n\n<li>\u5168\u3066\u306e\u5206\u5b50\u306b\u304a\u3044\u3066\u3001training\u306f\u30e9\u30f3\u30c0\u30e0\u306b\u6f14\u7b97\u5b50\u3092\u9078\u629e\u3057\u305f\u5834\u5408\u3088\u308a\u3082\u7cbe\u5ea6\u304c\u9ad8\u304f\u3001\u7279\u306bN\u2082\u3067\u306f\u305d\u306e\u5dee\u304c\u9855\u8457\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li>\u53b3\u5bc6\u89e3\u3068\u306e\u5dee\u304cchemical accuracy(\u5316\u5b66\u73fe\u8c61\u3092\u5b9a\u91cf\u7684\u306b\u6b63\u3057\u304f\u4e88\u6e2c\u3059\u308b\u305f\u3081\u306e\u3001\u8a08\u7b97\u4e0a\u306e\u4e00\u3064\u306e\u76ee\u6a19\u7cbe\u5ea6:1.6\u00d710 \u207b \u00b3 Hartree)\u3092\u8d85\u3048\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u3042\u3063\u305f\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u306a\u304a\u3001\u672c\u8ad6\u6587\u4e2d\u3067\u306f\u65e2\u5b58\u306e\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0VQE\u3084UCCSD\u3068\u306e\u6bd4\u8f03\u306f\u884c\u308f\u308c\u3066\u3044\u307e\u305b\u3093\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"702\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-8-1024x702.png\" alt=\"\" class=\"wp-image-8147\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-8-1024x702.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-8-300x206.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-8-768x526.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-8.png 1373w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f37. training\u306e\u7d50\u679c\uff08Ver.1\u306eFig.4\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"717\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-9-1024x717.png\" alt=\"\" class=\"wp-image-8148\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-9-1024x717.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-9-300x210.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-9-768x538.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-9.png 1213w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f38. training\u306e\u7d50\u679c\u3068benchmark\u306e\u6bd4\u8f03\uff08Ver.1\u306eFig.7\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n\n\n\n<p>\u5b9f\u969b\u306b\u5f97\u3089\u308c\u305f\u91cf\u5b50\u56de\u8def\u306e\u4e00\u3064\u3092\u56f39\u306b\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u306fH\u2082\u306b\u5bfe\u5fdc\u3059\u308b\u91cf\u5b50\u56de\u8def\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u521d\u671f\u72b6\u614b $\\ket{1100}$\u3092\u7528\u610f\u3059\u308b\u305f\u3081\u306e\u5148\u982d\u306e\u6f14\u7b97\u5b50 $XX$\u3068\u3001\u305d\u306e\u3042\u3068\u306b\u7d9a\u304f10\u30c8\u30fc\u30af\u30f3\u5206\u306e\u6f14\u7b97\u5b50 $\\exp(-i\\hat Pt)$\u304b\u3089\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"305\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-10-1024x305.png\" alt=\"\" class=\"wp-image-8149\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-10-1024x305.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-10-300x89.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-10-768x229.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-10-1536x457.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-10.png 1825w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f39. training\u3067\u5f97\u3089\u308c\u305fH\u2082\u306e\u91cf\u5b50\u56de\u8def\uff08Ver.1\u306eFig.5\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"pre-training-2\"><\/span>pre-training<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>pre-training\u306e\u624b\u6cd5\u3092\u3001config-to-config transfer scenario\u306b\u9069\u7528\u3057\u3066\u52b9\u679c\u3092\u691c\u8a3c\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u539f\u5b50\u9593\u8ddd\u96e2 1.2 \u00c5 \u306eN\u2082\u306b\u304a\u3051\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u30011.4 \u00c5\u306eN\u2082\u306e\u7cfb\u306e\u5b66\u7fd2\u306b\u4f7f\u3046\u3053\u3068\u3092\u76ee\u6a19\u3068\u3057\u307e\u3059\u3002\u5177\u4f53\u7684\u306a\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u3042\u3089\u304b\u3058\u3081 1.2 \u00c5\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u5bfe\u3057500step\u306e\u5b66\u7fd2\u3092\u884c\u3046\n<ul class=\"wp-block-list\">\n<li>\u5404step\u306750\u500b\u306e\u91cf\u5b50\u56de\u8def\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3068 $E_N$\u306e\u6e2c\u5b9a\u3092\u884c\u3046<\/li>\n\n\n\n<li>\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u30b5\u30a4\u30ba\u306f500\u00d750=25000\u500b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304b\u3089 $E_N$\u304c\u57fa\u6e96\u5024 -107.45 Hartree\u3088\u308a\u9ad8\u3044\u30c7\u30fc\u30bf\u306f\u6368\u3066\u308b\n<ul class=\"wp-block-list\">\n<li>\u4eca\u56de\u3001\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u30b5\u30a4\u30ba\u306f\u7d0414700\u306b\u524a\u6e1b\u3055\u308c\u305f<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092294\u500b\u306e\u30d0\u30c3\u30c1\u306b\u5206\u5272\u3059\u308b\n<ul class=\"wp-block-list\">\n<li>\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u306f14700\/294=50<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>1.4 \u00c5\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u5bfe\u3057\u3001pre-training\u306a\u3057\u306etraining(500step)\u3068pre-training\u3042\u308a\u306etraining(500step)\u3092\u884c\u3044\u3001\u7d50\u679c\u3092\u6bd4\u8f03\u3059\u308b\n<ul class=\"wp-block-list\">\n<li>\u305d\u308c\u305e\u308c10\u56de\u5b9f\u9a13\u3092\u884c\u3046<\/li>\n\n\n\n<li>10\u56de\u306e\u5b9f\u9a13\u306b\u304a\u3051\u308b\u3001step $s$ \u3067\u306e $E_N$\u306e\u6700\u5c0f\u5024\u3092 $E_\\mathrm{min}(s)$\u3001\u5e73\u5747\u5024\u3092 $E_\\mathrm{avg}(s)$\u3068\u3057\u3066\u8a18\u9332\u3059\u308b<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u5b9f\u9a13\u7d50\u679c\u3092\u56f310\u306b\u793a\u3057\u307e\u3059\u3002\u3053\u306e\u56f3\u304b\u3089\u3001<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$E_N$ \u306e\u6700\u5c0f\u5024 $E_\\mathrm{min}(s)$\u306fpre-training\u3042\u308a\u306e\u65b9\u304c\u4f4e\u304f\u306a\u3063\u305f<\/li>\n\n\n\n<li>\u5e73\u5747\u5024 $E_\\mathrm{ave}(s)$\u306f\u5909\u5316\u304c\u898b\u3089\u308c\u306a\u304b\u3063\u305f<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u7d50\u679c\u306f\u3001\u4e8b\u524d\u5b66\u7fd2\u306b\u3088\u3063\u3066\u3088\u308a\u5e83\u3044\u9818\u57df\u306e\u63a2\u7d22\u304c\u53ef\u80fd\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"369\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-11-1024x369.png\" alt=\"\" class=\"wp-image-8150\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-11-1024x369.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-11-300x108.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-11-768x277.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-11-1536x554.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-11.png 1830w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f310. pre-training\u3042\u308a\u3068\u306a\u3057\u306b\u304a\u3051\u308b$E_N$\u306e\u6bd4\u8f03\uff08Ver.1\u306eFig.6\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u3053\u306e\u8ad6\u6587\u3067\u306f\u3001\u751f\u6210\u30e2\u30c7\u30eb\u3092\u7528\u3044\u3066\u76ee\u7684\u306e\u91cf\u5b50\u56de\u8def\u3092\u5f97\u308b\u65b0\u305f\u306a\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 GQE \u304c\u63d0\u6848\u3055\u308c\u307e\u3057\u305f\u3002\u7279\u306b\u3001Transformer\u3092\u7528\u3044\u305fGPT-QE\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5177\u4f53\u7684\u306a\u5b9f\u884c\u65b9\u6cd5\u3068\u3057\u3066\u3001training\u30b9\u30ad\u30fc\u30e0\u3068pre-training\u30b9\u30ad\u30fc\u30e0\u306e\u4e8c\u3064\u304c\u8003\u6848\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u6226\u7565\u306b\u3088\u308a\u3001GPT-QE\u306f\u65e2\u5b58\u306e\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0VQE\u306b\u6bd4\u3079\u3066\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u306e\u5b9f\u884c\u56de\u6570\u3092\u524a\u6e1b\u3067\u304d\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\u3002GPU\u3092\u7528\u3044\u305f\u91cf\u5b50\u8a08\u7b97\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u5206\u5b50\u306e\u57fa\u5e95\u72b6\u614b\u63a2\u7d22\u554f\u984c\u306b\u304a\u3044\u3066\u3001training\u3068pre-training\u306e\u53cc\u65b9\u304c\u6709\u52b9\u6027\u3092\u767a\u63ee\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>GPT-QE\u306e\u4eca\u5f8c\u306e\u5c55\u671b\u3068\u3057\u3066\u3001\u307e\u305a\u306f\u5b9f\u969b\u306e\u91cf\u5b50\u30c7\u30d0\u30a4\u30b9\u4e0a\u3067\u305d\u306e\u6027\u80fd\u3092\u691c\u8a3c\u3059\u308b\u3053\u3068\u304c\u4e0d\u53ef\u6b20\u3067\u3059\u3002\u307e\u305f\u3001\u3088\u308a\u5927\u304d\u306a\u5206\u5b50\u306e\u7cfb\u3067\u5b9f\u9a13\u3092\u884c\u3044\u3001\u6700\u9069\u5316\u306e\u6319\u52d5\u3092\u8a55\u4fa1\u3059\u308b\u3053\u3068\u3082\u5fc5\u8981\u3067\u3059\u3002\u3055\u3089\u306a\u308b\u767a\u5c55\u306e\u65b9\u5411\u6027\u3068\u3057\u3066\u3001ADAPT-VQE\u3092\u306f\u3058\u3081\u3068\u3059\u308b\u4ed6\u306e\