{"id":454,"date":"2018-06-20T16:00:27","date_gmt":"2018-06-20T07:00:27","guid":{"rendered":"http:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=454"},"modified":"2018-06-20T16:00:27","modified_gmt":"2018-06-20T07:00:27","slug":"%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/","title":{"rendered":"\u30b0\u30e9\u30d5\u5206\u5272\u554f\u984c \u3092D-Wave 2000Q\u3067\u89e3\u304f\uff08\u5b9f\u8df5\u7de8\uff09"},"content":{"rendered":"\n<p>T-Wave\u958b\u8a2d\u4ee5\u6765\u3001\u3044\u304f\u3064\u304b\u306e\u5148\u884c\u7814\u7a76\u3084\u5c0e\u5165\u4e8b\u4f8b\u306b\u95a2\u3059\u308b\u8a18\u4e8b\u304c\u51fa\u3066\u3044\u308b\u4e2d\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u5177\u4f53\u7684\u306a\u554f\u984c\u3092D-Wave\u30de\u30b7\u30f3\u3067\u89e3\u304f\u306e\u304b\u3068\u3044\u3046\u3053\u3068\u306f\u7686\u3055\u3093\u6c17\u306b\u306a\u3063\u3066\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f<a href=\"\/T-Wave\/?p=122\"> \u30b0\u30e9\u30d5\u5206\u5272\u554f\u984c <\/a>\u3092\u4f8b\u306b\u3001\u30b5\u30dd\u30fc\u30c8\u30c4\u30fc\u30eb\u3067\u3042\u308bqbsolv\u3092\u7528\u3044\u3066D-Wave\u30de\u30b7\u30f3\u306b\u89e3\u304b\u305b\u308b\u904e\u7a0b\u3092\u793a\u3057\u307e\u3059\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\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/#%E5%95%8F%E9%A1%8C%E3%82%92%E8%A7%A3%E3%81%8F%E9%81%8E%E7%A8%8B%E3%81%AE%E6%A6%82%E7%95%A5\" >\u554f\u984c\u3092\u89e3\u304f\u904e\u7a0b\u306e\u6982\u7565<\/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\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/#Step_1_%E3%82%B0%E3%83%A9%E3%83%95%E5%88%86%E5%89%B2%E5%95%8F%E9%A1%8C%E3%81%AE%E3%83%8F%E3%83%9F%E3%83%AB%E3%83%88%E3%83%8B%E3%82%A2%E3%83%B3%E3%81%AE%E7%A2%BA%E8%AA%8D\" >Step 1. \u30b0\u30e9\u30d5\u5206\u5272\u554f\u984c\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u78ba\u8a8d<\/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\/2018\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/#Step_2_QUBO%E8%A1%8C%E5%88%97%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AE%E8%A8%88%E7%AE%97\" >Step 2. QUBO\u884c\u5217\u306e\u8981\u7d20\u306e\u8a08\u7b97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/#Step_3_QUBO%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB%E3%81%AE%E4%BD%9C%E6%88%90\" >Step 3. QUBO\u30d5\u30a1\u30a4\u30eb\u306e\u4f5c\u6210<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/#Step_4_qbsolv%E3%82%B3%E3%83%9E%E3%83%B3%E3%83%89%E3%81%AE%E5%AE%9F%E8%A1%8C%E3%81%A8%E7%B5%90%E6%9E%9C\" >Step 