{"id":418,"date":"2018-06-18T19:00:00","date_gmt":"2018-06-18T10:00:00","guid":{"rendered":"http:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=418"},"modified":"2018-06-18T19:00:00","modified_gmt":"2018-06-18T10:00:00","slug":"%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/06\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/","title":{"rendered":"\u5bae\u57ce\u770c\u306e\u5e02\u533a\u753a\u6751\u3092\u5857\u308a\u5206\u3051\u308d &#8211; \u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c \u3092D-Wave\u30de\u30b7\u30f3\u3067\u89e3\u304f"},"content":{"rendered":"\n<p>\u672c\u8a18\u4e8b\u3067\u306f<a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=43\">Karp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c<\/a>\u306e\u4e00\u3064\u3067\u3042\u308b \u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c (Graph Coloring)\u3068\u305d\u306eQUBO\u8868\u73fe\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3001\u5177\u4f53\u7684\u306a\u5fdc\u7528\u4f8b\u3068\u3057\u3066\u5bae\u57ce\u770c\u306b\u304a\u3051\u308b\u5e02\u533a\u753a\u6751\u306e\u5857\u308a\u5206\u3051\u3092\u3068\u308a\u3042\u3052\u3001D-Wave 2000Q\u3067\u306e\u5b9f\u88c5\u4f8b\u3092Python SAPI\u306a\u3089\u3073\u306bqbsolv\u3092\u7528\u3044\u3066\u89e3\u3044\u305f\u5b9f\u884c\u7d50\u679c\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3059\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\/06\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#%E3%82%B0%E3%83%A9%E3%83%95%E5%BD%A9%E8%89%B2%E5%95%8F%E9%A1%8C\" >\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c<\/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\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#%E3%82%B0%E3%83%A9%E3%83%95%E5%BD%A9%E8%89%B2%E5%95%8F%E9%A1%8C%E3%81%AEQUBO%E8%A1%A8%E7%8F%BE%E3%81%AB%E3%82%88%E3%82%8B%E5%AE%9A%E5%BC%8F%E5%8C%96\" >\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\u306eQUBO\u8868\u73fe\u306b\u3088\u308b\u5b9a\u5f0f\u5316<\/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\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#%E5%AE%9F%E8%A1%8C%E7%B5%90%E6%9E%9C\" >\u5b9f\u884c\u7d50\u679c<\/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\/2018\/06\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#1_SAPI%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E5%A0%B4%E5%90%88\" >(1) SAPI\u3092\u7528\u3044\u305f\u5834\u5408<\/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\/2018\/06\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#2_qbsolv%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E5%A0%B4%E5%90%88\" >(2) qbsolv\u3092\u7528\u3044\u305f\u5834\u5408<\/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\/2018\/06\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#%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-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/06\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#%E5%8F%82%E8%80%83\" >\u53c2\u8003<\/a><\/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\/06\/18\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\/#%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=\"%E3%82%B0%E3%83%A9%E3%83%95%E5%BD%A9%E8%89%B2%E5%95%8F%E9%A1%8C\"><\/span>\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c (Graph Coloring