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u306e\u7d71\u5408\u3084\u3001\u53e4\u5178\u30e2\u30c7\u30eb\u81ea\u4f53\u306e\u6539\u826f\u3082\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u3042\u308b\u3044\u306f\u3001GQE\u306e\u67a0\u7d44\u307f\u3092\u57fa\u5e95\u72b6\u614b\u4ee5\u5916\u306e\u554f\u984c\u3078\u62e1\u5f35\u3057\u3066\u3044\u304f\u3053\u3068\u3082\u671f\u5f85\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><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\n\n\n<p>\u3053\u308c\u307e\u3067\u4eba\u529b\u3067\u8a2d\u8a08\u3055\u308c\u3066\u3044\u305f\u91cf\u5b50\u56de\u8def\u3092\u3001\u6df1\u5c64\u5b66\u7fd2\u3092\u7528\u3044\u3066\u751f\u6210\u3059\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u305f\u70b9\u304c\u753b\u671f\u7684\u3060\u3068\u611f\u3058\u307e\u3057\u305f\u3002\u8ad6\u6587\u4e2d\u306e\u691c\u8a3c\u3067\u306f\u3001GPT-QE\u306b\u3088\u308b\u57fa\u5e95\u63a2\u7d22\u304cHartree-Fock\u72b6\u614b\u3084\u30e9\u30f3\u30c0\u30e0\u306a\u91cf\u5b50\u56de\u8def\u3088\u308a\u3082\u9ad8\u3044\u7cbe\u5ea6\u3092\u793a\u3059\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u304c\u3001VQE\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5bfe\u3057\u3066\u3082\u512a\u4f4d\u6027\u304c\u3042\u308b\u306e\u304b\u6c17\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u307e\u305f\u3001\u7570\u306a\u308b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u9593\u3067\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u3084\u308a\u53d6\u308a\u306f\u672c\u8ad6\u6587\u4e2d\u3067\u3082\u5177\u4f53\u7684\u306a\u65b9\u6cd5\u304c\u8003\u6848\u3055\u308c\u3066\u304a\u3089\u305a\u3001GPT-QE\u3092\u3088\u308a\u6c4e\u7528\u7684\u306a\u624b\u6cd5\u306b\u767a\u5c55\u3055\u305b\u308b\u305f\u3081\u306b\u89e3\u6c7a\u3059\u3079\u304d\u8ab2\u984c\u3060\u3068\u611f\u3058\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Appendix\"><\/span>Appendix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Appendix\u3067\u306f\u3001\u672c\u6587\u4e2d\u306b\u767b\u5834\u3057\u305f\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u306e\u7528\u8a9e\u3084\u6982\u5ff5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u672c\u7ae0\u3067\u306e\u89e3\u8aac\u306f\u3001\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u306e\u30ec\u30d3\u30e5\u30fc\u8ad6\u6587 [2] \u3092\u53c2\u8003\u306b\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%8F%E3%83%9F%E3%83%AB%E3%83%88%E3%83%8B%E3%82%A2%E3%83%B3%E3%81%8C%E3%83%91%E3%82%A6%E3%83%AA%E6%BC%94%E7%AE%97%E5%AD%90%E3%81%A7%E8%A1%A8%E3%81%9B%E3%82%8B%E7%90%86%E7%94%B1\"><\/span>\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u3067\u8868\u305b\u308b\u7406\u7531<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u672c\u6587\u306b\u304a\u3044\u3066\u3001\u5206\u5b50\u4e2d\u306b\u304a\u3051\u308b\u96fb\u5b50\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u304c\u3001\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d $\\hat P$\u3092\u7528\u3044\u3066<\/p>\n\n\n\n<p>$$ \\hat H(\\vec \\Delta)=\\sum_lh_l(\\vec\\Delta)\\hat P_l $$<\/p>\n\n\n\n<p>\u3068\u8868\u305b\u308b\u3053\u3068\u3092\u8a8d\u3081\u307e\u3057\u305f\u3002\u672c\u7bc0\u3067\u306f\u3001\u3053\u306e\u7406\u7531\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e8c\u91cf\u5b50\u5316<\/h4>\n\n\n\n<p>\u7b2c\u4e8c\u91cf\u5b50\u5316\u3068\u306f\u3001\u5206\u5b50\u5185\u306e\u500b\u3005\u306e\u96fb\u5b50\u3092\u8ffd\u8de1\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u3069\u306e\u8ecc\u9053\u306b\u96fb\u5b50\u304c\u4f55\u500b\u5b58\u5728\u3059\u308b\u304b\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u3067\u3001\u7cfb\u306e\u72b6\u614b\u3092\u8a18\u8ff0\u3059\u308b\u8003\u3048\u65b9\u3067\u3059\u3002\u96fb\u5b50\u306f\u672c\u6765\u533a\u5225\u3067\u304d\u306a\u3044\u7c92\u5b50\u306a\u306e\u3067\u3001\u591a\u4f53\u554f\u984c\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u969b\u306b\u306f\u3053\u306e\u7b2c\u4e8c\u91cf\u5b50\u5316\u304c\u4e0d\u53ef\u6b20\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u7b2c\u4e8c\u91cf\u5b50\u5316\u3092\u884c\u3046\u3068\u3001\u5206\u5b50\u4e2d\u306b\u304a\u3051\u308b\u96fb\u5b50\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u3001\u751f\u6210\u6d88\u6ec5\u6f14\u7b97\u5b50 $a^\\dagger,a$\u3092\u7528\u3044\u3066<\/p>\n\n\n\n<p>$$ \\hat H=\\sum_{p,q}h_{pq}a_p^\\dagger a_q+\\frac{1}{2}\\sum_{p,q,r,s}h_{pqrs}a_p^\\dagger a_q^\\dagger a_ra_s $$<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5f0f\u306f2\u3064\u306e\u90e8\u5206\u304b\u3089\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u7b2c\u4e00\u9805<\/p>\n\n\n\n<p>$$ \\sum_{p,q}h_{pq}a_p^\\dagger a_q $$<\/p>\n\n\n\n<p>\u306f\u4e00\u96fb\u5b50\u306e\u751f\u6210\u3068\u6d88\u6ec5\u3092\u8868\u3057\u307e\u3059\u3002 $a^\\dagger_p$\u306f\u751f\u6210\u6f14\u7b97\u5b50\u3068\u547c\u3070\u308c\u308b\u6f14\u7b97\u5b50\u3067\u3042\u308a\u3001\u8ecc\u9053 $p$ \u306b\u96fb\u5b50\u3092\u4e00\u3064\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3092\u8868\u3057\u307e\u3059\u3002\u4e00\u65b9 $a_q$ \u306f\u6d88\u6ec5\u6f14\u7b97\u5b50\u3068\u547c\u3070\u308c\u308b\u6f14\u7b97\u5b50\u3067\u3042\u308a\u3001\u8ecc\u9053 $q$\u304b\u3089\u96fb\u5b50\u3092\u4e00\u3064\u524a\u9664\u3059\u308b\u3053\u3068\u3092\u8868\u3057\u307e\u3059\u3002\u4fc2\u6570\u306e $h_{pq}$ \u306f\u4e00\u96fb\u5b50\u7a4d\u5206\u3068\u547c\u3070\u308c\u3001\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n\n\n\n<p>$$ <br>\\begin{align}<br>h_{pq}&amp;=\\int d\\mathbf{r}\\phi_p^*(\\mathbf{r})\\hat h\\phi_q(\\mathbf{r})\\\\ <br>\\hat h&amp;=-\\frac{\\nabla^2}{2}-\\sum_I\\frac{Z_I}{|{\\mathbf{r}-\\mathbf{R}_I}|} <br>\\end{align}<br>$$<\/p>\n\n\n\n<p>$\\phi_p(\\bm x)$\u306f\u8ecc\u9053 $p$ \u306e\u6ce2\u52d5\u95a2\u6570\u3067\u3042\u308a\u3001\u6f14\u7b97\u5b50 $\\hat h$ \u306f\u4ed6\u306e\u96fb\u5b50\u306b\u3088\u308b\u5f71\u97ff\u3092\u7121\u8996\u3057\u305f\u3068\u304d\u306e\u4e00\u96fb\u5b50\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3067\u3059\u3002 $Z_I,\\mathbf{R}_I$ \u306f\u305d\u308c\u305e\u308c $I$ \u756a\u76ee\u306e\u539f\u5b50\u6838\u306e\u96fb\u8377\u3068\u4f4d\u7f6e\u3092\u8868\u3057\u307e\u3059\u3002\u4e00\u96fb\u5b50\u7a4d\u5206\u306f\u3001\u96fb\u5b50\u304c\u8ecc\u9053 $q$\u304b\u3089\u8ecc\u9053 $p$\u306b\u9077\u79fb\u3059\u308b\u3068\u304d\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5909\u5316\u3068\u307f\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001\u7b2c\u4e8c\u9805<\/p>\n\n\n\n<p>$$ \\frac{1}{2}\\sum_{p,q,r,s}h_{pqrs}a_p^\\dagger a_q^\\dagger a_ra_s $$<\/p>\n\n\n\n<p>\u306f\u4e8c\u96fb\u5b50\u306e\u751f\u6210\u3001\u6d88\u6ec5\u3092\u8868\u3057\u307e\u3059\u3002\u4fc2\u6570 $h_{pqrs}$\u306f\u4e8c\u96fb\u5b50\u7a4d\u5206\u3068\u547c\u3070\u308c\u3001\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n\n\n\n<p>$$ h_{pqrs}=\\int d\\mathbf{r}_1d\\mathbf{r}_2\\frac{\\phi_p^*(\\mathbf{r}_1)\\phi_q^*(\\mathbf{r}_2)\\phi_r(\\mathbf{r}_2)\\phi_s(\\mathbf{r}_1)}{|\\mathbf{r}_1-\\mathbf{r}_2|} $$<\/p>\n\n\n\n<p>\u4e8c\u96fb\u5b50\u7a4d\u5206\u306f\u30012\u3064\u306e\u96fb\u5b50\u304c\u8ecc\u9053 $s,r$ \u304b\u3089\u8ecc\u9053 $p,q$\u306b\u540c\u6642\u306b\u9077\u79fb\u3059\u308b\u3068\u304d\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5909\u5316\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Jordan-Wigner \u5909\u63db<\/h4>\n\n\n\n<p>Jordan-Wigner\u5909\u63db\u306f\u3001\u751f\u6210\u6d88\u6ec5\u6f14\u7b97\u5b50 $a^\\dagger,a$\u3092\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50 $I,X,Y,Z$\u3067\u7f6e\u304d\u63db\u3048\u308b\u5909\u63db\u3067\u3059\u3002\u3053\u306e\u64cd\u4f5c\u306b\u3088\u308a\u3001\u3053\u306e\u8ecc\u9053\u306b\u96fb\u5b50\u304c\u5b58\u5728\u3059\u308b\u304b\u3057\u306a\u3044\u304b\u306e\u4e8c\u72b6\u614b\u3092\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u306e $|0\\rangle,|1\\rangle$\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306f\u305d\u308c\u305e\u308c\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n\n\n\n<p>$$ I=\\left(\\begin{array}{rr}1&amp;0\\\\0&amp;1\\end{array}\\right),\\ X=\\left(\\begin{array}{rr}0&amp;1\\\\1&amp;0\\end{array}\\right), \\ Y=\\left(\\begin{array}{rr}0&amp;-i\\\\i&amp;0\\end{array}\\right),\\ Z=\\left(\\begin{array}{rr}1&amp;0\\\\0&amp;-1\\end{array}\\right) $$<\/p>\n\n\n\n<p>\u751f\u6210\u6d88\u6ec5\u6f14\u7b97\u5b50\u3068\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u9593\u306b\u6b21\u306e\u5bfe\u5fdc\u95a2\u4fc2\u3092\u5b9a\u3081\u307e\u3059\u3002\u3053\u306e\u5909\u63db\u306f\u3001\u30d5\u30a7\u30eb\u30df\u30aa\u30f3\u306e\u751f\u6210\u6d88\u6ec5\u6f14\u7b97\u5b50\u306e\u4ea4\u63db\u95a2\u4fc2\u3092\u6e80\u305f\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$ <br>\\begin{align}<br>a_p&amp;=\\Bigg(\\bigotimes_{t=1}^{p-1}Z_t\\Bigg)\\otimes(X_p+iY_p)\\\\ a_p^\\dagger&amp;=\\Bigg(\\bigotimes_{t=1}^{p-1}Z_t\\Bigg)\\otimes(X_p-iY_p) <br>\\end{align}<br>$$<\/p>\n\n\n\n<p>\u3053\u308c\u3092\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u4ee3\u5165\u3059\u308b\u3053\u3068\u3067\u3001\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u3067\u8868\u3055\u308c\u305f\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5404\u9805\u306f\u3001 $p&lt;q&lt;r&lt;s$ \u3068\u3057\u305f\u3068\u304d<\/p>\n\n\n\n<p>$$ <br>\\begin{align}<br>h_{pq}a_p^\\dagger a_q<br>&amp;=h_{pq}\\Bigg\\{\\Bigg(\\bigotimes_{t=1}^{p-1}Z_t\\Bigg)\\otimes(X_p-iY_p)\\Bigg\\}\\Bigg\\{\\Bigg(\\bigotimes_{t=1}^{q-1}Z_t\\Bigg)\\otimes(X_q+iY_q) \\Bigg\\}\\\\<br>&amp;=h_{pq}\\Bigg(\\bigotimes_{t=1}^{p-1}I\\Bigg)\\otimes(X_p-iY_p)Z_p\\otimes\\Bigg(\\bigotimes_{t=p+1}^{q-1}Z_t\\Bigg)\\otimes(X_q+iY_q) <br>\\end{align}<br>$$<\/p>\n\n\n\n<p>$$ <br>\\begin{align}<br>h_{pqrs}a_p^\\dagger a_q^\\dagger a_r a_s<br>&amp;=h_{pqrs}\\Bigg\\{\\Bigg(\\bigotimes_{t=1}^{p-1}Z_t\\Bigg)\\otimes(X_p-iY_p)\\Bigg\\}\\Bigg\\{\\Bigg(\\bigotimes_{t=1}^{q-1}Z_t\\Bigg)\\otimes(X_q-iY_q)\\Bigg\\}<br>\\Bigg\\{\\Bigg(\\bigotimes_{t=1}^{r-1}Z_t\\Bigg)\\otimes(X_r+iY_r)\\Bigg\\}\\Bigg\\{\\Bigg(\\bigotimes_{t=1}^{s-1}Z_t\\Bigg)\\otimes(X_s+iY_s)\\Bigg\\}\\\\<br>&amp;=\\cdots <br>\\end{align}<br>$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u3092 $\\hat P$ \u3068\u8868\u3059\u3053\u3068\u306b\u3059\u308c\u3070\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f<\/p>\n\n\n\n<p>$$ \\hat H=\\sum_l h_l\\hat P_l $$<\/p>\n\n\n\n<p>\u3068\u66f8\u3051\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u539f\u5b50\u9593\u8ddd\u96e2\u3092\u5909\u3048\u305f\u3068\u304d\u3001\u6ce2\u52d5\u95a2\u6570\u306e\u5909\u66f4\u306b\u3088\u308a\u4e00\u96fb\u5b50\u7a4d\u5206 $h_{pq}$\u3068\u4e8c\u96fb\u5b50\u7a4d\u5206 $h_{pqrs}$\u306e\u5024\u306f\u5909\u5316\u3057\u307e\u3059\u304c\u3001\u8ecc\u9053\u306e\u6570\u81ea\u4f53\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u4fc2\u6570\u306e\u307f\u304c\u539f\u5b50\u9593\u8ddd\u96e2\u306b\u4f9d\u5b58\u3059\u308b\u5f62<\/p>\n\n\n\n<p>$$ \\hat H(\\vec \\Delta)=\\sum_lh_l(\\vec\\Delta)\\hat P_l $$<\/p>\n\n\n\n<p>\u3067\u8868\u305b\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u6700\u3082\u57fa\u672c\u7684\u306a\u5909\u63db\u3067\u3042\u308bJordan-Wigner\u5909\u63db\u3092\u89e3\u8aac\u3057\u307e\u3057\u305f\u304c\u3001\u5b9f\u969b\u306b\u306f\u3088\u308a\u52b9\u7387\u5316\u3055\u308c\u305fBravyi-Kitaev\u5909\u63db\u306a\u3069\u3082\u7528\u3044\u3089\u308c\u307e\u3059 [3]\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"UCCSD%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6\"><\/span>UCCSD\u306b\u3064\u3044\u3066<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u57fa\u5e95\u72b6\u614b\u3092\u8fd1\u4f3c\u7684\u306b\u6c42\u3081\u308b\u4ee3\u8868\u7684\u306a\u624b\u6cd5\u3068\u3057\u3066\u3001\u53e4\u5178\u8a08\u7b97\u306eCC(Coupled Cluster\/\u7d50\u5408\u30af\u30e9\u30b9\u30bf\u30fc\u6cd5)\u3068\u91cf\u5b50\u8a08\u7b97\u306eUCC(Unitary Coupled Cluster\/\u30e6\u30cb\u30bf\u30ea\u7d50\u5408\u30af\u30e9\u30b9\u30bf\u30fc\u6cd5)\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u306f [4] \u306e\u8a18\u8ff0\u3092\u53c2\u8003\u306b\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">CC\u30fbCCSD<\/h4>\n\n\n\n<p>CC(Coupled Cluster\/\u7d50\u5408\u30af\u30e9\u30b9\u30bf\u30fc\u6cd5)\u306f\u3001\u5206\u5b50\u306e\u96fb\u5b50\u72b6\u614b\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u624b\u6cd5\u306e\u4e00\u3064\u3067\u3059\u3002Hartree-Fock\u6cd5\u306a\u3069\u306b\u3088\u308a\u6c42\u3081\u305f\u5358\u7d14\u306a\u8fd1\u4f3c\u89e3\u3092\u3001\u96fb\u5b50\u76f8\u95a2\u306e\u52b9\u679c\u3092\u53d6\u308a\u5165\u308c\u305f\u3088\u308a\u53b3\u5bc6\u306a\u89e3\u306b\u8fd1\u3065\u3051\u308b\u305f\u3081\u306b\u4f7f\u308f\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u96fb\u5b50\u76f8\u95a2\u306e\u52b9\u679c\u3092\u53d6\u308a\u5165\u308c\u308b\u305f\u3081\u306b\u30af\u30e9\u30b9\u30bf\u30fc\u6f14\u7b97\u5b50 $T$ \u3092\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<p>$$ <br>\\begin{gather}<br>\\hat T=\\sum_i \\hat T_i\\\\ \\hat T_1=\\sum_{i\\in\\mathrm{\u975e\u5360\u6709},\\alpha,\\in\\mathrm{\u5360\u6709}}t_{i\\alpha}a_i^\\dagger a_\\alpha\\\\ \\hat T_2=\\sum_{i,j\\in\\mathrm{\u975e\u5360\u6709},\\alpha,\\beta\\in\\mathrm{\u5360\u6709}}t_{ij\\alpha\\beta}a_i^\\dagger a_j^\\dagger a_\\alpha a_\\beta\\\\ \\vdots <br>\\end{gather}$$<\/p>\n\n\n\n<p>\u4fc2\u6570 $t_{i\\alpha},t_{ij\\alpha\\beta},\\dots$ \u306f\u672a\u77e5\u306e\u5909\u6570\u3067\u3059\u3002\u6f14\u7b97\u5b50 $\\hat T_1,\\hat T_2,\\hat T_3\\dots$\u306f\u9806\u306b\u4e00\u96fb\u5b50\u52b1\u8d77\u3001\u4e8c\u96fb\u5b50\u52b1\u8d77\u3001\u4e09\u96fb\u5b50\u52b1\u8d77\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002CC\u306b\u3088\u308b\u91cf\u5b50\u72b6\u614b $|\\psi_\\text{CC}\\rangle$\u306f\u3001\u30af\u30e9\u30b9\u30bf\u30fc\u6f14\u7b97\u5b50 $\\hat T$\u3068HF\u6cd5\u306b\u3088\u308b\u8fd1\u4f3c\u89e3 $|\\psi_\\text{HF}\\rangle$\u3092\u7528\u3044\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<p>$$ |\\psi_{\\mathrm C\\mathrm C}\\rangle=e^{\\hat T}|\\psi_{\\mathrm{}\\mathrm H\\mathrm F}\\rangle $$<\/p>\n\n\n\n<p>\u3053\u306e\u3068\u304d\u3001\u4fc2\u6570 $t_{i\\alpha},t_{ij\\alpha\\beta},\\dots$\u3092\u30b7\u30e5\u30ec\u30fc\u30c7\u30a3\u30f3\u30ac\u30fc\u65b9\u7a0b\u5f0f\u304b\u3089\u5f97\u3089\u308c\u308b\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f<\/p>\n\n\n\n<p>$$<br>\\begin{align} <br>\\langle\\psi_\\text{CC}|\\hat H|\\psi_\\text{CC}\\rangle &amp;= \\langle\\psi_{\\mathrm H\\mathrm F}|e^{-\\hat T}\\hat He^{\\hat T}|\\psi_{\\mathrm H\\mathrm F}\\rangle=E\\\\<br>\\langle\\mu|e^{-\\hat T}\\hat H|\\psi_\\text{CC}\\rangle &amp;= \\langle\\mu|e^{-\\hat T}\\hat He^{\\hat T}|\\psi_{\\mathrm H\\mathrm F}\\rangle=0\u3000(|\\mu\\rangle\u306f\u52b1\u8d77\u72b6\u614b) <br>\\end{align}<br>$$<\/p>\n\n\n\n<p>\u306e\u89e3\u3068\u3057\u3066\u5b9a\u3081\u308b\u3053\u3068\u3067\u3001 $|\\psi_{CC}\\rangle$\u306f\u57fa\u5e95\u72b6\u614b\u3068\u306a\u308a\u307e\u3059\u3002CC\u3092\u4e8c\u96fb\u5b50\u52b1\u8d77\u307e\u3067\u3067\u6253\u3061\u5207\u3063\u305f\u3082\u306e\u306fCCSD(Coupled Cluster Singles and Doubles\/\u7d50\u5408\u30af\u30e9\u30b9\u30bf\u30fc\u6cd5 \u4e00\u30fb\u4e8c\u96fb\u5b50\u52b1\u8d77\u8fd1\u4f3c)\u3068\u547c\u3070\u308c\u3001\u7cbe\u5ea6\u306e\u9ad8\u3055\u3068\u8a08\u7b97\u306e\u3057\u3084\u3059\u3055\u304b\u3089\u6700\u3082\u6a19\u6e96\u7684\u306aCC\u3068\u3057\u3066\u5e83\u304f\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">UCC\u30fbUCCSD<\/h4>\n\n\n\n<p>UCC(Unitary Coupled Cluster\/\u30e6\u30cb\u30bf\u30ea\u7d50\u5408\u30af\u30e9\u30b9\u30bf\u30fc\u6cd5)\u306f\u3001CC\u3092\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4e0a\u3067\u884c\u3048\u308b\u5f62\u306b\u6539\u826f\u3057\u305f\u3082\u306e\u3067\u3059\u3002CCSD\u3068\u540c\u69d8\u306b\u3001UCC\u3092\u4e8c\u96fb\u5b50\u52b1\u8d77\u307e\u3067\u3067\u6253\u3061\u5207\u3063\u305f\u3082\u306e\u3092UCCSD\u3068\u547c\u3073\u307e\u3059\u3002\u5f93\u6765\u306eCCSD\u3067\u306f\u3001\u6f14\u7b97\u5b50 $e^{\\hat T}$\u304c\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u3067\u306a\u3044\u305f\u3081\u3001\u91cf\u5b50\u30b2\u30fc\u30c8\u64cd\u4f5c\u3068\u3057\u3066\u53d6\u308a\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002UCCSD\u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u6539\u826f\u3057\u307e\u3059\uff1a<\/p>\n\n\n\n<p>$$ |\\psi_{\\mathrm U\\mathrm C\\mathrm C}\\rangle=e^{\\hat T-\\hat T^\\dagger}|\\psi_{\\mathrm{}\\mathrm H\\mathrm F}\\rangle $$<\/p>\n\n\n\n<p>$\\hat T$ \u3092 $\\hat T-\\hat T^\\dagger$\u306b\u5909\u66f4\u3057\u305f\u3053\u3068\u3067\u6f14\u7b97\u5b50\u304c\u30e6\u30cb\u30bf\u30ea\u306b\u306a\u308a\u3001\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u4e0a\u3067\u5b9f\u884c\u53ef\u80fd\u306a\u64cd\u4f5c\u306b\u306a\u308a\u307e\u3059\u3002CCSD\u3067\u306f\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u3067\u4fc2\u6570 $t_{i\\alpha},t_{ij\\alpha\\beta}$\u3092\u6c42\u3081\u307e\u3057\u305f\u304c\u3001UCCSD\u3067\u306fVQE\u306b\u3088\u308a\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6c42\u3081\u307e\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u5909\u5206\u539f\u7406<\/p>\n\n\n\n<p>$$ \\braket {\\hat H}=\\langle\\psi_{\\mathrm U\\mathrm C\\mathrm C}|\\hat H|\\psi_{\\mathrm U\\mathrm C\\mathrm C}\\rangle=\\langle\\psi_{\\mathrm H\\mathrm F}|e^{\\hat T^\\dagger-\\hat T}\\hat He^{\\hat T-\\hat T^\\dagger}|\\psi_{\\mathrm H\\mathrm F}\\rangle\\ge E_0 $$<\/p>\n\n\n\n<p>\u306b\u57fa\u3065\u304d $t_{i\\alpha},t_{ij\\alpha\\beta}$\u3092\u6700\u9069\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u671f\u5f85\u5024 $\\braket{\\hat H}$\u3092\u771f\u306e\u57fa\u5e95\u30a8\u30cd\u30eb\u30ae\u30fc $E_0$\u306b\u8fd1\u3065\u3051\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50\u306f\u3001\u5358\u7d14\u306a\u91cf\u5b50\u30b2\u30fc\u30c8\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u5206\u89e3\u3067\u304d\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001UCCSD\u3067\u7528\u3044\u308b\u30e6\u30cb\u30bf\u30ea\u6f14\u7b97\u5b50 $e^{\\hat T-\\hat