{"id":8676,"date":"2026-09-18T06:41:12","date_gmt":"2026-09-17T21:41:12","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=8676"},"modified":"2026-09-18T06:43:43","modified_gmt":"2026-09-17T21:43:43","slug":"%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/","title":{"rendered":"\u91cf\u5b50\u56de\u8def\u5b66\u7fd2"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_88 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 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href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E9%87%8F%E5%AD%90%E7%B3%BB\" >\u91cf\u5b50\u7cfb<\/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\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88\" >\u91cf\u5b50\u30d3\u30c3\u30c8<\/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\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%A4%9A%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88%E7%B3%BB\" >\u591a\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E9%87%8F%E5%AD%90%E6%93%8D%E4%BD%9C\" >\u91cf\u5b50\u64cd\u4f5c<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E9%87%8F%E5%AD%90%E3%82%B2%E3%83%BC%E3%83%88\" >\u91cf\u5b50\u30b2\u30fc\u30c8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%A4%9A%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88%E7%B3%BB%E3%81%AB%E4%BD%9C%E7%94%A8%E3%81%99%E3%82%8B%E3%82%B2%E3%83%BC%E3%83%88\" >\u591a\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306b\u4f5c\u7528\u3059\u308b\u30b2\u30fc\u30c8<\/a><\/li><li class='ez-toc-page-1 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class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%83%96%E3%83%AD%E3%83%83%E3%83%9B%E7%90%83\" >\u30d6\u30ed\u30c3\u30db\u7403<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E7%B4%94%E7%B2%8B%E7%8A%B6%E6%85%8B%E3%81%A8%E6%B7%B7%E5%90%88%E7%8A%B6%E6%85%8B\" >\u7d14\u7c8b\u72b6\u614b\u3068\u6df7\u5408\u72b6\u614b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%AF%86%E5%BA%A6%E6%BC%94%E7%AE%97%E5%AD%90\" >\u5bc6\u5ea6\u6f14\u7b97\u5b50<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%83%91%E3%82%A6%E3%83%AA%E6%BC%94%E7%AE%97%E5%AD%90\" >\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%AF%86%E5%BA%A6%E6%BC%94%E7%AE%97%E5%AD%90%E7%A9%BA%E9%96%93\" >\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%83%91%E3%83%A9%E3%83%A1%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF%E3%82%B2%E3%83%BC%E3%83%88\" >\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%82%AA%E3%83%96%E3%82%B6%E3%83%BC%E3%83%90%E3%83%96%E3%83%AB\" >\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E6%9C%9F%E5%BE%85%E5%80%A4\" >\u671f\u5f85\u5024<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%83%91%E3%83%A9%E3%83%A1%E3%83%BC%E3%82%BF%E3%82%B7%E3%83%95%E3%83%88%E3%83%AB%E3%83%BC%E3%83%AB\" >\u30d1\u30e9\u30e1\u30fc\u30bf\u30b7\u30d5\u30c8\u30eb\u30fc\u30eb<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E6%8F%90%E6%A1%88%E6%89%8B%E6%B3%95\" >\u63d0\u6848\u624b\u6cd5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E7%AC%A6%E5%8F%B7%E5%8C%96\" >\u7b26\u53f7\u5316<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#1%E3%81%A4%E3%81%AE%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E8%A4%87%E6%95%B0%E3%81%AE%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88%E3%81%B8%E3%81%AE%E5%9F%8B%E3%82%81%E8%BE%BC%E3%81%BF\" >1\u3064\u306e\u5165\u529b\u30c7\u30fc\u30bf\u306e\u8907\u6570\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u3078\u306e\u57cb\u3081\u8fbc\u307f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%A4%9A%E6%AC%A1%E5%85%83%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E5%9F%8B%E3%82%81%E8%BE%BC%E3%81%BF\" >\u591a\u6b21\u5143\u30c7\u30fc\u30bf\u306e\u57cb\u3081\u8fbc\u307f<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%83%91%E3%83%A9%E3%83%A1%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF%E3%82%B2%E3%83%BC%E3%83%88%E3%81%AE%E9%81%A9%E7%94%A8\" >\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8\u306e\u9069\u7528<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%87%BA%E5%8A%9B%E3%81%AE%E6%B1%BA%E5%AE%9A\" >\u51fa\u529b\u306e\u6c7a\u5b9a<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%82%B3%E3%82%B9%E3%83%88%E9%96%A2%E6%95%B0%E3%81%AE%E6%9C%80%E9%81%A9%E5%8C%96\" >\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u6700\u9069\u5316<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%AE%9F%E9%A8%93%E8%A8%AD%E5%AE%9A\" >\u5b9f\u9a13\u8a2d\u5b9a<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%9B%9E%E8%B7%AF%E8%A8%AD%E8%A8%88\" >\u56de\u8def\u8a2d\u8a08<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%83%8E%E3%82%A4%E3%82%BA%E3%81%AE%E4%BB%98%E5%8A%A0\" >\u30ce\u30a4\u30ba\u306e\u4ed8\u52a0<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E9%9D%9E%E7%B7%9A%E5%BD%A2%E9%96%A2%E6%95%B0%E3%81%AE%E8%BF%91%E4%BC%BC\" >\u975e\u7dda\u5f62\u95a2\u6570\u306e\u8fd1\u4f3c<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%95%8F%E9%A1%8C%E5%AE%9A%E7%BE%A9\" >\u554f\u984c\u5b9a\u7fa9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-34\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E7%B5%90%E6%9E%9C\" >\u7d50\u679c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-35\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%88%86%E9%A1%9E%E5%95%8F%E9%A1%8C\" >\u5206\u985e\u554f\u984c<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-36\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%95%8F%E9%A1%8C%E5%AE%9A%E7%BE%A9-2\" >\u554f\u984c\u5b9a\u7fa9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-37\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E7%B5%90%E6%9E%9C-2\" >\u7d50\u679c