{"id":136,"date":"2018-05-16T19:00:50","date_gmt":"2018-05-16T10:00:50","guid":{"rendered":"http:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=136"},"modified":"2018-05-16T19:00:50","modified_gmt":"2018-05-16T10:00:50","slug":"navigating-a-maze-using-a-quantum-annealershuhei-imai","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/","title":{"rendered":"\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3067 \u8ff7\u8def \u304b\u3089\u8131\u51fa\u3059\u308b &#8220;Navigating a Maze using a Quantum Annealer&#8221; by Scott Pakin"},"content":{"rendered":"\n<p>\u672c\u8a18\u4e8b\u3067\u53d6\u308a\u4e0a\u3052\u308b\u8ad6\u6587\u3067\u306f \u8ff7\u8def \u306b\u304a\u3051\u308b\u6700\u77ed\u7d4c\u8def\u3092\u6c42\u3081\u308b\u554f\u984c\u3092\u30a4\u30b8\u30f3\u30b0\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u3068\u3057\u3066\u5b9a\u5f0f\u5316\u3057\u3001D-Wave 2X\u3092\u7528\u3044\u3066\u89e3\u3044\u305f\u7d50\u679c\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u88dc\u52a9\u30c4\u30fc\u30eb\u3068\u3057\u3066\u3001\u554f\u984c\u3092\u5c0f\u554f\u984c\u306b\u5206\u5272\u3057\u3001D-Wave\u30de\u30b7\u30f3\u306e\u30ad\u30e1\u30e9\u30b0\u30e9\u30d5\u306b\u30de\u30c3\u30d7\u3059\u308b<a href=\"https:\/\/github.com\/lanl\/qmasm\">QMASM(quantum macro assembler)<\/a>\u3092\u7528\u3044\u3066\u3044\u308b\u3002\u5165\u51fa\u529b\u3084\u30a4\u30b8\u30f3\u30b0\u6a21\u578b\u3078\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3001\u3055\u3089\u306b\u306f \u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0 \u306b\u304b\u304b\u308b\u6642\u9593\u306e\u30d9\u30f3\u30c1\u30de\u30fc\u30af\u3084\u3001\u305d\u3057\u3066\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u6642\u9593\u306b\u3088\u308b\u89e3\u306e\u6642\u9593\u5bfe\u7cbe\u5ea6\u306a\u3069\u306b\u3064\u3044\u3066\u3082\u8003\u5bdf\u3092\u3057\u3066\u3044\u308b\u3002<\/p>\n\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\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%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\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E8%BF%B7%E8%B7%AF%E3%81%AE%E7%B5%84%E5%90%88%E3%81%9B%E6%9C%80%E9%81%A9%E5%8C%96%E5%95%8F%E9%A1%8C%E3%81%A8%E3%81%97%E3%81%A6%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >\u8ff7\u8def\u306e\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3068\u3057\u3066\u306e\u5b9a\u5f0f\u5316<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E8%BF%B7%E8%B7%AF%E3%81%AE%E5%AE%9A%E7%BE%A9%E3%81%A8%E8%A7%A3%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%81%8C%E6%BA%80%E3%81%9F%E3%81%99%E3%81%B9%E3%81%8D%E6%9D%A1%E4%BB%B6\" >\u8ff7\u8def\u306e\u5b9a\u7fa9\u3068\u89e3\u306e\u7d4c\u8def\u304c\u6e80\u305f\u3059\u3079\u304d\u6761\u4ef6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E