{"id":293,"date":"2018-05-15T13:22:19","date_gmt":"2018-05-15T04:22:19","guid":{"rendered":"http:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=293"},"modified":"2018-05-15T13:22:19","modified_gmt":"2018-05-15T04:22:19","slug":"%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/","title":{"rendered":"\u885d\u7a81\u56de\u907f\u306e\u305f\u3081\u306e\u6700\u9069\u306a \u822a\u7a7a\u7d4c\u8def\u9078\u629e \u3078\u306e\u5fdc\u7528 &#8220;Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management&#8221; by Tobias Stollenwerk et al. (2017)."},"content":{"rendered":"\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\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#%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\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#%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\/2018\/05\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#%E5%95%8F%E9%A1%8C\" >\u554f\u984c<\/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\/05\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#%E6%9C%80%E9%81%A9%E5%8C%96%E5%95%8F%E9%A1%8C%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\" >\u6700\u9069\u5316\u554f\u984c\u306e\u5b9a\u5f0f\u5316<\/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\/05\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#%E7%94%A8%E3%81%84%E3%81%9F%E3%83%87%E3%83%BC%E3%82%BF%E3%82%BB%E3%83%83%E3%83%88\" >\u7528\u3044\u305f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8<\/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\/05\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#D-Wave%E3%83%9E%E3%82%B7%E3%83%B3%E5%AE%9F%E8%A3%85%E4%B8%8A%E3%81%AE%E5%B7%A5%E5%A4%AB\" >D-Wave\u30de\u30b7\u30f3\u5b9f\u88c5\u4e0a\u306e\u5de5\u592b<\/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\/05\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#%E7%B5%90%E6%9E%9C\" >\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-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2018\/05\/15\/%e8%88%aa%e7%a9%ba%e4%ba%a4%e9%80%9a%e7%ae%a1%e7%90%86%e3%81%ab%e3%81%8a%e3%81%84%e3%81%a6%e8%a1%9d%e7%aa%81%e3%82%92%e5%9b%9e%e9%81%bf%e3%81%99%e3%82%8b%e6%9c%80%e9%81%a9%e3%81%aa%e8%bb%8c%e9%81%93\/#%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=\"%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>\u30bf\u30a4\u30c8\u30eb <a href=\"https:\/\/arxiv.org\/abs\/1711.04889\"> Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management <\/a><br>\u8457\u8005 Tobias Stollenwerk, Bryan O&#8217;Gorman, Davide Venturelli, Salvatore Mandra, Olga Rodionova, Hok K. Ng, Banavar Sridhar, Eleanor G. Rieffel, and Rupak Biswas<br>arXiv:1711.04889 [quant-ph]<\/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>\u5927\u897f\u6d0b\u6a2a\u65ad\u98db\u884c\u306b\u304a\u3044\u3066\u3001\u98a8\u306b\u5bfe\u3059\u308b\u6700\u9069\u306a\u8ecc\u9053\u3092\u63a1\u7528\u3059\u308b\u3053\u3068\u3067\u751f\u3058\u308b\u30d5\u30e9\u30a4\u30c8\u9593\u306e\u885d\u7a81\u3092\u3001\u30d5\u30e9\u30a4\u30c8\u306e\u9045\u5ef6\u306b\u3088\u3063\u3066\u56de\u907f\u3059\u308b\u3068\u3044\u3046\u554f\u984c\u304c\u3042\u308b\u3002\u3053\u308c\u3092D-Wave 2X\u304a\u3088\u3073D-Wave 