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-38\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E9%87%8F%E5%AD%90%E5%A4%9A%E4%BD%93%E7%B3%BB%E3%83%80%E3%82%A4%E3%83%8A%E3%83%9F%E3%82%AF%E3%82%B9%E3%81%AE%E8%BF%91%E4%BC%BC\" >\u91cf\u5b50\u591a\u4f53\u7cfb\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u306e\u8fd1\u4f3c<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-39\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E5%95%8F%E9%A1%8C%E5%AE%9A%E7%BE%A9-3\" >\u554f\u984c\u5b9a\u7fa9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-40\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E7%B5%90%E6%9E%9C-3\" >\u7d50\u679c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-41\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E7%B5%90%E8%AB%96\" >\u7d50\u8ad6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-42\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-43\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#Appendix\" >Appendix<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-44\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E7%A9%8D\" >\u30c6\u30f3\u30bd\u30eb\u7a4d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-45\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#Uthetae-itheta_H%E3%81%AE%E5%B0%8E%E5%87%BA\" >$U(\\theta)=e^{-i\\theta H}$\u306e\u5c0e\u51fa<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-46\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2026\/09\/18\/%e9%87%8f%e5%ad%90%e5%9b%9e%e8%b7%af%e5%ad%a6%e7%bf%92\/#%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<!-- \/wp:post-content -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li>\u30bf\u30a4\u30c8\u30eb\uff1aQuantum Circuit Learning<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>\u8457\u8005\uff1aK. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>DOI\uff1a<a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.98.032309\">https:\/\/doi.org\/10.1103\/PhysRevA.98.032309<\/a><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>\u51fa\u7248\u5e74\uff1a2018<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:heading -->\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<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u56de\u8def\u5b66\u7fd2\u3068\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6301\u3063\u305f\u91cf\u5b50\u56de\u8def\u5168\u4f53\u3092\u5b66\u7fd2\u30e2\u30c7\u30eb\u3068\u3057\u3066\u6271\u3044\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u53cd\u5fa9\u7684\u306a\u66f4\u65b0\u306b\u3088\u308a\u4e0e\u3048\u3089\u308c\u305f\u30bf\u30b9\u30af\u3092\u5b66\u7fd2\u3059\u308b\u67a0\u7d44\u307f\u3067\u3059\u3002\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306b\u304a\u3051\u308b\u9577\u671f\u7684\u306a\u8ab2\u984c\u3068\u3057\u3066\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u306f\u5468\u56f2\u306e\u74b0\u5883\u3068\u306e\u76f8\u4e92\u4f5c\u7528\u3084\u30b2\u30fc\u30c8\u64cd\u4f5c\u306e\u8aa4\u5dee\u306b\u3088\u3063\u3066\u3001\u91cf\u5b50\u72b6\u614b\u3092\u6b63\u78ba\u306b\u4fdd\u6301\u3067\u304d\u308b\u6642\u9593\u304c\u9650\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5b9f\u884c\u6642\u9593\u304c\u9577\u304f\u3001\u30b2\u30fc\u30c8\u6570\u306e\u591a\u3044\u6df1\u3044\u91cf\u5b50\u56de\u8def\u3092\u9ad8\u3044\u7cbe\u5ea6\u3067\u5b9f\u884c\u3059\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u91cf\u5b50\u56de\u8def\u5b66\u7fd2\u306f\u6bd4\u8f03\u7684\u6d45\u3044\u91cf\u5b50\u56de\u8def\u3067\u5b9f\u88c5\u3067\u304d\u308b\u305f\u3081\u3001\u3053\u306e\u3088\u3046\u306a\u5236\u7d04\u306e\u3042\u308b\u73fe\u5728\u306e\u91cf\u5b50\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u306b\u3082\u9069\u3057\u305f\u67a0\u7d44\u307f\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u672c\u8ad6\u6587\u3067\u306f\u91cf\u5b50\u56de\u8def\u5b66\u7fd2\u306b\u3088\u3063\u3066\u975e\u7dda\u5f62\u95a2\u6570\u306e\u8fd1\u4f3c\u3001\u5206\u985e\u554f\u984c\u3001\u91cf\u5b50\u591a\u4f53\u7cfb\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u306e\u8fd1\u4f3c\u306e\u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u884c\u3044\u3001\u7d50\u679c\u3068\u3057\u3066\u305d\u308c\u3089\u5168\u3066\u306b\u5bfe\u3057\u3066\u6709\u52b9\u306b\u6a5f\u80fd\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF\"><\/span>\u80cc\u666f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E7%B3%BB\"><\/span>\u91cf\u5b50\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88\"><\/span>\u91cf\u5b50\u30d3\u30c3\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u30d3\u30c3\u30c8\u3068\u306f\u3001\u6e2c\u5b9a\u306b\u5bfe\u3057\u72b6\u614b\u306b\u3088\u3063\u3066\u78ba\u7387\u7684\u306b$0$\u304b$1$\u3092\u8fd4\u3059\u30d3\u30c3\u30c8\u306e\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$0$\u306e\u78ba\u7387\u3092$|\\alpha|^2$\u3001$1$\u306e\u78ba\u7387\u3092$|\\beta|^2$\u3068\u3057\u3066\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b$\\ket{\\psi}$\u306f\u4ee5\u4e0b\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ket{\\psi}=\\alpha\\ket{0}+\\beta\\ket{1}=\\begin{pmatrix}\\alpha\\\\\\beta\\end{pmatrix}\\tag{1}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067\u3001$\\alpha\u3001\\beta$\u306f\u3069\u306e\u7a0b\u5ea6\u306e\u91cd\u307f\u3067$0$\u72b6\u614b\u3068$1$\u72b6\u614b\u304c\u91cd\u306d\u5408\u308f\u3055\u3063\u3066\u3044\u308b\u304b\u3092\u8868\u3059\u8907\u7d20\u78ba\u7387\u632f\u5e45\u3067\u3059\u3002$\\alpha\u3001\\beta$\u304c\u8907\u7d20\u6570\u3067\u3042\u308b\u7406\u7531\u306f\u3001\u91cf\u5b50\u306e\u4e16\u754c\u306b\u304a\u3044\u3066$0$\u72b6\u614b\u3068$1$\u72b6\u614b\u306e\u3088\u3046\u306a\u96e2\u6563\u7684\u306a