4. qbsolv\u30b3\u30de\u30f3\u30c9\u306e\u5b9f\u884c\u3068\u7d50\u679c<\/a><\/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\/2018\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/#%E3%81%BE%E3%81%A8%E3%82%81\" >\u307e\u3068\u3081<\/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\/2018\/06\/20\/%e3%82%b0%e3%83%a9%e3%83%95%e5%88%86%e5%89%b2%e5%95%8f%e9%a1%8c%e3%82%92d-wave%e3%81%a7%e8%a7%a3%e3%81%8f%ef%bc%88%e5%ae%9f%e8%b7%b5%e7%b7%a8%ef%bc%89\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%95%8F%E9%A1%8C%E3%82%92%E8%A7%A3%E3%81%8F%E9%81%8E%E7%A8%8B%E3%81%AE%E6%A6%82%E7%95%A5\"><\/span>\u554f\u984c\u3092\u89e3\u304f\u904e\u7a0b\u306e\u6982\u7565<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4e00\u822c\u7684\u306bqbsolv\u3092\u7528\u3044\u3066D-Wave\u30de\u30b7\u30f3\u3067\u3001\u7d44\u5408\u305b\u6700\u9069\u5316\u3092\u884c\u3046\u969b\u306b\u5fc5\u8981\u3068\u306a\u308b\u30b9\u30c6\u30c3\u30d7\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<p>Step 1. \u554f\u984c\u306eQUBO\u8868\u73fe\u306e\u78ba\u8a8d\uff08\u4e8c\u5024\u5909\u6570\u306e\u610f\u5473\u3001\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306a\u3069\uff09<br>Step 2. QUBO\u884c\u5217$Q_{ij}$\u306e\u8981\u7d20\u306e\u8a08\u7b97<br>Step 3. qubo\u30d5\u30a1\u30a4\u30eb\u306e\u751f\u6210<br>Step 4. qbsolv\u30b3\u30de\u30f3\u30c9\u306e\u5b9f\u884c\u3068\u7d50\u679c\u306e\u89e3\u91c8<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Step_1_%E3%82%B0%E3%83%A9%E3%83%95%E5%88%86%E5%89%B2%E5%95%8F%E9%A1%8C%E3%81%AE%E3%83%8F%E3%83%9F%E3%83%AB%E3%83%88%E3%83%8B%E3%82%A2%E3%83%B3%E3%81%AE%E7%A2%BA%E8%AA%8D\"><\/span>Step 1. \u30b0\u30e9\u30d5\u5206\u5272\u554f\u984c\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u78ba\u8a8d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30b0\u30e9\u30d5\u4e2d\u306e\u30ce\u30fc\u30c9\u30922\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u5272\uff08\u6700\u5c0f\u30ab\u30c3\u30c8\uff09\u3059\u308b\u5834\u5408\u306b\u306f\u3001\u3042\u308b\u30ce\u30fc\u30c9\u304c\u6240\u5c5e\u3059\u308b\u30b0\u30eb\u30fc\u30d7\u3092\u8868\u30592\u5024\u5909\u6570$s_i \\in \\{ -1, 1 \\}$\u3092\u8003\u3048\u3001\u6700\u5c0f\u5316\u3059\u3079\u304d\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\uff08\u76ee\u7684\u95a2\u6570\uff09\u306f\u3001<\/p>\n\n\n\n$$\n\\mathrm{Obj}(\\mathbf{s}) = \\sum_{(i, j) \\in E} (s_i &#8211; s_j)^2 + \\alpha \\left( \\sum_i s_i \\right)^2\n$$\n\n\n\n<p>\u3067\u3059\u3002\u3053\u3053\u3067\u3001$E$\u306f\u30a8\u30c3\u30b8\u306e\u96c6\u5408\u3092\u8868\u3057\u3066\u304a\u308a\u3001$\\sum_{(i, j) \\in