8%BF%B7%E8%B7%AF%E5%95%8F%E9%A1%8C%E3%81%AE%E3%82%A4%E3%82%B8%E3%83%B3%E3%82%B0%E8%A1%A8%E7%8F%BE%E3%81%A8%E3%81%97%E3%81%A6%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >\u8ff7\u8def\u554f\u984c\u306e\u30a4\u30b8\u30f3\u30b0\u8868\u73fe\u3068\u3057\u3066\u306e\u5b9a\u5f0f\u5316<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E6%9D%A1%E4%BB%B6%E2%91%A0_%E5%85%A5%E5%8F%A3%E3%81%A8%E5%87%BA%E5%8F%A3%E3%81%AF%E5%BF%85%E3%81%9A%E3%81%A9%E3%81%A1%E3%82%89%E3%82%82%E5%90%AB%E3%81%BE%E3%82%8C%E3%82%8B\" >\u6761\u4ef6\u2460 \u5165\u53e3\u3068\u51fa\u53e3\u306f\u5fc5\u305a\u3069\u3061\u3089\u3082\u542b\u307e\u308c\u308b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E6%9D%A1%E4%BB%B6%E2%91%A1_%E5%A3%81%E3%82%92%E9%80%9A%E3%82%8A%E6%8A%9C%E3%81%91%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AF%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84\" >\u6761\u4ef6\u2461 \u58c1\u3092\u901a\u308a\u629c\u3051\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E6%9D%A1%E4%BB%B6%E2%91%A2_%E3%83%9E%E3%82%B9%E3%81%AB%E5%85%A5%E3%81%A3%E3%81%9F%E3%82%89%E5%BF%85%E3%81%9A%E5%87%BA%E3%81%AA%E3%81%8F%E3%81%A6%E3%81%AF%E3%81%84%E3%81%91%E3%81%AA%E3%81%84%E3%80%82%E3%81%BE%E3%81%9F%E3%80%81%E8%A4%87%E6%95%B0%E5%9B%9E%E3%83%9E%E3%82%B9%E3%81%AB%E5%85%A5%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AF%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84\" >\u6761\u4ef6\u2462 \u30de\u30b9\u306b\u5165\u3063\u305f\u3089\u5fc5\u305a\u51fa\u306a\u304f\u3066\u306f\u3044\u3051\u306a\u3044\u3002\u307e\u305f\u3001\u8907\u6570\u56de\u30de\u30b9\u306b\u5165\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E5%AE%9F%E8%A1%8C%E7%B5%90%E6%9E%9C\" >\u5b9f\u884c\u7d50\u679c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/16\/navigating-a-maze-using-a-quantum-annealershuhei-imai\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E4%BD%9C%E6%88%90%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u4f5c\u6210\u8005<\/a><\/li><\/ul><\/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<p>Scott Pakin, &#8220;Navigating a Maze using a Quantum Annealer&#8221;, <a href=\"https:\/\/dl.acm.org\/citation.cfm?doid=3149526.3149532\" target=\"_blank\" rel=\"noopener\">Proceeding of PMES&#8217;17 Proceedings of the Second International Workshop on Post Moores Era Supercomputing, 30-36 (2017)<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%BF%B7%E8%B7%AF%E3%81%AE%E7%B5%84%E5%90%88%E3%81%9B%E6%9C%80%E9%81%A9%E5%8C%96%E5%95%8F%E9%A1%8C%E3%81%A8%E3%81%97%E3%81%A6%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>\u8ff7\u8def\u306e\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3068\u3057\u3066\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%BF%B7%E8%B7%AF%E3%81%AE%E5%AE%9A%E7%BE%A9%E3%81%A8%E8%A7%A3%E3%81%AE%E7%B5%8C%E8%B7%AF%E3%81