\u91cf\u3082\u6ce2\u306e\u6027\u8cea\u3092\u6301\u3061\u4e92\u3044\u306b\u5e72\u6e09\u3059\u308b\u3068\u8003\u3048\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001$\\ket{0}$\u3068$\\ket{1}$\u306f\u4ee5\u4e0b\u306e\u5217\u30d9\u30af\u30c8\u30eb\u3092\u8868\u3057\u307e\u3059\u3002\u3059\u308b\u3068\u3001\u72b6\u614b$\\ket{\\psi}$\u306f$2$\u500b\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb$\\ket{0}$\u3001$\\ket{1}$\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u305b\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ket{0}=\\begin{pmatrix}1\\\\0\\end{pmatrix}, \\ket{1}=\\begin{pmatrix}0\\\\1\\end{pmatrix}\\tag{2}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3068\u304d\u3001$|\\alpha|^2$\u3001$|\\beta|^2$\u306f\u78ba\u7387\u3067\u3042\u308a\u3001\u305d\u306e\u7dcf\u548c\u306f$1$\u306a\u306e\u3067\u3001$|\\alpha|^2+|\\beta|^2=1$\u306e\u6761\u4ef6\u304c\u8ab2\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%A4%9A%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88%E7%B3%BB\"><\/span>\u591a\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u8907\u6570\u5b58\u5728\u3059\u308b\u5834\u5408\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u53e4\u5178\u30d3\u30c3\u30c8\u304c$N$\u500b\u3042\u308b\u3068\u304d\u3001\u305d\u306e\u72b6\u614b\u306f$N$\u500b\u306e$0,1$\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u3088\u308a$2^N$\u500b\u306e\u30d1\u30bf\u30fc\u30f3\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u306e\u4e16\u754c\u3067\u306f$2^N$\u500b\u306e\u30d1\u30bf\u30fc\u30f3\u5168\u3066\u306e\u91cd\u306d\u5408\u308f\u305b\u72b6\u614b\u304c\u8a31\u3055\u308c\u308b\u305f\u3081\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u304c$N$\u500b\u3042\u308b\u3068\u304d\u3001\u305d\u306e\u7cfb\u306e\u72b6\u614b$\\ket{\\psi}$\u306f$2^N$\u500b\u306e\u8907\u7d20\u6570\u3068$2^N$\u500b\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066$N=2$\u306e\u3068\u304d\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ket{\\psi}=C_{00}\\ket{00}+C_{01}\\ket{01}+C_{10}\\ket{10}+C_{11}\\ket{11}=\\begin{pmatrix}C_{00}\\\\C_{01}\\\\C_{10}\\\\C_{11}\\end{pmatrix}s.t.\\sum_{i_1,i_2}|C_{i_1i_2}|^2=1\\tag{3}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067$|C_{00}|^2$\u306f$1$\u30d3\u30c3\u30c8\u76ee\u304c$0$\u304b\u3064$2$\u30d3\u30c3\u30c8\u76ee\u304c$0$\u306e\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001$\\ket{00}$\u306f\u30c6\u30f3\u30bd\u30eb\u7a4d$\\ket{0}\\otimes\\ket{0}$\u306e\u7c21\u7565\u8868\u73fe\u3068\u3057\u3066\u7528\u3044\u3066\u3044\u307e\u3059\u3002(\u30c6\u30f3\u30bd\u30eb\u7a4d\u306b\u3064\u3044\u3066\u306fAppendix\u306b\u8a18\u8f09\u3057\u307e\u3057\u305f)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E6%93%8D%E4%BD%9C\"><\/span>\u91cf\u5b50\u64cd\u4f5c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E3%82%B2%E3%83%BC%E3%83%88\"><\/span>\u91cf\u5b50\u30b2\u30fc\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u53e4\u5178\u30d3\u30c3\u30c8\u306b\u5bfe\u3059\u308bNOT\u3001AND\u306a\u3069\u306e\u30b2\u30fc\u30c8\u306e\u3088\u3046\u306b\u3001\u91cf\u5b50\u30b2\u30fc\u30c8\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u5bfe\u3059\u308b\u6f14\u7b97\u306b\u76f8\u5f53\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p><style>.tooltip-word{ position:relative; cursor:pointer; border-bottom:1px dotted #555; } .tooltip-box{ display:none; position:absolute; top:100%; left:0; margin-top:8px; background:#333; color:#fff; padding:10px; border-radius:6px; min-width:300px; max-width:80vw; white-space:normal; z-index:99999; } .tooltip-word:hover .tooltip-box{ display:block; } .wp-block-image.is-resized{ display:block !important; width:auto !important; } .wp-block-image.is-resized img{ display:block; margin-left:auto; margin-right:auto; } .wp-block-image figcaption, .wp-block-image.is-resized figcaption{ display:block !important; width:100% !important; max-width:100% !important; text-align:center !important; } <\/style> \u72b6\u614b$\\ket{\\psi}$\u306b\u91cf\u5b50\u30b2\u30fc\u30c8\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u306f\u3001 $\\ket{\\psi}$\u306b <span class=\"tooltip-word\">\u30e6\u30cb\u30bf\u30ea\u884c\u5217 <span class=\"tooltip-box\">\u5171\u5f79\u8ee2\u7f6e\u884c\u5217$U^\\dagger$\u304c\u81ea\u8eab\u306e\u9006\u884c\u5217$U^{-1}$\u306b\u306a\u308b\u884c\u5217$U$ $\\left( \\begin{pmatrix} a &amp; b \\\\ c &amp; d \\\\ \\end{pmatrix}^\\dagger = \\begin{pmatrix} a^* &amp; b^* \\\\ c^* &amp; d^* \\\\ \\end{pmatrix} \\right)$ <\/span> <\/span> $U$\u306b\u3088\u308b\u7dda\u5f62\u5909\u63db\u3092\u884c\u3046\u3053\u3068\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u72b6\u614b$\\ket{\\psi}=\\begin{pmatrix}\\alpha\\\\\\beta\\end{pmatrix}$\u306b\u4f5c\u7528\u3059\u308b\u91cf\u5b50\u30b2\u30fc\u30c8\u306e\u4f8b\u3068\u3057\u3066$X=\\begin{pmatrix}0 &amp; 1\\\\1 &amp; 0\\end{pmatrix}$\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$X\\ket{\\psi}=\\begin{pmatrix}0 &amp; 1\\\\1 &amp; 0\\end{pmatrix}\\begin{pmatrix}\\alpha\\\\\\beta\\end{pmatrix}=\\begin{pmatrix}\\beta\\\\\\alpha\\end{pmatrix}\\tag{4}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306b$0$\u72b6\u614b\u3068$1$\u72b6\u614b\u306e\u78ba\u7387\u632f\u5e45\u304c\u53cd\u8ee2\u3059\u308b\u305f\u3081\u3001$X$\u30b2\u30fc\u30c8\u306f\u53e4\u5178\u30d3\u30c3\u30c8\u306b\u304a\u3051\u308bNOT\u30b2\u30fc\u30c8\u306e\u3088\u3046\u306a\u30b2\u30fc\u30c8\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30b2\u30fc\u30c8\u9069\u7528\u5f8c\u306e\u72b6\u614b$\\ket{\\psi&#8217;}=\\begin{pmatrix}\\alpha&#8217;\\\\\\beta&#8217;\\end{pmatrix}$\u3082\u9069\u7528\u524d\u306e\u72b6\u614b\u3068\u540c\u69d8\u306b$|\\alpha&#8217;|^2$\u3001$|\\beta&#8217;|^2$\u306f\u78ba\u7387\u3067\u3042\u308b\u305f\u3081\u3001${|\\alpha|}^2+{|\\beta|}^2={|\\alpha\\prime|}^2+{|\\beta\\prime|}^2=1$\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u91cf\u5b50\u30b2\u30fc\u30c8\u306f\u5143\u306e\u30d9\u30af\u30c8\u30eb\u306e\u30ce\u30eb\u30e0$1$\u3092\u7dad\u6301\u3059\u308b\u7dda\u5f62\u5909\u63db\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30e6\u30cb\u30bf\u30ea\u884c\u5217$U$\u306f$U^\\dagger