E}$\u306f\u30ce\u30fc\u30c9$i$\u3068\u30ce\u30fc\u30c9$j$\u304c\u30a8\u30c3\u30b8$(i, j)$\u3067\u7d50\u3070\u308c\u3066\u3044\u308b\u3088\u3046\u306a$i, j$\u306e\u7d44\u306b\u3064\u3044\u3066\u548c\u3092\u53d6\u308b\u3068\u3044\u3046\u610f\u5473\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Step_2_QUBO%E8%A1%8C%E5%88%97%E3%81%AE%E8%A6%81%E7%B4%A0%E3%81%AE%E8%A8%88%E7%AE%97\"><\/span>Step 2. QUBO\u884c\u5217\u306e\u8981\u7d20\u306e\u8a08\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4e00\u822c\u306bQUBO\u5f62\u5f0f\u306e\u554f\u984c\u306e\u76ee\u7684\u95a2\u6570\u306f\u3001<\/p>\n\n\n\n$$\n\\mathrm{Obj}(\\mathbf{x}) = \\sum_{i, j} Q_{ij} x_i x_j\n$$\n\n\n\n<p>\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002D-Wave\u30de\u30b7\u30f3\u306b\u304a\u3051\u308b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3068\u306f\u3001\u884c\u5217$Q_{ij}$\u306e\u8981\u7d20\u3092\u554f\u984c\u306b\u5fdc\u3058\u3066\u4e0e\u3048\u308b\u3053\u3068\u306b\u4ed6\u306a\u308a\u307e\u305b\u3093\u3002\u3067\u306f\u3001\u5148\u307b\u3069\u306e\u30b0\u30e9\u30d5\u5206\u5272\u306b\u95a2\u3059\u308b\u76ee\u7684\u95a2\u6570\u3092\u5143\u306b\u884c\u5217$Q_{ij}$\u306e\u8981\u7d20\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u6700\u521d\u306b\u6ce8\u610f\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u306e\u306f\u3001qbsolv\u30b3\u30de\u30f3\u30c9\u3092\u7528\u3044\u308b\u969b\u306b\u306fIsing\u8868\u73fe ($s_i \\in \\{-1, 1 \\}$)\u3067\u306f\u306a\u304f\u3001QUBO\u8868\u73fe\uff08$x_i \\in \\{0, 1 \\}$\uff09\u3067\u76ee\u7684\u95a2\u6570\u3092\u8a18\u8ff0\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u3001\u5f93\u3063\u3066\u3001Step 1.\u3067\u8a18\u8ff0\u3057\u305f\u76ee\u7684\u95a2\u6570\u3092\u5909\u6570\u5909\u63db<\/p>\n\n\n\n$$\ns_{i} = 2x_{i}-1\n$$\n\n\n\n<p>\u3067\u5909\u63db\u3057\u3066\u3001\u5f0f\u3092\u5c55\u958b\u3057\u3066\u3044\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u5f8c\u3001\u9806\u3005\u306b\u5f0f\u5909\u5f62\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u3054\u89a7\u306b\u5165\u308c\u307e\u3059\u3002<\/p>\n\n\n\n$$\n\\begin{aligned}\n\\mathrm{Obj}(\\mathbf{x})\n&amp;=\n\\sum_{(i, j) \\in E} ((2x_i &#8211; 1) &#8211; (2x_j-1))^2\n+ \\alpha \\left( \\sum_i (2 x_i &#8211; 1) \\right)^2\n\\\\\n&amp;=\n\\sum_{(i, j) \\in E} 4(x_i &#8211; x_j)^2\n+ \\alpha \\left( \\sum_i x_i &#8211; N \\right) \\left( \\sum_j 2x_j &#8211; N\\right)\n\\\\\n&amp;=\n\\sum_{(i, j) \\in E} 4 (x_i^2 + x_j^2 &#8211; 2x_i x_j)\n+ \\alpha \\left[ \\sum_i \\sum_j 4 x_i x_j &#8211; 4N \\sum_i x_i + N^2 \\right]\n\\end{aligned}\n$$\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u304c\u3001\u5909\u6570\u306b\u3088\u3089\u306a\u3044\u5b9a\u6570\u548c\u3001\u304a\u3088\u3073\u5b9a\u6570\u500d\u306e\u90e8\u5206\u306f\u76ee\u7684\u95a2\u6570\u304b\u3089\u9664\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u30010, 