Problem)\u3068\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u30b0\u30e9\u30d5\u306b\u5bfe\u3057\u3066\u3001\u9802\u70b9\u3084\u8fba\u306a\u3069\u306e\u8981\u7d20\u304c\u3042\u308b\u5236\u7d04\u3092\u6e80\u305f\u3059\u3088\u3046\u306b\u8272\u3092\u5272\u308a\u5f53\u3066\u308b\u5834\u5408\u306b\u3001\u5fc5\u8981\u304b\u3064\u6700\u5c0f\u306a\u8272\u6570 (\u5f69\u8272\u6570\uff1aColoring Number)\u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u96a3\u308a\u5408\u3046\u9802\u70b9\u540c\u58eb\u304c\u7570\u306a\u308b\u8272\u306b\u306a\u308b\u3088\u3046\u306b\u5f69\u8272\u3059\u308b\u5834\u5408\u3092\u9802\u70b9\u5f69\u8272\u554f\u984c (Vertex Coloring)\u3001 \u96a3\u308a\u5408\u3046\u8fba\u540c\u58eb\u304c\u7570\u306a\u308b\u8272\u306b\u306a\u308b\u3088\u3046\u306b\u5f69\u8272\u3059\u308b\u5834\u5408\u3092\u8fba\u5f69\u8272\u554f\u984c(Edge Coloring)\u3001\u9802\u70b9\u5f69\u8272\u3068\u8fba\u5f69\u8272\u306e\u3044\u305a\u308c\u3082\u8003\u616e\u3059\u308b\u5834\u5408\u3092\u5168\u5f69\u8272\u554f\u984c (Total Coloring)\u3068\u3044\u3046\u3002<\/p>\n\n\n\n<p>\u5f69\u8272\u554f\u984c (Coloring Problem)\u306b\u306f\u69d8\u3005\u306a\u7a2e\u985e\u304c\u3042\u308b\u3002Karp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c\u306e\u4e2d\u306b\u306f\u3001\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c (\u672c\u8a18\u4e8b)\u3001<a href=\"\/T-Wave\/?p=434\">\u30af\u30ea\u30fc\u30af\u88ab\u8986\u554f\u984c (Clique Cover Problem)<\/a>\u3001<a href=\"\/T-Wave\/?p=133\">\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u554f\u984c (Job Sequencing with Integer Lengths)<\/a>\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u5bae\u57ce\u770c\u306b\u304a\u3051\u308b\u5e02\u533a\u753a\u6751\u3092\u9802\u70b9\u3001\u96a3\u63a5\u3059\u308b\u5e02\u533a\u753a\u6751\u3092\u8fba\u3067\u7d50\u3093\u3060\u30b0\u30e9\u30d5\u306e\u9802\u70b9\u5f69\u8272\u554f\u984c\u306b\u53d6\u308a\u7d44\u3080\u3002\u5bae\u57ce\u770c\u306b\u306f35\u306e\u5e02\u753a\u6751\u304c\u3042\u308a\u3001\u770c\u5e81\u6240\u5728\u5730\u306e\u4ed9\u53f0\u5e02\u306f\u30015\u3064\u306e\u533a\u306b\u5206\u304b\u308c\u308b\u3002\u305d\u308c\u3089\u3092\u5408\u308f\u305b\u305f39\u306e\u5e02\u533a\u753a\u6751\u306b\u304a\u3051\u308b\u5f69\u8272\u554f\u984c\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/229914.jpg\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/229914.jpg\" alt=\"\u5bae\u57ce\u770c\u306e\u5e02\u533a\u753a\u6751\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\"><a href=\"https:\/\/www.pref.miyagi.jp\/soshiki\/sisetsu\/kakukyoui.html\">\u5bae\u57ce\u770c\u306e\u5e02\u533a\u753a\u6751<\/a><\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%B0%E3%83%A9%E3%83%95%E5%BD%A9%E8%89%B2%E5%95%8F%E9%A1%8C%E3%81%AEQUBO%E8%A1%A8%E7%8F%BE%E3%81%AB%E3%82%88%E3%82%8B%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\u306eQUBO\u8868\u73fe\u306b\u3088\u308b\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>\u5909\u6570<\/strong>: $x_{i,k} \\in \\{0, 1\\}$ (\u90fd\u9053\u5e9c\u770c$i$\u304c\u8272$k \\in \\{1, 2, \\cdots, K_\\mathrm{max}\\}$\u3067\u3042\u308c\u3070$1$, \u305d\u3046\u3067\u306a\u3051\u308c\u3070$0$)<br><strong>\u76ee\u7684\u95a2\u6570<\/strong>:<\/p>\n\n\n\n$$\nH\n=\nA \\sum_{v} \\left( 1- \\sum_{i=1}^n x_{v,i} \\right)^2\n+ B \\sum_{(u,v) \\in E} \\sum_{i=1}^n x_{u,i} x_{v,i}\n$$\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/cost_function-1.