U=I$\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u72b6\u614b$\\ket{\\psi}$\u306b\u4f5c\u7528\u3055\u305b\u3066\u3082\u3001<\/p>\n<p>$$<br \/>\\|U\\ket{\\psi}\\|^2<br \/>=(U\\ket{\\psi})^\\dagger U\\ket{\\psi}=\\bra{\\psi}U^\\dagger U\\ket{\\psi}<br \/>=\\left\\langle\\psi|\\psi\\right\\rangle=\\|\\ket{\\psi}\\|^2\\tag{5}<br \/>$$<\/p>\n<p>\u3068\u306a\u308a\u3001\u30ce\u30eb\u30e0\u3092\u4fdd\u5b58\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%A4%9A%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88%E7%B3%BB%E3%81%AB%E4%BD%9C%E7%94%A8%E3%81%99%E3%82%8B%E3%82%B2%E3%83%BC%E3%83%88\"><\/span>\u591a\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306b\u4f5c\u7528\u3059\u308b\u30b2\u30fc\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>$N$\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306b\u4f5c\u7528\u3059\u308b\u30b2\u30fc\u30c8\u306f$2^N\\times2^N$ \u306e\u30e6\u30cb\u30bf\u30ea\u884c\u5217\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$2$\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306e\u72b6\u614b$\\ket{\\psi}=\\begin{pmatrix}C_{00}\\\\C_{01}\\\\C_{10}\\\\C_{11}\\end{pmatrix}$\u306b\u4f5c\u7528\u3059\u308b\u91cf\u5b50\u30b2\u30fc\u30c8\u306e\u4f8b\u3068\u3057\u3066$CNOT=\\left(\\begin{matrix}\\begin{matrix}1&amp;0\\\\0&amp;1\\\\\\end{matrix}&amp;\\begin{matrix}0&amp;0\\\\0&amp;0\\\\\\end{matrix}\\\\\\begin{matrix}0&amp;0\\\\0&amp;0\\\\\\end{matrix}&amp;\\begin{matrix}0&amp;1\\\\1&amp;0\\\\\\end{matrix}\\\\\\end{matrix}\\right)$\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$CNOT\\ket{\\psi}=\\left(\\begin{matrix}\\begin{matrix}1&amp;0\\\\0&amp;1\\\\\\end{matrix}&amp;\\begin{matrix}0&amp;0\\\\0&amp;0\\\\\\end{matrix}\\\\\\begin{matrix}0&amp;0\\\\0&amp;0\\\\\\end{matrix}&amp;\\begin{matrix}0&amp;1\\\\1&amp;0\\\\\\end{matrix}\\\\\\end{matrix}\\right)\\begin{pmatrix}C_{00}\\\\C_{01}\\\\C_{10}\\\\C_{11}\\end{pmatrix}=\\begin{pmatrix}C_{00}\\\\C_{01}\\\\C_{11}\\\\C_{10}\\end{pmatrix}\\tag{6}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306b\u30b2\u30fc\u30c8\u3092\u9069\u7528\u3059\u308b\u3068\u3001$C_{10}$\u3068$C_{11}$\u304c\u53cd\u8ee2\u3057\u305f\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$1$\u30d3\u30c3\u30c8\u76ee\u3068$2$\u30d3\u30c3\u30c8\u76ee\u306b\u5206\u3051\u3066\u8003\u3048\u308b\u3068\u3001$1$\u30d3\u30c3\u30c8\u76ee\u304c$0$\u306e\u6642\u4f55\u3082\u305b\u305a\u3001$1$\u30d3\u30c3\u30c8\u76ee\u304c$1$\u306e\u6642$2$\u30d3\u30c3\u30c8\u76ee\u3092\u53cd\u8ee2\u3059\u308b\u3088\u3046\u306a\u4f5c\u7528\u3067\u3042\u308b\u3068\u3082\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u30d3\u30c3\u30c8\u9593\u306b\u76f8\u95a2\u304c\u751f\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306b\u30d3\u30c3\u30c8\u9593\u306e\u76f8\u95a2\u3092\u751f\u307f\u51fa\u3059\u30b2\u30fc\u30c8\u306b\u3088\u308a\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%A8%E3%83%B3%E3%82%BF%E3%83%B3%E3%82%B0%E3%83%AB%E7%8A%B6%E6%85%8B\"><\/span>\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u5404\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u304c\u72ec\u7acb\u3067\u306a\u3044\u72b6\u614b\u3092\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u3001\u5404\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u72ec\u7acb\u306a\u72b6\u614b$\\ket{\\psi}$\u3092\u8003\u3048\u307e\u3059\u3002$2$\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u3067\u306f\u3001\u5404\u30d3\u30c3\u30c8\u306e\u72b6\u614b $\\ket{\\psi_1}=\\left(\\begin{matrix}\\alpha_1\\\\\\beta_1\\\\\\end{matrix}\\right)$\u3001$\\ket{\\psi_2}=\\left(\\begin{matrix}\\alpha_2\\\\\\beta_2\\\\\\end{matrix}\\right)$\u3092\u7528\u3044\u3066\u30c6\u30f3\u30bd\u30eb\u7a4d\u3067\u8868\u305b\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ket{\\psi}=\\ket{\\psi_1}\\bigotimes\\ket{\\psi_2}=\\begin{pmatrix}\\alpha_1\\alpha_2\\\\\\alpha_1\\beta_2\\\\\\beta_1\\alpha_2\\\\\\beta_1\\beta_2\\end{pmatrix}\\tag{7}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u304c\u5404\u30d3\u30c3\u30c8\u304c\u72ec\u7acb\u306a\u72b6\u614b\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u72b6\u614b\u306b\u5bfe\u3057\u3066\u3001$CNOT$\u30b2\u30fc\u30c8\u306e\u3088\u3046\u306a\u30d3\u30c3\u30c8\u9593\u306e\u76f8\u95a2\u3092\u751f\u307f\u51fa\u3059\u30b2\u30fc\u30c8\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066\u3001$\\ket{\\psi_1}=\\frac{1}{\\sqrt{2}}\\left(\\begin{matrix}1\\\\1\\\\\\end{matrix}\\right)$\u3001$\\ket{\\psi_2}=\\left(\\begin{matrix}1\\\\0\\\\\\end{matrix}\\right)$\u3068\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ket{\\psi}=\\ket{\\psi_1}\\bigotimes\\ket{\\psi_2}=\\frac{1}{\\sqrt{2}}\\left(\\begin{matrix}1\\\\1\\\\\\end{matrix}\\right)\\bigotimes\\left(\\begin{matrix}1\\\\0\\\\\\end{matrix}\\right)=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1\\\\0\\\\1\\\\0\\end{pmatrix}\\tag{8}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u306f\u30c6\u30f3\u30bd\u30eb\u7a4d\u3092\u7528\u3044\u3066\u8868\u73fe\u3067\u304d\u3066\u3044\u308b\u306e\u3067\u3001\u5404\u30d3\u30c3\u30c8\u306f\u72ec\u7acb\u3067\u3059\u3002\u3053\u3053\u306b\u524d\u8ff0\u3057\u305f$CNOT$\u3092\u9069\u7528\u3059\u308b