T^\\dagger}$\u3082\u91cf\u5b50\u56de\u8def\u4e0a\u306b\u5b9f\u88c5\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u672c\u8ad6\u6587\u4e2d\u306e\u6c34\u7d20\u5206\u5b50\u306e\u4f8b\u3067\u306f\u3001\u6f14\u7b97\u5b50 $e^{T-T^\\dagger}$\u304c\u6b21\u306e\u3088\u3046\u306a\u91cf\u5b50\u56de\u8def\u3067\u8868\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"698\" height=\"401\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-12.png\" alt=\"\" class=\"wp-image-8151\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-12.png 698w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-12-300x172.png 300w\" sizes=\"auto, (max-width: 698px) 100vw, 698px\" \/><figcaption class=\"wp-element-caption\">\u56f311. \u91cf\u5b50\u56de\u8def\u306e\u4f8b\uff08Ver.1\u306eFig.5\u3088\u308a\u5f15\u7528\uff09<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9F%BA%E5%BA%95%E9%96%A2%E6%95%B0\"><\/span>\u57fa\u5e95\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u57fa\u5e95\u95a2\u6570\u306f\u3001\u5206\u5b50\u8ecc\u9053\u306e\u6ce2\u52d5\u95a2\u6570\u3092\u8fd1\u4f3c\u7684\u306b\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u7528\u3044\u3089\u308c\u308b\u95a2\u6570\u306e\u7d44\u3067\u3059\u3002\u591a\u304f\u306e\u5834\u5408\u3001\u4e0e\u3048\u3089\u308c\u305f\u65b9\u7a0b\u5f0f\u3092\u53b3\u5bc6\u306b\u89e3\u3044\u3066\u5206\u5b50\u8ecc\u9053\u306e\u6ce2\u52d5\u95a2\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u76ee\u7684\u306e\u5206\u5b50\u8ecc\u9053\u306e\u6ce2\u52d5\u95a2\u6570 $\\phi$\u3092\u3001\u6271\u3044\u3084\u3059\u3044\u57fa\u5e95\u95a2\u6570\u306e\u7d44 $\\varphi_1,\\varphi_2,\\dots,\\varphi_N$\u306e\u7dda\u5f62\u7d50\u5408<\/p>\n\n\n\n<p>$$ \\phi=\\sum_ic_i\\varphi_i $$<\/p>\n\n\n\n<p>\u3067\u8868\u305b\u308b\u3068\u4eee\u5b9a\u3057\u3001\u4fc2\u6570 $c_i$\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3067\u5206\u5b50\u8ecc\u9053\u306e\u6ce2\u52d5\u95a2\u6570 $\\phi$\u3092\u6c42\u3081\u307e\u3059\u3002\u4ee3\u8868\u7684\u306a\u57fa\u5e95\u95a2\u6570\u3068\u3057\u3066\u3001Slater\u578b\u95a2\u6570\u3001Gauss\u578b\u95a2\u6570\u3001sto-3g\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Slater\u578b\u95a2\u6570<\/h4>\n\n\n\n<p>Slater\u578b\u95a2\u6570\u306f $e^{-|r|}$\u306e\u5f62\u3092\u3057\u305f\u95a2\u6570\u3067\u3059\u3002\u6c34\u7d20\u539f\u5b50\u306e1s\u8ecc\u9053\u306b\u53b3\u5bc6\u306b\u4e00\u81f4\u3057\u3001\u5206\u5b50\u8ecc\u9053\u3092\u6b63\u78ba\u306b\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u8a08\u7b97\u30b3\u30b9\u30c8\u304c\u9ad8\u3044\u3067\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Gauss\u578b\u95a2\u6570<\/h4>\n\n\n\n<p>Gauss\u578b\u95a2\u6570\u306f $e^{-r^2}$\u306e\u5f62\u3092\u3057\u305f\u95a2\u6570\u3067\u3059\u3002Slater\u578b\u306b\u6bd4\u3079\u6b63\u78ba\u6027\u306f\u843d\u3061\u307e\u3059\u304c\u3001\u8a08\u7b97\u30b3\u30b9\u30c8\u304c\u4f4e\u3044\u70b9\u3067\u512a\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">sto-3g<\/h4>\n\n\n\n<p>sto-3g\u306f\u3001Gauss\u578b\u95a2\u65703\u3064\u306e\u7dda\u5f62\u548c\u306b\u3088\u3063\u3066Slater\u578b\u95a2\u6570\u3092\u8fd1\u4f3c\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002\u8a08\u7b97\u30b3\u30b9\u30c8\u3092\u6291\u3048\u305f\u307e\u307e\u3001\u8fd1\u4f3c\u306e\u6b63\u78ba\u6027\u3092\u4e0a\u3052\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u672c\u8ad6\u6587\u4e2d\u306e\u5b9f\u9a13\u3067\u306f\u3001sto-3g\u304c\u7528\u3044\u3089\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><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><\/h2>\n\n\n\n<p>[1] <a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Nakaji,+K\">Kouhei Nakaji<\/a>, et al., \u201cThe generative quantum eigensolver (GQE) and its application for ground state search\u201d, <a href=\"https:\/\/doi.org\/10.48550\/arXiv.2401.09253\">https:\/\/doi.org\/10.48550\/arXiv.2401.09253<\/a><\/p>\n\n\n\n<p>[2] <a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=McArdle,+S\">Sam McArdle<\/a>,&nbsp;et al., \u201c<strong>Quantum computational chemistry<\/strong>\u201d, <a href=\"https:\/\/doi.org\/10.48550\/arXiv.1808.10402\">https:\/\/doi.org\/10.48550\/arXiv.1808.10402<\/a><\/p>\n\n\n\n<p>[3] <a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Seeley,+J+T\">Jacob T. Seeley<\/a>,&nbsp;et al., \u201d<strong>The Bravyi-Kitaev transformation for quantum computation of electronic structure<\/strong>\u201d, <a href=\"https:\/\/doi.org\/10.48550\/arXiv.1208.5986\">https:\/\/doi.org\/10.48550\/arXiv.1208.5986<\/a><\/p>\n\n\n\n<p>[4] <a href=\"https:\/\/arxiv.org\/search\/quant-ph?searchtype=author&amp;query=Romero,+J\">Jonathan