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/06\/cost_function-1.png\" alt=\"\u76ee\u7684\u95a2\u6570\u306e\u89e3\u8aac\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\">\u76ee\u7684\u95a2\u6570\u306e\u89e3\u8aac<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u4e0a\u8a18\u306e\u3088\u3046\u306b\u5b9a\u5f0f\u5316\u3057\u305fQUBO\u8868\u73fe\u3055\u308c\u305f\u76ee\u7684\u95a2\u6570\u304b\u3089\u884c\u5217Q\u306e\u8981\u7d20\u3092\u8a08\u7b97\u3059\u308bPython\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u4ee5\u4e0b\u306b\u793a\u3059\u3002<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-python\" data-lang=\"Python\"><code># \u5e02\u533a\u753a\u6751\u306e\u6570\nN_CITIES = 39\n\n# \u8272\u6570\nN_COLOR = 4\n\n# \u30a4\u30b8\u30f3\u30b0\u5909\u6570\u306e\u6570\nN = N_CITIES * N_COLOR\n\n# h(\u5c40\u6240\u78c1\u5834), J(\u76f8\u4e92\u4f5c\u7528\u306e\u4fc2\u6570), S(\u96a3\u63a5\u884c\u5217)\nJ = {}\nS = {}\nh = [0] * N\n\n# \u4e00\u3064\u306e\u5e02\u533a\u753a\u6751\u306b\u306f\u30011\u8272\u306e\u307f\u5272\u308a\u5f53\u3066\u308b\nparam_A = 1\nfor v in range(N_CITIES):\n    for i in range(N_COLOR):\n        h[v*N_COLOR+i] = -param_A\n\n        for j in range(i+1, N_COLOR):\n            if (v*N_COLOR + i, v*N_COLOR+j) not in J.keys():\n                J[v*N_COLOR + i, v*N_COLOR+j] = 2 * param_A\n            else:\n                J[v*N_COLOR + i, v*N_COLOR+j] += 2 * param_A\n\n# \u96a3\u308a\u5408\u3046\u5e02\u533a\u753a\u6751\u306b\u306f\u3001\u305d\u308c\u305e\u308c\u7570\u306a\u308b\u8272\u3092\u5272\u308a\u5f53\u3066\u308b\nparam_B = 2.5\nfor u, ne in neighbors.items():\n    for i in range(N_COLOR):\n        for v in (x-1 for x in ne):\n            if u &lt; v:\n                for i in range(N_COLOR):\n                    if (u*N_COLOR+i, v*N_COLOR+i) not in J.keys():\n                        J[u*N_COLOR+i, v*N_COLOR+i] = param_B\n                    else:\n                        J[u*N_COLOR+i, v*N_COLOR+i] += param_B\n\n# QUBO\u884c\u5217\u3092\u4f5c\u6210                  \nQ = J.copy()\nfor i in range(N):\n    if (i,i) not in Q.keys():\n        Q[i,i] = h[i]\n    Q[i,i] += h[i]\n\n# \u96a3\u63a5\u884c\u5217\u3092\u4f5c\u6210\nS = {}\nfor i in range(N):\n    for j in range(N):\n        if (i,j )in Q.keys() and Q[i,j] != 0:\n            S[i,j] = 1\n<\/code><\/pre><\/div>\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>\u4eca\u56de\u3001(1)SAPI (D-Wave\u306e\u30bd\u30eb\u30d0\u30fcAPI)\u3068\u3001(2) qbsolv\u001c\u001c\uff08D-Wave\u304c\u958b\u767a\u3057\u3066\u3044\u308b\u30bd\u30eb\u30d0\u30fc\u3001<a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=454\">\u8a73\u7d30\u306f\u3053\u306e\u8a18\u4e8b\u3092\u53c2\u7167<\/a>\uff09\u3092\u7528\u3044\u3066\u3053\u306e\u554f\u984c\u3092\u89e3\u3044\u305f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"1_SAPI%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E5%A0%B4%E5%90%88\"><\/span>(1) SAPI\u3092\u7528\u3044\u305f\u5834\u5408<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u306e\u554f\u984c\u3092D-Wave 2000Q\u306b1000\u56de\u89e3\u304b\u305b\u3001\u305d\u306e\u4e2d\u3067\u6700\u3082\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u4f4e\u3044\u89e3\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u96a3\u308a\u5408\u3046\u5e02\u533a\u753a\u6751\u306b\u540c\u3058\u8272\u304c\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u3082\u306e\u304c\u542b\u307e\u308c\u3066\u3044\u305f\u3002\u307e\u305f\u3001D-Wave\u304c\u63d0\u4f9b\u3057\u3066\u3044\u308b\u57cb\u3081\u8fbc\u307f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u7528\u3044\u308b\u3068\u3001\u57cb\u3081\u8fbc\u307f\u306b\u6642\u9593\u304c\u304b\u304b\u3063\u305f\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/colored_graph0613220535.