\u3068\u3001<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$CNOT\\ket{\\psi}= \\frac{1}{\\sqrt{2}}\\begin{pmatrix}1\\\\0\\\\0\\\\1\\end{pmatrix}\\tag{9}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3068\u306a\u308a\u3001\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u72b6\u614b\u304c\u72ec\u7acb\u3067\u306a\u3044\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u3082\u3057\u3053\u306e\u72b6\u614b\u304c\u72ec\u7acb\u3067\u3042\u308b\u3053\u3068\u3092\u4eee\u5b9a\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u73fe\u3067\u304d\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1\\\\0\\\\0\\\\1\\end{pmatrix} = \\begin{pmatrix}\\alpha_1\\\\\\beta_1\\end{pmatrix}\\otimes\\begin{pmatrix}\\alpha_2\\\\\\beta_2\\end{pmatrix} = \\begin{pmatrix}\\alpha_1\\alpha_2\\\\\\alpha_1\\beta_2\\\\\\beta_1\\alpha_2\\\\\\beta_1\\beta_2\\end{pmatrix}\\tag{10}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3057\u304b\u3057\u3053\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u3053\u3046\u3068\u3059\u308b\u3068\u3001$\\alpha_1\\beta_2=0$ \u304b\u3064 $\\beta_1\\alpha_2=0$ \u3067\u3042\u308a\u306a\u304c\u3089 $\\alpha_1\\alpha_2\\neq0$ \u304b\u3064 $\\beta_1\\beta_2\\neq0$ \u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u3001\u77db\u76fe\u304c\u751f\u3058\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3088\u3063\u3066\u80cc\u7406\u6cd5\u306b\u3088\u308a\u4eee\u5b9a\u304c\u9593\u9055\u3063\u3066\u3044\u305f\u3053\u3068\u304c\u308f\u304b\u308b\u306e\u3067\u3001\u3053\u306e\u72b6\u614b\u306f\u3044\u304b\u306a\u308b$1$\u91cf\u5b50\u30d3\u30c3\u30c8\u72b6\u614b\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u3067\u3082\u8868\u305b\u305a\u3001\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u72ec\u7acb\u306a\u72b6\u614b\u3067\u306f\u5404\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u3092\u8868\u3059\u5909\u6570\u306e\u7a4d\u3067\u8868\u73fe\u3055\u308c\u308b\u306e\u306b\u5bfe\u3057\u3066\u3001\u72ec\u7acb\u3067\u306a\u3044\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3067\u306f\u5404\u6b21\u5143\u306b\u5bfe\u3057\u3066$1$\u3064\u306e\u5909\u6570\u3092\u7528\u3044\u3066\u8868\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u30d3\u30c3\u30c8\u6570 $N$ \u304c\u5897\u3048\u308b\u307b\u3069\u3053\u306e\u5dee\u306f\u9855\u8457\u306b\u306a\u308a\u3001\u72ec\u7acb\u306a\u72b6\u614b\u306e\u5909\u6570\u6570 $2\\times N$ \u306b\u5bfe\u3057\u3066\u4e00\u822c\u306e\u72b6\u614b\u306e\u5909\u6570\u6570\u306f $2^N$ \u3068\u6307\u6570\u7684\u306b\u5897\u52a0\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3092\u6d3b\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u306f\u3058\u3081\u3066 $2^N$ \u6b21\u5143\u306e\u72b6\u614b\u7a7a\u9593\u304c\u6301\u3064\u8c4a\u304b\u306a\u8868\u73fe\u529b\u3092\u5168\u3066\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b)$3$\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306e\u72ec\u7acb\u306a\u72b6\u614b$\\ket{\\psi}$\u3001\u72ec\u7acb\u3067\u306a\u3044\u72b6\u614b$\\ket{\\psi&#8217;}$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ket{\\psi}=\\ket{\\psi_1}\\bigotimes\\ket{\\psi_2}\\bigotimes\\ket{\\psi_3}=\\left(\\begin{matrix}\\begin{matrix}\\begin{matrix}\\alpha_1\\alpha_2\\alpha_3\\\\\\alpha_1\\alpha_2\\beta_3\\\\\\end{matrix}\\\\\\begin{matrix}\\alpha_1\\beta_2\\alpha_3\\\\\\alpha_1\\beta_2\\beta_3\\\\\\end{matrix}\\\\\\end{matrix}\\\\\\begin{matrix}\\begin{matrix}\\beta_1\\alpha_2\\alpha_3\\\\\\beta_1\\alpha_2\\beta_3\\\\\\end{matrix}\\\\\\begin{matrix}\\beta_1\\beta_2\\alpha_3\\\\\\beta_1\\beta_2\\beta_3\\\\\\end{matrix}\\\\\\end{matrix}\\\\\\end{matrix}\\right),\\hspace{5pt}\\ket{\\psi&#8217;}=\\left(\\begin{matrix}C_{000}\\\\C_{001}\\\\C_{010}\\\\C_{011}\\\\C_{100}\\\\C_{101}\\\\C_{110}\\\\C_{111}\\end{matrix}\\right)\\tag{11}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u72ec\u7acb\u306a\u72b6\u614b\u3067\u306f\u3001\u30c6\u30f3\u30bd\u30eb\u7a4d\u306b\u3088\u308b\u56e0\u6570\u5206\u89e3\u304c\u3067\u304d\u308b\u3068\u6349\u3048\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E5%9B%9E%E8%B7%AF\"><\/span>\u91cf\u5b50\u56de\u8def<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u56de\u8def\u3068\u306f\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u9069\u7528\u3059\u308b\u91cf\u5b50\u30b2\u30fc\u30c8\u306e\u7a2e\u985e\u3084\u9806\u5e8f\u3001\u6e2c\u5b9a\u306e\u4f4d\u7f6e\u3092\u8868\u3057\u305f\u8a2d\u8a08\u56f3\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u56de\u8def\u56f3\u306e\u4f8b\u3092\u56f31\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8884,\"width\":\"402px\",\"height\":\"auto\",\"aspectRatio\":\"3.072702331961591\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"974\" height=\"317\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image.png\" alt=\"\" class=\"wp-image-8884\" style=\"aspect-ratio: 3.072702331961591; width: 402px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image.png 974w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-300x98.