%8C%E6%BA%80%E3%81%9F%E3%81%99%E3%81%B9%E3%81%8D%E6%9D%A1%E4%BB%B6\"><\/span>\u8ff7\u8def\u306e\u5b9a\u7fa9\u3068\u89e3\u306e\u7d4c\u8def\u304c\u6e80\u305f\u3059\u3079\u304d\u6761\u4ef6<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a6\u00d76\u306e\u30de\u30b9\u304b\u3089\u69cb\u6210\u3055\u308c\u308b\u8ff7\u8def\u3092\u8003\u3048\u308b\u3002\u4efb\u610f\u306e\u30de\u30b9\u3092<strong>(\u5217, \u884c)<\/strong>\u3067\u8868\u3059\u3053\u3068\u306b\u3059\u308b\u3002\uff08\u4e0b\u56f3\u3067\u306f\u3001\u4f8b\u3048\u3070(A1)\u306f\u6700\u3082\u5de6\u4e0a\u306e\u30de\u30b9\u3067\u3042\u308a\u3001\u5165\u53e3\u3068\u51fa\u53e3\u304c(B6), (F1)\u3067\u3042\u308b\u3002\uff09<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/maze1.png\" alt=\"\" class=\"wp-image-256\"\/><\/figure>\n<\/div>\n\n\n<p>\u89e3\u3068\u306a\u308b\u6700\u77ed\u7d4c\u8def\u306f\u4ee5\u4e0b\u306e3\u3064\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u2460. \u5165\u53e3\u3068\u51fa\u53e3\u306f\u5fc5\u305a\u3069\u3061\u3089\u3082\u542b\u307e\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u2461. \u58c1\u3092\u901a\u308a\u629c\u3051\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u2462. \u30de\u30b9\u306b\u5165\u3063\u305f\u3089\u5fc5\u305a\u51fa\u306a\u304f\u3066\u306f\u3044\u3051\u306a\u3044\u3002\u307e\u305f\u3001\u8907\u6570\u56de\u30de\u30b9\u306b\u5165\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%BF%B7%E8%B7%AF%E5%95%8F%E9%A1%8C%E3%81%AE%E3%82%A4%E3%82%B8%E3%83%B3%E3%82%B0%E8%A1%A8%E7%8F%BE%E3%81%A8%E3%81%97%E3%81%A6%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>\u8ff7\u8def\u554f\u984c\u306e\u30a4\u30b8\u30f3\u30b0\u8868\u73fe\u3068\u3057\u3066\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u5909\u6570\uff1a$\\sigma \\in \\{ +1, -1 \\}$ (\u7d4c\u8def\u306b\u542b\u307e\u308c\u308b\u306a\u3089+1, \u305d\u3046\u3067\u306a\u3051\u308c\u3070-1)<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u4e0a\u306e\u56f3\u306e\u53f3\u4e0a\u306b\u6ce8\u76ee\u3059\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/maze2.png\" alt=\"\" class=\"wp-image-264\"\/><\/figure>\n<\/div>\n\n\n<p>\u3053\u308c\u306f\u3001(E1)\u3068(F1)\u306e\u30de\u30b9\u306b\u7740\u76ee\u3057\u305f\u56f3\u3067\u3042\u308b\u3002$\\sigma_{\\mathrm{i}}$\u306f\u8ff7\u8def\u306e\u5165\u308a\u53e3\u3092\u8868\u3059\u5909\u6570\u3067\u3042\u308a\u3001\u305d\u308c\u4ee5\u5916\u306e$\\sigma$\u306f\u5404\u30de\u30b9\u306e\u4e2d\u306e\u5404\u65b9\u5411\u306e\u7d4c\u8def\u3092\u8868\u3059\u5909\u6570\u3067\u3042\u308b\u3002$\\sigma$\u306f\u3069\u3061\u3089\u3082\u00b11\u306e\u3069\u3061\u3089\u304b\u306e\u5024\u3092\u3068\u308a\u3001\u6700\u77ed\u8def\u306b\u542b\u307e\u308c\u308b$\\sigma$\u306f+1\u3092\u3001\u542b\u307e\u308c\u306a\u3044$\\sigma$\u306f-1\u3092\u3068\u308b\u3082\