1\u306e\u4e8c\u5024\u5909\u6570\u306e\u5834\u5408\u3001\u5e38\u306b$x_i = x_i^2$\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u304b\u3089\u3001\u4e0a\u306e\u5f0f\u306e\u4e00\u6b21\u306e\u9805\u306f$x_i = x_i^2$\u3067\u66f8\u304d\u76f4\u3057\u3066\u3001<\/p>\n\n\n\n$$\n\\mathrm{Obj}(\\mathbf{x})\n=\n\\sum_{(i, j) \\in E} (x_i^2 + x_j^2 &#8211; 2x_i x_j)\n+ \\alpha \\left[ \\sum_i \\sum_j x_i x_j &#8211; N \\sum_i x_i^2 \\right]\n$$\n\n\n\n<p>\u3068\u66f8\u3051\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u884c\u5217$Q$\u306e\u8981\u7d20\u306f\u5404\u4e8c\u6b21\u5f0f$x_i x_j$\u306b\u4ed8\u304f\u4fc2\u6570\u3067\u3057\u305f\u304b\u3089\u3001\u305d\u308c\u305e\u308c\u306e$i, j$\u306e\u7d44\u306b\u3064\u3044\u3066\u3001\u4e0a\u306e\u5f0f\u3092\u5143\u306b\u5834\u5408\u5206\u3051\u3092\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002$Q_{ij}$\u3092\u4e0a\u5f0f\u306e\u7b2c1\u9805\u304b\u3089\u306a\u308b\u6210\u5206$f_{ij}$\u3068\u7b2c2\u9805\u304b\u3089\u306a\u308b\u6210\u5206$g_{ij}$\u306b\u308f\u3051\u3066\u3001\u305d\u308c\u305e\u308c\u5177\u4f53\u7684\u306b\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n$$\nf_{ij}\n=\n\\left\\{\n    \\begin{aligned}\n    &amp; d_i &amp;&amp; \\text{if $i = j$,} \\\\\n    &amp; -2  &amp;&amp; \\text{if $i &lt; j, (i,j) \\in E$,} \\\\\n    &amp; 0   &amp;&amp; \\text{otherwise}\n    \\end{aligned}\n\\right.\n$$\n\n\n\n<p>\u3053\u3053\u3067$d_i$\u306f\u9802\u70b9$i$\u304b\u3089\u4f38\u3073\u308b\u8fba\u306e\u6570\uff08\u6b21\u6570\uff09\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u8981\u7d20\u306f\u76ee\u7684\u95a2\u6570\u306e\u7b2c1\u9805\u306e\u548c\u306b\u73fe\u308c\u308b$x_i^2$\u306b\u8d77\u56e0\u3057\u307e\u3059\u3002$d_i = \\sum_{(i, j) \\in E} 1$\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n$$\ng_{ij}\n=\n\\left\\{ \\begin{aligned}\n    &amp; \\alpha (1 &#8211; N) &amp;&amp; \\text{if $i = j$,} \\\\\n    &amp; 2 \\alpha       &amp;&amp; \\text{if $i &lt; j$,} \\\\\n    &amp; 0              &amp;&amp; \\text{otherwise}\n\\end{aligned} \\right.\n$$\n\n\n\n<p>\u3053\u3053\u3067\u3001$f_{ij}, g_{ij}$\u304c\u4e0a\u4e09\u89d2\u884c\u5217\u306b\u306a\u308b\u3088\u3046\u306b\u8a08\u7b97\u3057\u3066\u3044\u307e\u3059\u304c\u3053\u308c\u306f\u5f8c\u8ff0\u306eQUBO\u30d5\u30a1\u30a4\u30eb\u3092\u4f5c\u6210\u3059\u308b\u305f\u3081\u306e\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u4e0a\u306e\u4ed5\u69d8\u3068\u8003\u3048\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p>\u51fa\u6765\u4e0a\u304c\u3063\