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-768x250.png 768w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f31: \u91cf\u5b50\u56de\u8def\u56f3\u306e\u4f8b<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u6a2a\u7dda\u304c\u305d\u308c\u305e\u308c$1$\u3064\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u3092\u8868\u3057\u3001\u6642\u9593\u306f\u5de6\u304b\u3089\u53f3\u3078\u9032\u307f\u307e\u3059\u3002\u6a2a\u7dda\u4e0a\u306e\u56db\u89d2\u5f62\u306f\u3001\u305d\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u4f5c\u7528\u3059\u308b\u91cf\u5b50\u30b2\u30fc\u30c8\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u7e26\u7dda\u3067\u7d50\u3070\u308c\u305f\u9ed2\u4e38\u3068\u2295\u306f$CNOT$\u30b2\u30fc\u30c8\u3092\u8868\u3057\u3001\u9ed2\u4e38\u304c\u64cd\u4f5c\u3092\u5236\u5fa1\u3059\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u3001\u2295\u304c\u64cd\u4f5c\u306e\u5bfe\u8c61\u3068\u306a\u308a\u53cd\u8ee2\u3057\u3046\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u3092\u8868\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u30e1\u30fc\u30bf\u30fc\u72b6\u306e\u8a18\u53f7\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u6e2c\u5b9a\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u56f31\u4e2d\u306e$X$\u30b2\u30fc\u30c8\u3001$H$\u30b2\u30fc\u30c8\u3001$CNOT$\u30b2\u30fc\u30c8\u306f\u3001\u305d\u308c\u305e\u308c\u4ee5\u4e0b\u306e\u884c\u5217\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$X=\\left(\\begin{matrix}0&amp;1\\\\1&amp;0\\end{matrix}\\right),\\qquad H=\\frac{1}{\\sqrt{2}}\\left(\\begin{matrix}1&amp;1\\\\1&amp;-1\\end{matrix}\\right)\\tag{12}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$CNOT=\\left(\\begin{matrix}\\begin{matrix}1&amp;0\\\\0&amp;1\\\\\\end{matrix}&amp;\\begin{matrix}0&amp;0\\\\0&amp;0\\\\\\end{matrix}\\\\\\begin{matrix}0&amp;0\\\\0&amp;0\\\\\\end{matrix}&amp;\\begin{matrix}0&amp;1\\\\1&amp;0\\\\\\end{matrix}\\\\\\end{matrix}\\right)\\tag{13}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%8A%B6%E6%85%8B%E3%81%AE%E8%A1%A8%E7%8F%BE\"><\/span>\u72b6\u614b\u306e\u8868\u73fe<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%96%E3%83%AD%E3%83%83%E3%83%9B%E7%90%83\"><\/span>\u30d6\u30ed\u30c3\u30db\u7403<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u306f\u4e09\u89d2\u95a2\u6570\u3068\u5927\u304d\u3055$1$\u306e\u8907\u7d20\u6570$e^{i\\phi_\\alpha}$\u3001$e^{i\\phi_\\beta}$\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ket{\\psi}=e^{i\\phi_\\alpha}\\cos\\left(\\frac{\\theta}{2}\\right)\\ket0+e^{i\\phi_\\beta}\\sin\\left(\\frac{\\theta}{2}\\right)\\ket1=e^{i\\phi_\\alpha}\\left\\{\\cos\\left(\\frac{\\theta}{2}\\right)\\ket0+e^{i(\\phi_\\beta-\\phi_\\alpha)}\\sin\\left(\\frac{\\theta}{2}\\right)\\ket1\\right\\}\\tag{14}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067\u5168\u4f53\u306b\u4fc2\u308b$e^{i\\phi_\\alpha}$(\u30b0\u30ed\u30fc\u30d0\u30eb\u4f4d\u76f8)\u306f$0$\u3068$1$\u306e\u78ba\u7387\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u306a\u3044\u305f\u3081\u3001\u7269\u7406\u7684\u306a\u610f\u5473\u304c\u3042\u308a\u307e\u305b\u3093\u3002(<span>\u4ed6\u306e\u72b6\u614b\u3068\u91cd\u306d\u5408\u308f\u305b\u305f\u3068\u304d\u306f\u76f8\u5bfe\u4f4d\u76f8\u3068\u306a\u308b\u305f\u3081\u3001\u72b6\u614b\u306e\u5b9a\u7fa9\u3068\u3057\u3066\u306f\u5fc5\u8981\u3067\u3059<\/span>)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u305d\u306e\u305f\u3081\u3001\u30b0\u30ed\u30fc\u30d0\u30eb\u4f4d\u76f8\u3092\u7121\u8996\u3057\u3001$\\phi=\\phi_\\beta-\\phi_\\alpha$\u3068\u3059\u308b\u3068\u3001$\\ket{\\psi}$\u306f\u56f32\u306e\u7403\u9762\u4e0a\u306e\u70b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3053\u306e\u7403\u3092\u30d6\u30ed\u30c3\u30db\u7403\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8899,\"width\":\"370px\",\"height\":\"auto\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"698\" height=\"694\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-4.png\" alt=\"\" class=\"wp-image-8899\" style=\"width: 370px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-4.png 698w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-4-300x298.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-4-150x150.png 150w\" sizes=\"auto, (max-width: 698px) 100vw, 698px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f32: \u30d6\u30ed\u30c3\u30db\u7403<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u3044\u304f\u3064\u304b\u306e\u72b6\u614b\u3092\u4f8b\u3068\u3057\u3066\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$\\ket{\\psi}=\\left(\\begin{matrix}1\\\\0\\\\\\end{matrix}\\right)$\u306e\u3068\u304d\u3001$\\theta=0\u3001\\phi=0$\u306a\u306e\u3067\u56f33\u306e\u70b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8901,\"width\":\"296px\",\"height\":\"auto\",\"aspectRatio\":\"0.9949475320637389\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"982\" height=\"987\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5.png\" alt=\"\" class=\"wp-image-8901\" style=\"aspect-ratio: 0.9949475320637389; width: 296px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5.png 982w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5-298x300.png 298w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5-150x150.png 150w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5-768x772.png 768w\" sizes=\"auto, (max-width: 982px) 100vw, 982px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f33: $\\ket{\\psi}=\\left(\\begin{matrix}1\\\\0\\end{matrix}\\right)$\u306b\u5bfe\u5fdc\u3059\u308b\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u306e\u70b9<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>$\\ket{\\psi}=\\left(\\begin{matrix}\\frac{1}{\\sqrt{2}}\\\\\\frac{1}{\\sqrt{2}}\\\\\\end{matrix}\\right)$\u306e\u3068\u304d\u3001$\\theta=\\frac{\\pi}{2}\u3001\\phi=0$\u306a\u306e\u3067\u56f34\u306e\u70b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8902,\"width\":\"290px\",\"height\":\"auto\",\"aspectRatio\":\"1.0148757834327569\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1009\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-6-1024x1009.png\" alt=\"\" class=\"wp-image-8902\" style=\"aspect-ratio: 1.0148757834327569; width: 290px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-6-1024x1009.