Romero<\/a>, et al., \u201c<strong>Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz<\/strong>\u201d, <a href=\"https:\/\/doi.org\/10.48550\/arXiv.1701.02691\">https:\/\/doi.org\/10.48550\/arXiv.1701.02691<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><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><\/h2>\n\n\n<div class=\"sabox-plus-item\"><div class=\"saboxplugin-wrap\" itemtype=\"http:\/\/schema.org\/Person\" itemscope itemprop=\"author\"><div class=\"saboxplugin-tab\"><div class=\"saboxplugin-gravatar\"><img alt='Kosuke Saito' src='https:\/\/secure.gravatar.com\/avatar\/3dae0c67e433996af1ff54b2444f196f1b571778a7860f11215735131e00f340?s=100&#038;d=mm&#038;r=g' srcset='https:\/\/secure.gravatar.com\/avatar\/3dae0c67e433996af1ff54b2444f196f1b571778a7860f11215735131e00f340?s=200&#038;d=mm&#038;r=g 2x' class='avatar avatar-100 photo' height='100' width='100' itemprop=\"image\"\/><\/div><div class=\"saboxplugin-authorname\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/author\/kosuke-saito\/\" class=\"vcard author\" rel=\"author\"><span class=\"fn\">Kosuke Saito<\/span><\/a><\/div><div class=\"saboxplugin-desc\"><div itemprop=\"description\"><p>\u6771\u4eac\u79d1\u5b66\u5927\u5b66 \u7406\u5b66\u9662 \u7269\u7406\u5b66\u7cfb \u5b66\u58eb\u8ab2\u7a0b<\/p>\n<\/div><\/div><div class=\"clearfix\"><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Transformer\u3092\u7528\u3044\u3066\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0GPT-QE\u306e\u6709\u52b9\u6027\u3092\u3001\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u30bf\u30b9\u30af\u3067\u5b9f\u8a3c\u3057\u305f\u8ad6\u6587\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u65e2\u5b58\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u305f\u4e8b\u524d\u5b66\u7fd2\u3068\u3001\u4e8b\u524d\u77e5\u8b58\u306a\u3057\u3067\u306e\u5b66\u7fd2\u306e\u53cc\u65b9\u306b\u3088\u308a\u3001\u91cf\u5b50\u8a08\u7b97\u30b3\u30b9\u30c8\u3092\u524a\u6e1b\u3057\u305f\u5b66\u7fd2\u3092\u884c\u3046\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"author":28,"featured_media":8134,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[151,104,150],"class_list":["post-8081","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-review","tag-transformer","tag-104","tag-150"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>GPT-QE : Transformer\u306b\u3088\u308b\u91cf\u5b50\u56de\u8def\u306e\u6700\u9069\u5316 - T-QARD Harbor<\/title>\n<meta name=\"description\" content=\"Transformer\u3092\u7528\u3044\u3066\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0GPT-QE\u306e\u6709\u52b9\u6027\u3092\u3001\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u30bf\u30b9\u30af\u3067\u5b9f\u8a3c\u3057\u305f\u8ad6\u6587\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u65e2\u5b58\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u305f\u4e8b\u524d\u5b66\u7fd2\u3068\u3001\u4e8b\u524d\u77e5\u8b58\u306a\u3057\u3067\u306e\u5b66\u7fd2\u306e\u53cc\u65b9\u306b\u3088\u308a\u3001\u91cf\u5b50\u8a08\u7b97\u30b3\u30b9\u30c8\u3092\u524a\u6e1b\u3057\u305f\u5b66\u7fd2\u3092\u884c\" \/>\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\/2025\/10\/10\/gpt-qe-transformer\u306b\u3088\u308b\u91cf\u5b50\u56de\u8def\u306e\u6700\u9069\u5316\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GPT-QE : Transformer\u306b\u3088\u308b\u91cf\u5b50\u56de\u8def\u306e\u6700\u9069\u5316 - T-QARD Harbor\" \/>\n<meta property=\"og:description\" content=\"Transformer\u3092\u7528\u3044\u3066\u91cf\u5b50\u56de\u8def\u3092\u751f\u6210\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0GPT-QE\u306e\u6709\u52b9\u6027\u3092\u3001\u91cf\u5b50\u5316\u5b66\u8a08\u7b97\u30bf\u30b9\u30af\u3067\u5b9f\u8a3c\u3057\u305f\u8ad6\u6587\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u65e2\u5b58\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u305f\u4e8b\u524d\u5b66\u7fd2\u3068\u3001\u4e8b\u524d\u77e5\u8b58\u306a\u3057\u3067\u306e\u5b66\u7fd2\u306e\u53cc\u65b9\u306b\u3088\u308a\u3001\u91cf\u5b50\u8a08\u7b97\u30b3\u30b9\u30c8\u3092\u524a\u6e1b\u3057\u305f\u5b66\u7fd2\u3092\u884c\" \/>\n<meta property=\"og:url\" content=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/10\/gpt-qe-transformer\u306b\u3088\u308b\u91cf\u5b50\u56de\u8def\u306e\u6700\u9069\u5316\/\" \/>\n<meta property=\"og:site_name\" content=\"T-QARD Harbor\" \/>\n<meta property=\"article:published_time\" content=\"2025-10-10T01:08:17+00:00\" \/>\n<meta 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