u305f\u884c\u5217\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306a\u5f62\u3068\u306a\u3063\u3066\u3044\u308b\u3067\u3057\u3087\u3046\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\/06\/e3ffe650d26cca5c381f2c7c4d60b45f.png\" alt=\"\" class=\"wp-image-455\"\/><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Step_3_QUBO%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB%E3%81%AE%E4%BD%9C%E6%88%90\"><\/span>Step 3. QUBO\u30d5\u30a1\u30a4\u30eb\u306e\u4f5c\u6210<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>qbsolv\u30b3\u30de\u30f3\u30c9\u3092\u5b9f\u884c\u3059\u308b\u969b\u306eQUBO\u30d5\u30a1\u30a4\u30eb\u306f\u4ee5\u4e0b\u306e\u5f62\u5f0f\u3092\u53d6\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-plain\"><code>p qubo 0 [\u5909\u6570\u306e\u6570N] [\u975e\u30bc\u30ed\u5bfe\u89d2\u6210\u5206\u6570] [\u975e\u30bc\u30ed\u975e\u5bfe\u89d2\u6210\u5206\u6570]\n\nc \u30b3\u30e1\u30f3\u30c8\u884c\u306f\u884c\u982d\u306bc\u3068\u3060\u3051\u8a18\u8ff0\nc \u5bfe\u89d2\u6210\u5206\u3092\u5148\u306b\u66f8\u304f\nc [i] [i] [Qii]\n0 0 -1\n1 1 -2\nc \u306a\u3069\u306e\u3088\u3046\u306b\n\nc \u7d9a\u3044\u3066\u975e\u5bfe\u89d2\u6210\u5206\u3092\u8a18\u8ff0\nc [i] [j] [Qij]\nc \u3053\u3053\u3067\u5fc5\u305ai &lt; j\u3067\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\n0 1 100\n3 6 49\nc \u306a\u3069\u306e\u3088\u3046\u306b<\/code><\/pre><\/div>\n\n\n\n<p>\u3055\u3066\uff0c\u3053\u3053\u304b\u3089\u306fPython\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u4f7f\u3063\u3066QUBO\u30d5\u30a1\u30a4\u30eb\u3092\u4f5c\u3063\u3066\u3044\u304d\u307e\u3059\uff0e\u307e\u305a\uff0c\u7b2c\u4e00\u9805\u306eE\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u3069\u306e\u70b9\u3068\u3069\u306e\u70b9\u304c\u7e4b\u304c\u3063\u3066\u3044\u308b\u304b\u3092\u5165\u529b\u3057\u307e\u3059\uff0e\u52a0\u3048\u3066\uff0c\u884c\u5217\u306e\u30b5\u30a4\u30ba\u3068n\u3092\u8abf\u3079\u308b\u305f\u3081\u306b\u70b9\u306e\u6570\u3082\u5165\u529b\u3057\u307e\u3059\uff0e\u3053\u3053\u3067\u306f\u70b9\u306e\u6570\u3092node\uff0c\u7dda\u306e\u60c5\u5831\u3092\u59cb\u70b9\u3068\u7d42\u70b9\u306e\u60c5\u5831\u3092\u6301\u3063\u305fm\u00d72\u884c\u5217\u3068\u3057\u3066\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\uff0e<\/p>\n\n\n\n<p>\u884c\u5217\u8981\u7d20\u306e\u8a08\u7b97\u306b\u95a2\u3059\u308bPython\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-python\" data-lang=\"Python\"><code>N = 10         # \u30ce\u30fc\u30c9\u6570\nalpha = 100    # \u03b1\u306e\u5024\u3092\u8a2d\u5b9a\nedges = [[0, 1], [0, 4], [0, 5], [0, 7], [1, 2], [1, 5], [1, 7],\n        [2, 3], [2, 6], [2, 