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/colored_graph0613220535.png\" alt=\"SAPI\u3092\u7528\u3044\u305f\u5834\u5408\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\">SAPI\u3092\u7528\u3044\u305f\u5834\u5408<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"2_qbsolv%E3%82%92%E7%94%A8%E3%81%84%E3%81%9F%E5%A0%B4%E5%90%88\"><\/span>(2) qbsolv\u3092\u7528\u3044\u305f\u5834\u5408<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>SAPI\u3092\u7528\u3044\u3066\u89e3\u3092\u6c42\u3081\u308b\u4e2d\u3067\u898b\u3064\u3051\u305f\u30d1\u30e9\u30e1\u30fc\u30bf(A, B)\u306b\u8a2d\u5b9a\u3057\u3001qbsolv\u3092\u7528\u3044\u3066\u89e3\u3044\u305f\u7d50\u679c\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u305f\u3002\u4e2d\u592e\u90e8\u306e\u5e02\u533a\u753a\u6751\u304c\u5bc6\u96c6\u3057\u305f\u90e8\u5206\u3082\u304d\u308c\u3044\u306b\u5f69\u8272\u3067\u304d\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/ex_success.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/ex_success.png\" alt=\"\u6210\u529f\u4f8b\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\">qbsolv\u3092\u7528\u3044\u305f\u5834\u5408 \u6210\u529f\u4f8b<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/ex_fail.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/ex_fail.png\" alt=\"\u5931\u6557\u4f8b\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\">qbsolv\u3092\u7528\u3044\u305f\u5834\u5408 \u5931\u6557\u4f8b<\/figcaption><\/figure>\n<\/div>\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>qbsolv\u3092\u7528\u3044\u3066\u3001\u5bae\u57ce\u770c\u306b\u304a\u3051\u308b\u5e02\u533a\u753a\u6751\u3092\u3046\u307e\u304f\u5857\u308a\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u3002\u73fe\u5728\u306eD-Wave\u30de\u30b7\u30f3\u3067\u306f\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u554f\u984c\u306e\u5927\u304d\u3055\u306b\u9650\u754c\u304c\u3042\u308b\u304c\u3001\u4eca\u5f8c\u306e\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306e\u9032\u6b69\u306b\u5408\u308f\u305b\u3066\u3001\u3088\u308a\u5927\u304d\u306a\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u308b\u3002\u307e\u305f\u3001\u4eca\u56de\u306f\u9802\u70b9\u5f69\u8272\u554f\u984c\u3092\u6271\u3063\u305f\u304c\u3001\u307e\u305f\u6a5f\u4f1a\u304c\u3042\u308c\u3070\u8fba\u5f69\u8272\u554f\u984c\u3084\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u554f\u984c\u306b\u3082\u53d6\u308a\u7d44\u3093\u3067\u3044\u304d\u305f\u3044\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83\"><\/span>\u53c2\u8003<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"http:\/\/www.ecei.tohoku.ac.jp\/alg\/research_coloring.html\">\u5468\u30fb\u4f0a\u85e4\u7814\u7a76\u5ba4 \u30b0\u30e9\u30d5\u5f69\u8272<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/gist.github.com\/ki-chi\/5943096f5499115eb339be18218734aa#file-matplotlib_hokkaido-ipynb\">Pandas+Matplotlib\u3067\u5e02\u753a\u6751\u306e\u4eba\u53e3\u3092\u53ef\u8996\u5316\u3059\u308b<\/a><\/li>\n<\/ul>\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\n<p>\u4e38\u5c71\u5c1a\u8cb4<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u8a18\u4e8b\u3067\u306fKarp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c\u306e\u4e00\u3064\u3067\u3042\u308b \u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c (Graph Coloring)\u3068\u305d\u306eQUBO\u8868\u73fe\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3001\u5177\u4f53\u7684\u306a\u5fdc\u7528\u4f8b\u3068\u3057\u3066\u5bae\u57ce\u770c\u306b\u304a\u3051\u308b\u5e02\u533a\u753a\u6751\u306e\u5857\u308a\u5206\u3051\u3092\u3068\u308a\u3042\u3052\u3001D-Wave 2000 [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[11,21,38,52,55,112],"class_list":["post-418","post","type-post","status-publish","format-standard","hentry","category-hands-on","tag-d-wave-2000q","tag-karp21np","tag-sapi","tag-52","tag-55","tag-112"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u5bae\u57ce\u770c\u306e\u5e02\u533a\u753a\u6751\u3092\u5857\u308a\u5206\u3051\u308d - \u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c \u3092D-Wave\u30de\u30b7\u30f3\u3067\u89e3\u304f - 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\/18\/\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5bae\u57ce\u770c\u306e\u5e02\u533a\u753a\u6751\u3092\u5857\u308a\u5206\u3051\u308d - \u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c \u3092D-Wave\u30de\u30b7\u30f3\u3067\u89e3\u304f - T-QARD Harbor\" \/>\n<meta property=\"og:description\" content=\"\u672c\u8a18\u4e8b\u3067\u306fKarp\u306e21\u306eNP\u5b8c\u5168\u554f\u984c\u306e\u4e00\u3064\u3067\u3042\u308b \u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c (Graph Coloring)\u3068\u305d\u306eQUBO\u8868\u73fe\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3001\u5177\u4f53\u7684\u306a\u5fdc\u7528\u4f8b\u3068\u3057\u3066\u5bae\u57ce\u770c\u306b\u304a\u3051\u308b\u5e02\u533a\u753a\u6751\u306e\u5857\u308a\u5206\u3051\u3092\u3068\u308a\u3042\u3052\u3001D-Wave 2000 [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/06\/18\/\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\/\" \/>\n<meta property=\"og:site_name\" content=\"T-QARD Harbor\" \/>\n<meta property=\"article:published_time\" content=\"2018-06-18T10:00:00+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/229914.jpg\" \/>\n<meta name=\"author\" content=\"Naoki Maruyama\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u57f7\u7b46\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"Naoki Maruyama\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u63a8\u5b9a\u8aad\u307f\u53d6\u308a\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"7\u5206\" \/>\n<script type=\"application\/ld+json\" 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\u3092D-Wave\u30de\u30b7\u30f3\u3067\u89e3\u304f\",\"datePublished\":\"2018-06-18T10:00:00+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/qard.is.tohoku.ac.jp\\\/T-Wave\\\/2018\\\/06\\\/18\\\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\\\/\"},\"wordCount\":99,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/qard.is.tohoku.ac.jp\\\/T-Wave\\\/2018\\\/06\\\/18\\\/%e3%82%b0%e3%83%a9%e3%83%95%e5%bd%a9%e8%89%b2%e5%95%8f%e9%a1%8c\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/qard.is.tohoku.ac.jp\\\/T-Wave\\\/wp-content\\\/uploads\\\/2018\\\/05\\\/229914.jpg\",\"keywords\":[\"D-Wave 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