u306e\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u90e8\u5206\u3092\u4f8b\u984c\u306e\u90e8\u5206\u7684\u306a\u5177\u4f53\u4f8b\u3068\u3057\u305f\u3046\u3048\u3067\u4ee5\u4e0b\u3067\u4e0a\u306e3\u6761\u4ef6\u3092\u5b9a\u5f0f\u5316\u3059\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9D%A1%E4%BB%B6%E2%91%A0_%E5%85%A5%E5%8F%A3%E3%81%A8%E5%87%BA%E5%8F%A3%E3%81%AF%E5%BF%85%E3%81%9A%E3%81%A9%E3%81%A1%E3%82%89%E3%82%82%E5%90%AB%E3%81%BE%E3%82%8C%E3%82%8B\"><\/span>\u6761\u4ef6\u2460 \u5165\u53e3\u3068\u51fa\u53e3\u306f\u5fc5\u305a\u3069\u3061\u3089\u3082\u542b\u307e\u308c\u308b<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>\u5165\u53e3\u3067\u3042\u308b$\\sigma_{\\mathrm{i}}$\u306b\u7740\u76ee\u3059\u308b\u3002\u3059\u308b\u3068\u3001\u5165\u53e3\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n$$\n\\begin{aligned}\n\\mathcal{H}_{\\mathrm{ingress}}=h_{\\mathrm{N}} \\sigma_{\\mathrm{N}} + h_{\\mathrm{i}} \\sigma_{\\mathrm{i}} + J_{\\mathrm{N, i}} \\sigma_{\\mathrm{N}} \\sigma_{\\mathrm{i}} = &#8211; \\sigma_{\\mathrm{i}} &#8211; \\sigma_{\\mathrm{N}}\\sigma_{\\mathrm{i}}\n\\end{aligned}\n$$\n\n\n\n<p>\u3053\u3053\u3067\u3001$h_N=0, h_i=-1$,\u305d\u3057\u3066$J_N, i=-1$\u3068\u3057\u3066\u3044\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u3069\u3061\u3089\u306e$\\sigma$\u3082+1\u306e\u6642\u306b\u3053\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u6700\u5c0f\u5024\u3092\u3068\u308b\u3002\u3086\u3048\u306b\u3053\u306e\u5f0f\u306f\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3002\u3053\u308c\u3068\u540c\u69d8\u306b\u3057\u3066\u3001(B6)\u306e\u30de\u30b9\u306b\u3042\u308b\u51fa\u53e3\u3082\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n$$\n\\mathcal{H}_{\\mathrm{egress}}\n=\nh_{\\mathrm{S}} \\sigma_{\\mathrm{S}}\n+ h_{\\mathrm{e}} \\sigma_{\\mathrm{e}}\n+ J_{\\mathrm{S, e}} \\sigma_{\\mathrm{S}} \\sigma_{\\mathrm{e}}\n=\n\\sigma_{\\mathrm{e}} &#8211; \\sigma_{\\mathrm{S}}\\sigma_{\\mathrm{e}}\n$$\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9D%A1%E4%BB%B6%E2%91%A1_%E5%A3%81%E3%82%92%E9%80%9A%E3%82%8A%E6%8A%9C%E3%81%91%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AF%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84\"><\/span>\u6761\u4ef6\u2461 \u58c1\u3092\u901a\u308a\u629c\u3051\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>(E1)\u306e\u30de\u30b9\u306e$\\sigma_{\\mathrm{W}}$\u3092\u4f8b\u3068\u3059\u308b\u3002$\\sigma_{\\mathrm{W}}$\u65b9\u5411\u306b\u306f\u58c1\u304c\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u65b9\u5411\u306f\u6700\u77ed\u8def\u306b\u542b\u307e\u308c\u308b\u3053\u3068\u306f\u306a\u3044\u3002\u3086\u3048\u306b\u3001$\\sigma_{\\mathrm{W}}=-1$\u3068\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002\u307e\u305f\u3001$\\sigma_{\\mathrm{W}}