9], [3, 6], [3, 8], [3, 9],\n        [4, 5], [4, 7], [5, 6], [5, 7], [6, 8], [8, 9]] # \u30a8\u30c3\u30b8\u306e\u30ea\u30b9\u30c8\u4f8b\n\n#\u884c\u5217\u306e\u521d\u671f\u5316\nQ = [[0] * N] * N\n\n# \u30b3\u30b9\u30c8\u9805gij\nfor i in range(len(edges)):\n    x = edges[i][0]\n    y = edges[i][1]\n    Q[x][y] -= 2\n    Q[x][x] += 1\n    Q[y][y] += 1\n\n# \u30da\u30ca\u30eb\u30c6\u30a3\u9805\nfor i in range(len(edges)):\n    Q[i][i] += alpha * (1 - N)\n\n    for j in range(i + 1, len(edges)):\n        Q[i][j] += 2 * alpha<\/code><\/pre><\/div>\n\n\n\n<p>\u4eca\u56de\u306f\u3053\u306e\u3088\u3046\u306b\u8868\u73fe\u3057\u307e\u3057\u305f\uff0e\u3042\u3068\u306f\uff0c\u3053\u306e\u884c\u5217\u3092qubo\u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u51fa\u3059\u3060\u3051\u3067\u3059\uff0e\u51fa\u6765\u4e0a\u304c\u3063\u305f\u30d5\u30a1\u30a4\u30eb\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-plain\"><code>p qubo 0 10 10 45\nc diagonal (elements)\n0 0 -896\n1 1 -896\n2 2 -896\n3 3 -896\n4 4 -897\n5 5 -895\n6 6 -896\n7 7 -896\n8 8 -897\n9 9 -897\nc off-diagonal (couplers)\n0 1 198\n0 2 200\n0 3 200\n0 4 198\n0 5 198\n: :  :<\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Step_4_qbsolv%E3%82%B3%E3%83%9E%E3%83%B3%E3%83%89%E3%81%AE%E5%AE%9F%E8%A1%8C%E3%81%A8%E7%B5%90%E6%9E%9C\"><\/span>Step 4. qbsolv\u30b3\u30de\u30f3\u30c9\u306e\u5b9f\u884c\u3068\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>QUBO\u30d5\u30a1\u30a4\u30eb\u306f\u524d\u8ff0\u306e\u3088\u3046\u306a\u66f8\u5f0f\u3067\u30c6\u30ad\u30b9\u30c8\u30d5\u30a1\u30a4\u30eb\u306e\u5f62\u3067\u4fdd\u5b58\u3057\u3001qbsolv\u30b3\u30de\u30f3\u30c9\u3092<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-bash\" data-lang=\"Bash\"><code>$ qbsolv -i [QUBO\u30d5\u30a1\u30a4\u30eb\u540d]<\/code><\/pre><\/div>\n\n\n\n<p>\u306e\u5f62\u3067\u5b9f\u884c\u3057\u307e\u3059\u3002\u5b9f\u969b\u7684\u306b\u306fqbsolv\u30b3\u30de\u30f3\u30c9\u3092\u7528\u3044\u3066D-Wave\u30de\u30b7\u30f3\u306b\u63a5\u7d9a\u3059\u308b\u305f\u3081\u306b\u306f\u95a2\u9023\u30c4\u30fc\u30eb\u3067\u3042\u308bdw\u30b3\u30de\u30f3\u30c9\u306a\u3069\u3092\u5fc5\u8981\u3068\u3057\u307e\u3059\u304c\u3001\u672c\u8a18\u4e8b\u3067\u306f\u5177\u4f53\u7684\u306a\u30b3\u30de\u30f3\u30c9\u306e\u4f7f\u3044\u65b9\u306b\u3064\u3044\u3066\u306f\u89e6\u308c\u307e\u305b\u3093\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\/06\/1b3b3d914f64fefb6f99dff1754b43ab.png\" alt=\"\" class=\"wp-image-532\"\/><\/figure>\n<\/div>\n\n\n<p>\u4eca\u56de\u306f\u3053\u306e\u30b0\u30e9\u30d5\u306b\u5bfe\u3057\u3066\u30b0\u30e9\u30d5\u5206\u5272\u3092\u884c\u3044\u307e\u3059\uff0e<\/p>\