2000Q\u3092\u7528\u3044\u3066\u89e3\u3044\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%95%8F%E9%A1%8C\"><\/span>\u554f\u984c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u822a\u7a7a\u306b\u304a\u3051\u308b\u4ea4\u901a\u91cf\u306f\u5e74\u3005\u5897\u52a0\u3057\u3066\u304a\u308a\u3001\u4f7f\u7528\u53ef\u80fd\u306a\u7a7a\u57df\u304c\u9650\u3089\u308c\u3066\u304d\u3066\u3044\u308b\u3002\u5927\u897f\u6d0b\u306b\u5b58\u5728\u3059\u308b\u30b8\u30a7\u30c3\u30c8\u6c17\u6d41\u306e\u5f71\u97ff\u3092\u53d7\u3051\u308b\u5927\u897f\u6d0b\u6a2a\u65ad\u98db\u884c(NAT)\u306b\u304a\u3044\u3066\u98a8\u306b\u5bfe\u3059\u308b\u6700\u9069\u306a\u8ecc\u9053\u304c\u63a1\u7528\u3055\u308c\u308b\u3068\u3001\u6f5c\u5728\u7684\u306a\u885d\u7a81\u304c\u767a\u751f\u3059\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\/9510db1eef48de5611bc0107e00e99fb.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/9510db1eef48de5611bc0107e00e99fb.png\" alt=\"\u5927\u897f\u6d0b\u306e\u6c17\u6d41\u306e\u69d8\u5b50\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\">\u5927\u897f\u6d0b\u306e\u6c17\u6d41\u306e\u69d8\u5b50(<a href=\"http:\/\/www.surfline.com\/surfdata\/chart_viewer\/?chart=natlwind&amp;id=2142\">http:\/\/www.surfline.com\/surfdata\/chart_viewer\/?chart=natlwind&amp;id=2142<\/a>)<\/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\/ae700b40571cf7007438fcdddba59f31.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/ae700b40571cf7007438fcdddba59f31.png\" alt=\"\u6f5c\u5728\u7684\u306a\u885d\u7a81\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\">\u6f5c\u5728\u7684\u306a\u885d\u7a81<\/figcaption><\/figure>\n<\/div>\n\n\n<p>\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u554f\u984c\u3068\u3057\u3066\u6349\u3048\u308b\u3068\u3001\u6f5c\u5728\u7684\u306a\u885d\u7a81\u3092\u56de\u907f\u3059\u308b\u305f\u3081\u306b\u4ee5\u4e0b\u306e\u5bfe\u51e6\u65b9\u6cd5\u304c\u8003\u3048\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30d5\u30e9\u30a4\u30c8\u306e\u51fa\u767a\u6642\u9593\u3092\u9045\u3089\u305b\u308b<\/li>\n\n\n\n<li>\u30d5\u30e9\u30a4\u30c8\u306e\u8ecc\u9053\u3092\u5c40\u6240\u7684\u306b\u5909\u66f4\u3059\u308b<\/li>\n<\/ol>\n\n\n\n<p>\u4eca\u56de\u306f\u7c21\u5358\u306e\u305f\u3081\u306b\u51fa\u767a\u6642\u9593\u306e\u9045\u5ef6\u306e\u307f\u3092\u8003\u616e\u3057\u3001\u5168\u3066\u306e\u30d5\u30e9\u30a4\u30c8\u306b\u304a\u3051\u308b\u9045\u5ef6\u306e\u7dcf\u548c\u3068\u5168\u3066\u306e\u885d\u7a81\u306e\u7dcf\u548c\u3092\u6700\u5c0f\u5316\u3059\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9C%80%E9%81%A9%E5%8C%96%E5%95%8F%E9%A1%8C%E3%81%AE%E5%AE%9A%E5%BC%8F%E5%8C%96\"><\/span>\u6700\u9069\u5316\u554f\u984c\u306e\u5b9a\u5f0f\u5316<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u306e\u7a2e\u985e<\/strong>: \u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u554f\u984c<br><strong>\u5909\u6570<\/strong>: $d_{i,l} \\in \\{0,1\\}$ (\u51fa\u767a\u6642\u306e\u9045\u5ef6 $d_i (= 0,1,2 &#8230;, d_{\\mathrm{max}})$ \u304c$l$\u306e\u5834\u5408$1$, \u305d\u3046\u3067\u306a\u3051\u308c\u3070$0$)<br><strong>\u76ee\u7684\u95a2\u6570<\/strong>:<\/p>\n\n\n\n$$\nf = f_{\\mathrm{encoding}} + f_{\\mathrm{delay}} + f_{\\mathrm{conflict}}\n$$\n\n\n\n<p>\u305f\u3060\u3057\u3001$\\Delta_d$\u3092\u9045\u5ef6\u306e\u5206\u89e3\u80fd\u3001$N_d$\u3092\u9045\u5ef6\u306e\u7dcf\u6570\u3001$N_f$\u3092\u30d5\u30e9\u30a4\u30c8\u306e\u7dcf\u6570\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>1\u3064\u306e\u30d5\u30e9\u30a4\u30c8\u306e\u9045\u5ef6\u3092\u30011\u3064\u306b\u5236\u9650\u3059\u308b:<\/li>\n<\/ol>\n\n\n\n$$\nf_{\\mathrm{encoding}} = \\lambda_{\\mathrm{encoding}}\\sum_{i=1}^{N_f}(\\sum_{l=0}^{N_d}d_{i,l}-1)^2\n$$\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>\u5168\u3066\u306e\u30d5\u30e9\u30a4\u30c8\u306b\u304a\u3051\u308b\u9045\u5ef6\u306e\u7dcf\u548c:<\/li>\n<\/ol>\n\n\n\n$$\nf_{\\mathrm{delay}} = \\Delta_d\\sum_{i=1}^{N_f}\\sum_{l=0}^{N_d}ld_{i,l}\n$$\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>\u5168\u3066\u306e\u885d\u7a81\u306e\u7dcf\u548c:<\/li>\n<\/ol>\n\n\n\n$$\nf_{\\mathrm{conflict}}\n=\n\\lambda_{\\mathrm{conflict}}\n\\sum_{k}\n\\sum_{l,l&#8217;|\\Delta_d (l-l&#8217;) \\in D_k, i,j \\in I_k | i&lt;j}\nd_{i,l} d_{j,l}\n$$\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/cost.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/cost.png\" alt=\"\u76ee\u7684\u95a2\u6570\u306e\u89e3\u8aac\" class=\"wp-image-65\" width=\"480\" height=\"201\"\/><\/a><figcaption class=\"wp-element-caption\">\u76ee\u7684\u95a2\u6570\u306e\u89e3\u8aac<\/figcaption><\/figure>\n<\/div>\n\n\n<p><strong>\u885d\u7a81\u30b0\u30e9\u30d5<\/strong>: \u9802\u70b9\u3092\u5404\u30d5\u30e9\u30a4\u30c8\u3001\u8fba\u3092\u885d\u7a81(\u5c11\u306a\u304f\u3068\u30821\u3064\u885d\u7a81\u304c\u5b58\u5728\u3059\u308b\u30d5\u30e9\u30a4\u30c8\u9593\u3092\u7d50\u3076)\u3068\u3059\u308b\u30b0\u30e9\u30d5\u3002\u6700\u5927\u8a31\u5bb9\u9045\u5ef6\u6642\u9593$d_{\\mathrm{max}}$\u304c\u5927\u304d\u3044\u307b\u3069\u3001\u7d50\u5408\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8(\u63a5\u7d9a\u3055\u308c\u305f\u9802\u70b9\u306e\u307e\u3068\u307e\u308a)\u306f\u9ad8\u5bc6\u5ea6\u3068\u306a\u308a\u3001\u305d\u306e\u6570\u306f\u5c0f\u3055\u304f\u306a\u308b\u3002\u307e\u305f\u3001$d_{\\mathrm{max}}$\u306b\u5bfe\u3057\u3066\u3001\u7d4c\u9a13\u5247\u306e\u6307\u6570$\\alpha$\u306e\u4f9d\u5b58\u6027\u304c\u5b58\u5728\u3059\u308b\u3002\u554f\u984c\u8a2d\u5b9a\u304c\u56f0\u96e3\u306a\u5834\u5408\u306f\u885d\u7a81\u30b0\u30e9\u30d5\u3092\u6728\u5206\u89e3\u3057\u3001\u9045\u5ef6\u3092\u4f1d\u64ad\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u6700\u9069\u5024\u3092\u5bb9\u6613\u306b\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\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\/conflictgraph.png\"><img decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2018\/05\/conflictgraph.png\" alt=\"\u885d\u7a81\u30b0\u30e9\u30d5\" class=\"wp-image-65\"\/><\/a><figcaption class=\"wp-element-caption\">\u885d\u7a81\u30b0\u30e9\u30d5<\/figcaption><\/figure>\n<\/div>\n\n\n<p><strong>\u8a2d\u5b9a\u7a7a\u9593\u306e\u96e2\u6563\u5316<\/strong>: \u9045\u5ef6\u6642\u9593\u3092\u7d30\u304b\u304f\u96e2\u6563\u5316\u3059\u308b\u307b\u3069\u3001\u5fc5\u8981\u3068\u306a\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u6570\u306f\u5927\u304d\u304f\u306a\u308b\u3002\u96e2\u6563\u5316\u306e\u7c92\u5ea6\u304a\u3088\u3073\u6700\u5927\u9045\u5ef6\u8a31\u5bb9\u6642\u9593\u304c\u3001\u6700\u9069\u89e3\u306e\u8cea\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u8003\u3048\u308b\u3053\u3068\u306f\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3092\u6709\u52b9\u306b\u5229\u7528\u3059\u308b\u4e0a\u3067\u91cd\u8981\u3067\u3042\u308b\u3002$d_{\\mathrm{max}}=3$\u306e\u5834\u5408\u3092\u9664\u3044\u3066\u3001$d_{\\mathrm{max}}$\u3092\u3055\u3089\u306b\u5897\u52a0\u3055\u305b\u3066\u3082\u3001\u6700\u5c0f\u9045\u5ef6\u306e\u7dcf\u548c\u306f\u6e1b\u5c11\u3057\u306a\u3044\u305f\u3081\u3001\u3088\u308a\u5927\u304d\u306a\u554f\u984c\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3067\u3042\u3063\u3066\u3082\u3001\u3042\u308b\u7a0b\u5ea6\u5927\u304d\u3044$d_{\\mathrm{max}}$\u3067\u5341\u5206\u3067\u3042\u308b\u3002\u4e00\u65b9\u3001\u9045\u5ef6\u96e2\u6563\u5316$\\Delta_d$\u306f\u3001\u9ad8\u54c1\u8cea\u306e\u89e3\u3092\u5f97\u308b\u305f\u3081\u306b\u306f\u3067\u304d\u308b\u3060\u3051\u7d30\u304b\u3044\u3082\u306e\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%94%A8%E3%81%84%E3%81%9F%E3%83%87%E3%83%BC%E3%82%BF%E3%82%BB%E3%83%83%E3%83%88\"><\/span>\u7528\u3044\u305f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>2012\u5e747\u670829\u65e5\u5927\u897f\u6d0b\u6a2a\u65ad\u98db\u884c(NAT)\u306b\u304a\u3051\u308b984\u306e\u30d5\u30e9\u30a4\u30c8\u306b\u95a2\u3057\u3066\u3001\u4e8b\u524d\u306b\u8a08\u7b97\u3055\u308c\u305f\u98a8\u306b\u5bfe\u3059\u308b\u6700\u9069\u306a\u8ecc\u9053(\u5de1\u822a\u9ad8\u5ea6\u3068\u4e00\u5b9a\u306e\u901f\u5ea6\u3092\u542b\u3080)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"D-Wave%E3%83%9E%E3%82%B7%E3%83%B3%E5%AE%9F%E8%A3%85%E4%B8%8A%E3%81%AE%E5%B7%A5%E5%A4%AB\"><\/span>D-Wave\u30de\u30b7\u30f3\u5b9f\u88c5\u4e0a\u306e\u5de5\u592b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>\u30cf\u30a4\u30d1\u30fc\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u8a2d\u5b9a<\/strong>: \u6700\u59277\u56de\u306e\u98db\u884c\u30689\u56de\u306e\u885d\u7a81\u3092\u4f34\u3046\u3059\u3079\u3066\u306e\u5909\u6570\u306b\u304a\u3044\u3066\u3001$(\\lambda_{\\mathrm{conflict}},\\lambda_{\\mathrm{encoding}})$\u304c\u59a5\u5f53(\u4e21\u65b9\u304c\u5236\u7d04\u3092\u6e80\u305f\u3059)\u3067\u3042\u308b\u5834\u5408\u3068\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306e\u5883\u754c\u306f\u30dc\u30c3\u30af\u30b9\u72b6\u306b\u306a\u308a\u3001\u4e21\u8005\u306e\u59a5\u5f53\u6027\u304c\u72ec\u7acb\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p><strong>\u57cb\u3081\u8fbc\u307f<\/strong>: D-Wave 2X\u3067\u306f\u3001\u6700\u5927$N_f = 50$\u3001$N_c = 104$\u3001D-Wave 2000Q\u3067\u306f$N_f = 64$\u3001$N_c = 261$\u307e\u3067\u306e\u5909\u6570\u3092\u57cb\u3081\u8fbc\u3080\u305f\u3081\u306b\u3001D-Wave\u306e\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u57cb\u3081\u8fbc\u307f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C\"><\/span>\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>D-Wave 2X\u304a\u3088\u3073 D-Wave 