$\u65b9\u5411\u306e\u58c1\u3092\u8868\u3059\u5909\u6570\u3092$\\sigma_{\\mathrm{wall}}$\u3068\u3059\u308b\u3068\u3001\u3053\u308c\u306f\u5e38\u306b-1\u3067\u3042\u308b\u3002\u3086\u3048\u306b\u2460\u306e\u6642\u3068\u306f\u7570\u306a\u308a\u3001$h_{\\mathrm{W}}=0, h_{\\mathrm{wall}}&nbsp;=1$,\u305d\u3057\u3066$J_{\\mathrm{W, wall}}=-1$\u3068\u3059\u308b\u3068\u3001(E1)\u306e$\\sigma_{\\mathrm{W}}$\u65b9\u5411\u306e\u58c1\u306b\u95a2\u3059\u308b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f<\/p>\n\n\n\n$$\n\\begin{aligned}\n\\mathcal{H}_{\\mathrm{wall}}\n=\nh_{\\mathrm{W}} \\sigma_{\\mathrm{W}}\n+ h_{\\mathrm{wall}} \\sigma_{\\mathrm{wall}}\n+ J_{\\mathrm{W, wall}} \\sigma_{\\mathrm{W}} \\sigma_{\\mathrm{wall}}\n=\n\\sigma_{\\mathrm{wall}} &#8211; \\sigma_{\\mathrm{W}}\\sigma_{\\mathrm{wall}}\n\\end{aligned}\n$$\n\n\n\n<p>\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9D%A1%E4%BB%B6%E2%91%A2_%E3%83%9E%E3%82%B9%E3%81%AB%E5%85%A5%E3%81%A3%E3%81%9F%E3%82%89%E5%BF%85%E3%81%9A%E5%87%BA%E3%81%AA%E3%81%8F%E3%81%A6%E3%81%AF%E3%81%84%E3%81%91%E3%81%AA%E3%81%84%E3%80%82%E3%81%BE%E3%81%9F%E3%80%81%E8%A4%87%E6%95%B0%E5%9B%9E%E3%83%9E%E3%82%B9%E3%81%AB%E5%85%A5%E3%82%8B%E3%81%93%E3%81%A8%E3%81%AF%E3%81%A7%E3%81%8D%E3%81%AA%E3%81%84\"><\/span>\u6761\u4ef6\u2462 \u30de\u30b9\u306b\u5165\u3063\u305f\u3089\u5fc5\u305a\u51fa\u306a\u304f\u3066\u306f\u3044\u3051\u306a\u3044\u3002\u307e\u305f\u3001\u8907\u6570\u56de\u30de\u30b9\u306b\u5165\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<p>\u307e\u305a\u3001\u6761\u4ef6\u306e\u8996\u899a\u7684\u306a\u8aac\u660e\u3092\u3059\u308b\u3002\u2462\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u306e\u306f\u4ee5\u4e0b\u306e3\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/maze7.png\" alt=\"\" class=\"wp-image-274\"\/><\/figure>\n<\/div>\n\n\n<p>\u5de6\u306e\u56f3\u306f\u7d4c\u8def\u3068\u3057\u3066\u30de\u30b9\u304c\u4f7f\u308f\u308c\u306a\u3044\u5834\u5408\u3067\u3042\u308b\u3002\u307e\u305f\u3001\u771f\u3093\u4e2d\u3068\u53f3\u306e\u56f3\u306f\u3001\u4e00\u56de\u30de\u30b9\u306b\u5165\u308a\u305d\u306e\u307e\u307e\u30de\u30b9\u3092\u51fa\u3066\u623b\u3063\u3066\u304d\u3066\u3044\u306a\u3044\u5834\u5408\u3067\u3042\u308b\u3002\u3053\u306e\u3069\u3061\u3089\u306e\u5834\u5408\u3082\u6700\u77ed\u8def\u306b\u542b\u3080\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001\u2462\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044\u5834\u5408\u3067\u3042\u308b\u3002\u305d\u308c\u306f\u4ee5\u4e0b\u306e3\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/maze8.png\" alt=\"\" class=\"wp-image-275\"\/><\/figure>\n<\/div>\n\n\n<p>\u5de6\u306e\u56f3\u306f\u30de\u30b9\u306b\u5165\u3063\u305f\u307e\u307e\u51fa\u306a\u3044\u5834\u5408\u3067\u3042\u308b\u3002\u307e\u305f\u3001\u771f\u3093\u4e2d\u3068