n\n\n\n<p>\u3053\u306e\u5834\u5408\u3067\u306f\u9752\u306e\u30b0\u30eb\u30fc\u30d7\u3068\u8d64\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u3064\u306a\u304c\u308a\u304c\u5f37\u304f\uff0c\u305d\u308c\u3092\u7d50\u30762\u672c\u306e\u7dda\u3092\u5207\u3063\u3066\u4e8c\u5206\u5272\u3059\u308b\u3053\u3068\u304c\u6b63\u89e3\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u5b9f\u969b\u306b\u5148\u307b\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u30b0\u30e9\u30d5\u306e\u30c7\u30fc\u30bf\u3092\u5165\u529b\u3057\u3066\u3001qbsolv\u3092\u5b9f\u884c\u3057\u305f\u7d50\u679c\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u7d50\u679c\u304c\u30bf\u30fc\u30df\u30ca\u30eb\u30d7\u30ed\u30f3\u30d7\u30c8\u306b\u51fa\u529b\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-bash\" data-lang=\"Bash\"><code>$ qbsolv -i test.qubo\n10 bits, Quantum solver, find Min, SubMatrix= 64, -a o, timeout=2592000.0 sec\n1100110100\n-2498.00000 Energy of solution\n0 Number of Partitioned calls, 1 output sample\n0.00044 seconds of classic cpu time<\/code><\/pre><\/div>\n\n\n\n<p>3\u884c\u76ee\u304c\u7d50\u679c\u306e\u5909\u6570\u5217\u3067\u3001\u5de6\u304b\u3089\uff0c\u70b90,1,2&#8230;\u306b\u5bfe\u5fdc\u3057\u3066\u304a\u308a\uff0c0\u30681\u304c\u3069\u3061\u3089\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5c5e\u3059\u308b\u304b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u30021\u3067\u8868\u3055\u308c\u308b\u30b0\u30eb\u30fc\u30d7\u306f0,1,4,5,7\u3067\u3042\u308a\u56f3\u306e\u9752\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u76f8\u5f53\u3057\u30010\u3067\u8868\u3055\u308c\u308b\u30b0\u30eb\u30fc\u30d7\u306f2.3,6,8,9\u3067\u8d64\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u76f8\u5f53\u3059\u308b\u306e\u3067\u3001\u6b63\u3057\u304f\u6700\u5c0f\u30ab\u30c3\u30c8\u3092\u9078\u3076\u3088\u3046\u306b\u30b0\u30eb\u30fc\u30d7\u5206\u3051\u304c\u3055\u308c\u305f\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>0.00045\u79d2\u306e\u90e8\u5206\u306f\u3001qbsolv\u30b3\u30de\u30f3\u30c9\u306e\u5185\u90e8\u51e6\u7406\u306b\u304b\u304b\u3063\u305f\u6642\u9593\u3067\u3042\u308a\u3001\u30bf\u30fc\u30df\u30ca\u30eb\u4e0a\u306e\u5b9f\u884c\u6642\u9593\u306f2.2\u79d2\u7a0b\u5ea6\u3067\u3057\u305f\u3002<\/p>\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>D-Wave\u30de\u30b7\u30f3\u3067\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u306f\u884c\u5217\u306e\u8981\u7d20\u306e\u8a08\u7b97\u304c\u96e3\u3057\u3044\u3068\u611f\u3058\u307e\u3057\u305f\u3002\u884c\u5217\u306e\u8a08\u7b97\u306b\u306f\u4e8c\u5024\u95a2\u6570\u306e\u8a08\u7b97\u3001\u548c\u306e\u5c55\u958b\u3001\u