2000Q\u304b\u3089\u5f97\u3089\u308c\u305f\u7d50\u679c\u3092\u3001\u6b63\u78ba\u306a\u6700\u9069\u89e3\u304c\u6c42\u307e\u308bMax-SAT\u30bd\u30eb\u30d0\u30fc\u306e\u7d50\u679c\u3068\u6bd4\u8f03\u3057\u305f\u3002\u5404QUBO\u5909\u6570\u306b\u3064\u3044\u3066\u3001\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u51e6\u7406\u3092104\u301c106\u56de\u5b9f\u884c\u3057\u305f\u3002\u7d30\u304b\u306a\u96e2\u6563\u5316\u3068\u3088\u308a\u5927\u304d\u306a\u554f\u984c\u5909\u6570\u306e\u5834\u5408\u306b\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u308b\u6210\u529f\u78ba\u738799%\u306e\u89e3\u6642\u9593$T_{99}$\u306f\u5897\u5927\u3057\u3001\u6210\u529f\u78ba\u7387\u304c\u6e1b\u5c11\u3059\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u305f\u3002<\/p>\n\n\n\n$$\nT_{99}=\\frac{\\ln (1-0.99)}{\\ln (1-p)}T_{\\mathrm{Anneal}}\n$$\n\n\n\n<p>\u6210\u529f\u78ba\u7387\u306e\u539f\u56e0\u3068\u3057\u3066\u8003\u3048\u3089\u308c\u308bD-Wave\u4e0a\u306e\u4ed5\u69d8\u306e\u7cbe\u5ea6\u3092\u8868\u3059\u5c3a\u5ea6\u3068\u3057\u3066\u3001\u6700\u5927\u4fc2\u6570\u6bd4$C_{\\mathrm{max}}$\u304c\u7528\u3044\u3089\u308c\u308b\u3002<\/p>\n\n\n\n$$\nC_{\\mathrm{max}} = \\max\\left[\\frac{\\max|h_i|}{\\min|h_i|},\\frac{\\max|J_{ij}|}{\\min|J_{ij}|}\\right]\n$$\n\n\n\n<p>\u6210\u529f\u78ba\u7387\u306f\u3001\u5f37\u78c1\u6027\u5185\u90e8\u8ad6\u7406\u91cf\u5b50\u30d3\u30c3\u30c8\u7d50\u5408$J_F$\u306e\u9078\u629e\u306b\u4f9d\u5b58\u3059\u308b\u3002\u3059\u3079\u3066\u306e\u57cb\u3081\u8fbc\u307f\u53ef\u80fd\u306a\u5909\u6570\u306b\u5bfe\u3059\u308b$J_{\\mathrm{max}}$\u3092\u7528\u3044\u305f\u5834\u5408\u3001\u7cbe\u5ea6\u306e\u9ad8\u3044$C_{\\mathrm{max}}$\u304c\u5897\u52a0\u3059\u308b\u307b\u3069\u3001\u6700\u5927\u6210\u529f\u78ba\u7387\u304c\u5927\u304d\u304f\u4f4e\u4e0b\u3059\u308b\u3002\u6210\u529f\u78ba\u7387\u306f$C_{\\mathrm{max}} \\approx 30$\u4ed8\u8fd1\u3067\u6d88\u6ec5\u3059\u308b\u305f\u3081\u3001D-Wave 2000Q\u306e\u7cbe\u5ea6\u304c\u7d041\/30\u306b\u76f8\u5f53\u3059\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u4e00\u822c\u306b$C_{\\mathrm{max}}$\u306f\u3001\u554f\u984c\u306e\u5927\u304d\u3055\u3084\u7d30\u304b\u306a\u96e2\u6563\u5316\u3068\u3068\u3082\u306b\u5897\u52a0\u3059\u308b\u305f\u3081\u3001\u5927\u304d\u306a\u554f\u984c\u5909\u6570\u3068\u7d30\u304b\u306a\u96e2\u6563\u5316\u306b\u5bfe\u3059\u308b\u6700\u9069\u5316\u306b\u9577\u3044\u6642\u9593\u3092\u8981\u3059\u308b\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>\u4e38\u5c71\u5c1a\u8cb4<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6587\u732e\u60c5\u5831 \u30bf\u30a4\u30c8\u30eb Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management \u8457\u8005 Tobia [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[11,12,18,27,58,93,112,118],"class_list":["post-293","post","type-post","status-publish","format-standard","hentry","category-review","tag-d-wave-2000q","tag-d-wave-2x","tag-dlr","tag-nasa","tag-58","tag-93","tag-112","tag-118"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u885d\u7a81\u56de\u907f\u306e\u305f\u3081\u306e\u6700\u9069\u306a \u822a\u7a7a\u7d4c\u8def\u9078\u629e \u3078\u306e\u5fdc\u7528 &quot;Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management&quot; by Tobias Stollenwerk et al. 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