\u53f3\u306e\u56f3\u306f\u3001\u8907\u6570\u56de\u30de\u30b9\u306b\u5165\u3063\u3066\u3057\u307e\u3063\u3066\u3044\u308b\u3002\u3053\u308c\u3089\u306f\u6700\u77ed\u8def\u306b\u542b\u3080\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u306e\u3067\u3001\u3053\u306e\u3088\u3046\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u5b9a\u7fa9\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n$$\n\\begin{aligned}\n\\mathcal{H}_{\\mathrm{room}}\n&#038;=\n\\frac{1}{2}\n(\\sigma_{\\mathrm{N}}\n+ \\sigma_{\\mathrm{E}}\n+ \\sigma_{\\mathrm{W}}\n+ \\sigma_{\\mathrm{S}})\n+ \\sigma_{\\mathrm{a}}\n\\\\\n&#038;\\qquad\n+ \\frac{1}{4} (\\sigma_{\\mathrm{N}} \\sigma_{\\mathrm{E}}\n+ \\sigma_{\\mathrm{N}} \\sigma_{\\mathrm{W}}\n+ \\sigma_{\\mathrm{N}} \\sigma_{\\mathrm{S}}\n+ \\sigma_{\\mathrm{E}} \\sigma_{\\mathrm{W}}\n+ \\sigma_{\\mathrm{E}} \\sigma_{\\mathrm{S}}\n+ \\sigma_{\\mathrm{W}} \\sigma_{\\mathrm{S}})\n\\\\\n&#038;\\qquad\n+ \\frac{1}{2} (\\sigma_{\\mathrm{N}} \\sigma_{\\mathrm{a}}\n+ \\sigma_{\\mathrm{E}} \\sigma_{\\mathrm{a}}\n+ \\sigma_{\\mathrm{W}} \\sigma_{\\mathrm{a}}\n+ \\sigma_{\\mathrm{S}} \\sigma_{\\mathrm{a}})\n\\end{aligned}\n$$\n\n\n\n<p>\u2460\u3001\u2461\u306e\u3088\u3046\u306a\u5f62\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3067\u8868\u3057\u305f\u304b\u3063\u305f\u306e\u3060\u304c\u3001\u305d\u306e\u5f62\u3067\u306f\u3046\u307e\u304f\u8868\u305b\u306a\u3044\u305f\u3081h\u3068J\u3092\u9069\u5207\u306b\u9078\u629e\u3057\u305f\u3046\u3048\u3067\u88dc\u52a9\u5909\u6570$\\sigma_{\\mathrm{a}}$\u3092\u7528\u3044\u3066\u3044\u308b\u3002\u3053\u308c\u306f$\\sigma_{\\mathrm{N}}$\u304b\u3089$\\sigma_{\\mathrm{W}}$\u304c\u3059\u3079\u3066\u8ca0\u306e\u6642\u306b+1\u3092\u53d6\u308a\u3001\u305d\u308c\u4ee5\u5916\u306e\u6642\u306f-1\u3092\u53d6\u308b\u3002<\/p>\n\n\n\n$$\n\\mathcal{H}_{\\mathrm{E1}}\n=\n\\mathcal{H}_{\\mathrm{room}}\n+ \\mathcal{H}_{\\mathrm{wall}}(\\mathrm{N})\n+ \\mathcal{H}_{\\mathrm{wall}}(\\mathrm{W})\n$$\n\n\n\n$$\n\\mathcal{H}_{\\mathrm{F1}}\n=\n\\mathcal{H}_{\\mathrm{room}}\n+ \\mathcal{H}_{\\mathrm{wall}}(\\mathrm{E})\n+ \\mathcal{\\mathrm{H}}_{\\mathrm{ingress}}(\\mathrm{N})\n$$\n\n\n\n<p>\u3068\u306a\u308b\u3002\u3057\u304b\u3057\u3001\u30de\u30b9(E1)\u3068\u30de\u30b9(F1)\u306e\u4e8c\u3064\u306e\u30de\u30b9\u306e\u5168\u4f53\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u8003\u3048\u308b\u3068\u304d\u306f\u3001\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u30de\u30b9(E1)\u3068\u30de\u30b9(F1)\u306e\u58c1\u3067\u9694\u3066\u3089\u308c\u3066\u3044\u306a\u3044\u96a3\u308a\u5408\u3046\u7d4c\u8def\u306f\u3069\u3061\u3089\u3082+1\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u3088\u3063\u3066\u305d\u308c\u3092\u8e0f\u307e\u3048\u308b\u3068\u3001\u30de\u30b9(E1)\u3068\u30de\u30b9(F1)\u3092\u5168\u4f53\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n$$\n\\mathcal{H}_{\\mathrm{E1, F1}}\n=\n\\mathcal{H}_{\\mathrm{E1}}\n+ \\mathcal{H}_{\\mathrm{F1}}\n&#8211; \\sigma_{\\mathrm{E}}^{(\\mathrm{E1})} \\sigma_{\\mathrm{W}}^{(\\mathrm{F1})}\n$$\n\n\n\n<p>\u3053\u308c\u3092\u5404\u30de\u30b9\u306b\u3064\u3044\u3066\u8003\u3048\u3001\u3053\u306e\u64cd\u4f5c\u3092\u884c\u3046\u3053\u3068\u3067\u4f8b\u984c\u306e\u8ff7\u8def\u306e\u5168\u4f53\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E8%A1%8C%E7%B5%90%E6%9E%9C\"><\/span>\u5b9f\u884c\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>QMASM\u3092\u7528\u3044\u3066\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306b\u73fe\u308c\u308b219\u500b\u306e\u5909\u6570\u3092\u30ad\u30e1\u30e9\u30b0\u30e9\u30d5\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3057\u305f\u3068\u3053\u308d\u300160\u56de\u306e\u8a66\u884c\u3067580.25\u00b139.71\u500b\u306equbit\u3067\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u3002<\/p>\n\n\n\n<p>\u307e\u305f\u300120\u03bcs\u3067\u306e\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u309210000\u56de\u884c\u3046\u3068\u3044\u3063\u305f\u8a66\u884c\u3092\u884c\u3044\u3001\u5404\u6a5f\u80fd\u306e\u30d9\u30f3\u30c1\u30de\u30fc\u30af\u3092\u884c\u3063\u305f\u300230\u56de\u7e70\u308a\u8fd4\u3059\u3053\u3068\u306b\u3088\u308a\u4ee5\u4e0b\u306e\u8868\u304c\u5f97\u3089\u308c\u305f\u3002\u6570\u5024\u306f\u5e73\u5747\u5024\u3068\u6a19\u6e96\u504f\u5dee\u3067\u8868\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/maze13.png\" alt=\"\" class=\"wp-image-287\"\/><\/figure>\n<\/div>\n\n\n<p>20\u03bcs\u3067\u306e\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u309210000\u56de\u884c\u3046\u3068\u3044\u3063\u305f\u8a66\u884c\u306f\u5e73\u5747\u3057\u3066\u304a\u3088\u305d20.3\u79d2\u3082\u304b\u304b\u3063\u3066\u304a\u308a\u30016\u00d76\u306e\u8ff7\u8def\u3067\u5f97\u3089\u308c\u305f\u7d50\u679c\u3068\u3057\u3066\u306f\u4e9b\u304b\u4e0d\u6e80\u8db3\u306a\u7d50\u679c\u3068\u306a\u3063\u305f\u3002\u3057\u304b\u3057\u306a\u304c\u3089\u3001\u5b9f\u969b\u306bQPU\u3067\u51e6\u7406\u306b\u304b\u304b\u3063\u3066\u3044\u308b\u6642\u9593\u306f\u7d041.9\u79d2\u3067\u3042\u3063\u305f\u3002\u307e\u305f\u3001QMASM\u306b\u3088\u308a\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u304b\u306a\u308a\u306e\u9ad8\u901f\u5316\u304c\u671f\u5f85\u3067\u304d\u3066\u304a\u308a\u3001\u3053\u308c\u306f\u6700\u5927\u306e\u30dc\u30c8\u30eb\u30cd\u30c3\u30af\u3067\u3042\u3063\u305f\u3001D-Wave&#8217;s minor embedder\u306e\u51e6\u7406\u3092\u7c21\u7565\u306b\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3042\u308b\u3002\u66f4\u306b\u3001\u4e0a\u306e\u8868\u304b\u3089\u308f\u304b\u308b\u901a\u308aSAPI 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