5f0f\u306e\u89e3\u91c8\u306a\u3069\u6163\u308c\u306a\u3044\u3053\u3068\u304c\u591a\u304f\u3001\u9014\u4e2d\u4f55\u56de\u3082\u8a08\u7b97\u304c\u5408\u308f\u305a\u306b\u9593\u9055\u3063\u305f\u7d50\u679c\u304c\u8fd4\u3063\u3066\u304d\u307e\u3057\u305f\u3002D-Wave\u30de\u30b7\u30f3\u3092\u52d5\u304b\u3059\u3053\u3068\u306f\u5927\u5909\u3067\u3057\u305f\u304c\u6b63\u3057\u3044\u7d50\u679c\u304c\u8fd4\u3063\u3066\u304d\u305f\u3068\u304d\u306e\u611f\u52d5\u306f\u8a00\u8449\u3067\u8868\u305b\u306a\u3044\u307b\u3069\u5927\u304d\u306a\u3082\u306e\u3067\u3057\u305f\u3002\u305d\u3057\u3066\u3001\uff11\u5ea6\u52d5\u304b\u3057\u3066\u307f\u3066\u6163\u308c\u3066\u304d\u305f\u306e\u3067\uff12\u56de\u76ee\u4ee5\u964d\u306f\u305d\u308c\u307b\u3069\u82e6\u52b4\u3057\u306a\u3044\u304b\u306a\u3068\u3044\u3046\u5370\u8c61\u3067\u3059\u3002\u3053\u308c\u304b\u3089\u306f\u3001qbsolv\u4ee5\u5916\u306e\u65b9\u6cd5\u3067D-Wave\u30de\u30b7\u30f3\u3092\u52d5\u304b\u3059\u65b9\u6cd5\u3092\u5b66\u3093\u3060\u308a\u3001\u3053\u306e\u554f\u984c\u4ee5\u5916\u306e\u554f\u984c\u3092D-Wave\u30de\u30b7\u30f3\u3067\u89e3\u3044\u3066\u3044\u3053\u3046\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 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><\/h3>\n\n\n\n<p>\u91d1\u57a3\u3000\u8475\uff08\u7de8\u96c6\uff1a\u307f\u3084\u307e\u307e\u3055\u307f\u3061\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"<p>T-Wave\u958b\u8a2d\u4ee5\u6765\u3001\u3044\u304f\u3064\u304b\u306e\u5148\u884c\u7814\u7a76\u3084\u5c0e\u5165\u4e8b\u4f8b\u306b\u95a2\u3059\u308b\u8a18\u4e8b\u304c\u51fa\u3066\u3044\u308b\u4e2d\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u5177\u4f53\u7684\u306a\u554f\u984c\u3092D-Wave\u30de\u30b7\u30f3\u3067\u89e3\u304f\u306e\u304b\u3068\u3044\u3046\u3053\u3068\u306f\u7686\u3055\u3093\u6c17\u306b\u306a\u3063\u3066\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f \u30b0\u30e9\u30d5\u5206\u5272\u554f\u984c \u3092\u4f8b\u306b\u3001\u30b5\u30dd\u30fc\u30c8\u30c4 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[11,21,32,50,55,112],"class_list":["post-454","post","type-post","status-publish","format-standard","hentry","category-hands-on","tag-d-wave-2000q","tag-karp21np","tag-qbsolv","tag-50","tag-55","tag-112"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u30b0\u30e9\u30d5\u5206\u5272\u554f\u984c \u3092D-Wave 2000Q\u3067\u89e3\u304f\uff08\u5b9f\u8df5\u7de8\uff09 - T-QARD Harbor<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/06\/20\/\u30b0\u30e9\u30d5\u5206\u5272\u554f\u984c\u3092d-wave\u3067\u89e3\u304f\uff08\u5b9f\u8df5\u7de8\uff09\/\" 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