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-6-300x295.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-6-768x756.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-6.png 1195w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f34: $\\ket{\\psi}=\\left(\\begin{matrix}\\frac{1}{\\sqrt{2}}\\\\\\frac{1}{\\sqrt{2}}\\end{matrix}\\right)$\u306b\u5bfe\u5fdc\u3059\u308b\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u306e\u70b9<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>$\\ket{\\psi}=\\left(\\begin{matrix}\\frac{1}{\\sqrt{2}}\\\\\\frac{i}{\\sqrt{2}}\\\\\\end{matrix}\\right)$\u306e\u3068\u304d\u3001$\\theta=\\frac{\\pi}{2}\u3001\\phi=\\frac{\\pi}{2}$\u306a\u306e\u3067\u56f35\u306e\u70b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8903,\"width\":\"305px\",\"height\":\"auto\",\"aspectRatio\":\"1.0312138728323699\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"695\" height=\"674\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-7.png\" alt=\"\" class=\"wp-image-8903\" style=\"aspect-ratio: 1.0312138728323699; width: 305px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-7.png 695w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-7-300x291.png 300w\" sizes=\"auto, (max-width: 695px) 100vw, 695px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f35: $\\ket{\\psi}=\\left(\\begin{matrix}\\frac{1}{\\sqrt{2}}\\\\\\frac{i}{\\sqrt{2}}\\end{matrix}\\right)$\u306b\u5bfe\u5fdc\u3059\u308b\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u306e\u70b9<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B4%94%E7%B2%8B%E7%8A%B6%E6%85%8B%E3%81%A8%E6%B7%B7%E5%90%88%E7%8A%B6%E6%85%8B\"><\/span>\u7d14\u7c8b\u72b6\u614b\u3068\u6df7\u5408\u72b6\u614b<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u307e\u3067\u6271\u3063\u3066\u304d\u305f$\\ket{\\psi}$\u3067\u8868\u3055\u308c\u308b\u3088\u3046\u306a\u91cf\u5b50\u72b6\u614b\u3092\u7d14\u7c8b\u72b6\u614b\u3068\u3044\u3046\u306e\u306b\u5bfe\u3057\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u304c\u78ba\u7387\u7684\u306b\u6df7\u3056\u308a\u5408\u3063\u305f\u72b6\u614b\u3092\u6df7\u5408\u72b6\u614b\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066\u56f36\u306e\u3088\u3046\u306b\u3001\u30ce\u30a4\u30ba\u306a\u3069\u306e\u5f71\u97ff\u306b\u3088\u308a$50$\uff05\u3067\u30d3\u30c3\u30c8\u304c\u53cd\u8ee2($50$\uff05\u3067$X$\u30b2\u30fc\u30c8\u304c\u4f5c\u7528)\u3059\u308b\u72b6\u6cc1\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8888,\"width\":\"343px\",\"height\":\"auto\",\"aspectRatio\":\"1.982373981341495\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1009\" height=\"509\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-2.png\" alt=\"\" class=\"wp-image-8888\" style=\"aspect-ratio: 1.982373981341495; width: 343px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-2.png 1009w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-2-300x151.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-2-768x387.png 768w\" sizes=\"auto, (max-width: 1009px) 100vw, 1009px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f36: $50$\uff05\u306e\u78ba\u7387\u3067$X$\u30b2\u30fc\u30c8\u304c\u4f5c\u7528\u3059\u308b\u56de\u8def<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3068\u304d\u3001\u6e2c\u5b9a\u524d\u306e\u72b6\u614b\u306f$50$\uff05\u3067$\\ket0$\u3001$50$\uff05\u3067$\\ket1$\u3068\u306a\u308a\u3001\u6e2c\u5b9a\u3067\u306f$0$\u3068$1$\u304c$1:1$\u306e\u78ba\u7387\u3067\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306a\u72b6\u614b\u3092\u6df7\u5408\u72b6\u614b\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306a\u6df7\u5408\u72b6\u614b\u3067\u306f(\u6211\u3005\u306e\u8003\u616e\u3057\u304d\u308c\u306a\u3044\u5916\u7684\u8981\u56e0\u306b\u3088\u308b)\u30ce\u30a4\u30ba\u7b49\u306b\u3088\u3063\u3066\u91cf\u5b50\u306e\u72b6\u614b\u3068\u6e2c\u5b9a\u7d50\u679c\u304c\u6c7a\u5b9a\u3057\u306a\u3044\u306e\u306b\u5bfe\u3057\u3001\u7d14\u7c8b\u72b6\u614b\u3067\u306f\u91cf\u5b50\u306e\u72b6\u614b\u306f\u78ba\u5b9a\u3057\u3066\u304a\u308a\u3001\u91cf\u5b50\u306e\u4e0d\u78ba\u5b9a\u6027\u304b\u3089\u6e2c\u5b9a\u7d50\u679c\u304c\u6c7a\u5b9a\u3057\u306a\u3044\u305f\u3081\u3001\u3053\u306e\u4f8b\u3068$\\ket{\\psi}=\\frac{1}{\\sqrt{2}}\\left(\\begin{matrix}1\\\\1\\\\\\end{matrix}\\right)$\u306f\u660e\u78ba\u306b\u9055\u3046\u72b6\u614b\u3067\u3042\u308b\u3068\u3044\u3048\u307e\u3059(\u56f37)\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8890,\"width\":\"259px\",\"height\":\"auto\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"483\" height=\"127\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-3.png\" alt=\"\" class=\"wp-image-8890\" style=\"width: 259px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-3.png 483w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-3-300x79.png 300w\" sizes=\"auto, (max-width: 483px) 100vw, 483px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f37: \u6df7\u5408\u72b6\u614b\u3068\u7d14\u7c8b\u72b6\u614b$\\ket{\\psi}=\\frac{1}{\\sqrt{2}}\\left(\\begin{matrix}1\\\\1\\end{matrix}\\right)$\u306e\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u3067\u306e\u5bfe\u5fdc<\/figcaption>\n<\/figure>\n<p>\u3069\u3061\u3089\u3082 $0$ \u3068 $1$ \u304c $\\frac{1}{2}$ \u305a\u3064\u51fa\u308b\u305f\u3081\u3053\u306e\u307e\u307e\u6e2c\u5b9a\u3092\u3057\u3066\u3082\u533a\u5225\u3067\u304d\u307e\u305b\u3093\u304c\u3001$H=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1&amp;1\\\\1&amp;-1\\end{pmatrix}$\u306e\u30b2\u30fc\u30c8\u3092\u639b\u3051\u308b\u3068\u3001$\\ket{\\psi}$ \u306b\u3064\u3044\u3066\u306f $$H\\ket{\\psi}=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1&amp;1\\\\1&amp;-1\\end{pmatrix}\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1\\\\1\\end{pmatrix}=\\frac{1}{2}\\begin{pmatrix}2\\\\0\\end{pmatrix}=\\begin{pmatrix}1\\\\0\\end{pmatrix}=\\ket{0}\\tag{15}$$ \u3068\u306a\u308a\u3001\u5fc5\u305a $0$ \u304c\u51fa\u307e\u3059\u3002\u4e00\u65b9\u3001\u6df7\u5408\u72b6\u614b\u306f\u5143\u304c $\\ket{0}$ \u3067\u3042\u308c\u3070 $$H\\ket{0}=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1&amp;1\\\\1&amp;-1\\end{pmatrix}\\begin{pmatrix}1\\\\0\\end{pmatrix}=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1\\\\1\\end{pmatrix}\\tag{16}$$ \u5143\u304c $\\ket{1}$ \u3067\u3042\u308c\u3070 $$H\\ket{1}=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1&amp;1\\\\1&amp;-1\\end{pmatrix}\\begin{pmatrix}0\\\\1\\end{pmatrix}=\\frac{1}{\\sqrt{2}}\\begin{pmatrix}1\\\\-1\\end{pmatrix}\\tag{17}$$ \u3068\u306a\u308a\u3001\u3069\u3061\u3089\u306e\u5834\u5408\u3082 $0$ \u3068 $1$ \u304c $\\frac{1}{2}$ \u305a\u3064\u51fa\u308b\u305f\u3081\u3001$H$ \u3092\u639b\u3051\u305f\u5f8c\u3082 $\\frac{1}{2}$ \u305a\u3064\u306e\u307e\u307e\u3067\u3059\u3002<\/p>\n<!-- \/wp:image -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AF%86%E5%BA%A6%E6%BC%94%E7%AE%97%E5%AD%90\"><\/span>\u5bc6\u5ea6\u6f14\u7b97\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph \/-->\n\n<!-- wp:paragraph -->\n<p>\u7d14\u7c8b\u72b6\u614b\u3068\u6df7\u5408\u72b6\u614b\u3092\u7d71\u4e00\u7684\u306b\u8868\u73fe\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u308b\u5bc6\u5ea6\u6f14\u7b97\u5b50\u8868\u73fe\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho=\\sum\\nolimits_{i}{p_i|\\left. \\psi_i\\right\\rangle\\left\\langle\\psi_i\\right.|}\\tag{18}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067$p_i$\u306f$\\ket{\\psi_i}$\u306e\u72b6\u614b\u3068\u306a\u308b\u78ba\u7387\u3001$\\bra{\\psi_i}$\u306f$\\ket{\\psi_i}$\u306e\u5171\u5f79\u8ee2\u7f6e\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$\\rho$\u306f\u884c\u5217\u3068\u306a\u308a\u3001\u7d14\u7c8b\u72b6\u614b$\\ket{\\psi}=\\left(\\begin{matrix}\\alpha\\\\\\beta\\\\\\end{matrix}\\right)$\u306e\u3068\u304d\u3001<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho=\\binom{\\alpha}{\\beta}\\left(\\begin{matrix}\\alpha^\\ast&amp;\\beta^\\ast\\end{matrix}\\right)=\\left(\\begin{matrix}{|\\alpha|}^2&amp;\\alpha\\beta^\\ast\\\\\\alpha^\\ast\\beta&amp;{|\\beta|}^2\\end{matrix}\\right)\\tag{19}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u5bfe\u89d2\u6210\u5206\u304c$1$\u3068$0$\u306e\u6e2c\u5b9a\u3055\u308c\u308b\u78ba\u7387\u306b\u306a\u308b\u305f\u3081\u3001\u3053\u308c\u3092\u6df7\u5408\u72b6\u614b\u306b\u62e1\u5f35\u3057\u305f\u3068\u304d\u306b\u3001\u305d\u306e\u7d14\u7c8b\u72b6\u614b\u304c\u5f97\u3089\u308c\u308b\u78ba\u7387\u3092\u304b\u3051\u3066\u8db3\u3057\u5408\u308f\u305b\u308c\u3070\u6700\u7d42\u7684\u306a\u6e2c\u5b9a\u78ba\u7387\u306b\u4e00\u81f4\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u975e\u5bfe\u89d2\u6210\u5206\u306b\u95a2\u3057\u3066\u306f$\\alpha$\u3068$\\beta$\u306e\u4f4d\u76f8\u5dee\u306b\u95a2\u3059\u308b\u60c5\u5831\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u30b0\u30ed\u30fc\u30d0\u30eb\u4f4d\u76f8\u306e\u60c5\u5831\u306f\u5171\u5f79\u8ee2\u7f6e\u3092\u304b\u3051\u308b\u3053\u3068\u3067\u7121\u304f\u306a\u3063\u3066\u3044\u307e\u3059\u3002($e^{i\\phi}\\ket{\\psi}(e^{i\\phi}\\ket{\\psi})^*=e^{i\\phi}\\ket{\\psi}e^{-i\\phi}\\bra{\\psi}$)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30b2\u30fc\u30c8\u306e\u9069\u7528\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho\\prime=U\\rho\\operatorname{U}^\u2020\\tag{20}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067$U^\\dagger$\u3068\u306f$U$\u306e<span class=\"tooltip-word\">\u5171\u5f79\u8ee2\u7f6e\u884c\u5217<span class=\"tooltip-box\">$ \\begin{pmatrix} a &amp; b \\\\ c &amp; d \\end{pmatrix}^\\dagger = \\begin{pmatrix} a^* &amp; c^* \\\\ b^* &amp; d^* \\end{pmatrix} $<\/span><\/span>\u3067\u3059\u3002$\\ket{\\psi}$\u306b\u30b2\u30fc\u30c8$U$\u3092\u9069\u7528\u3059\u308b\u3068\u304d$U\\ket{\\psi}$\u3068\u66f8\u3051\u308b\u3053\u3068\u304b\u3089\u3001$U\\ket{\\psi}(U\\ket{\\psi})^\\dagger = U\\ket{\\psi}\\bra{\\psi}U^\\dagger$\u3068\u5c0e\u3051\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u5b9a\u7fa9\u304b\u3089\u3082\u660e\u3089\u304b\u306a\u3088\u3046\u306b\u3001\u5bc6\u5ea6\u6f14\u7b97\u5b50$\\rho$\u306f\u81ea\u8eab\u306e\u5171\u5f79\u8ee2\u7f6e\u884c\u5217\u304c\u81ea\u8eab\u306b\u4e00\u81f4\u3059\u308b\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%91%E3%82%A6%E3%83%AA%E6%BC%94%E7%AE%97%E5%AD%90\"><\/span>\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306f\u4ee5\u4e0b\u306e\u884c\u5217\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$X=\\left(\\begin{matrix}0&amp;1\\\\1&amp;0\\end{matrix}\\right), Y=\\left(\\begin{matrix}0&amp;-i\\\\i&amp;0\\end{matrix}\\right), Z=\\left(\\begin{matrix}1&amp;0\\\\0&amp;-1\\end{matrix}\\right)\\tag{21}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u3089\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306f\u81ea\u8eab\u306e\u5171\u5f79\u8ee2\u7f6e\u884c\u5217\u304c\u81ea\u8eab\u306b\u4e00\u81f4\u3059\u308b\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u3067\u3042\u308a\u3001\u307e\u305f\u81ea\u8eab\u306e\u5171\u5f79\u8ee2\u7f6e\u884c\u5217\u304c\u81ea\u8eab\u306e\u9006\u884c\u5217\u306b\u4e00\u81f4\u3059\u308b\u30e6\u30cb\u30bf\u30ea\u884c\u5217\u3067\u3082\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u81ea\u5206\u81ea\u8eab\u304c\u81ea\u5206\u306e\u9006\u884c\u5217\u3067\u3042\u308b\u305f\u3081\u3001$X^2=I, Y^2=I, Z^2=I$\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AF%86%E5%BA%A6%E6%BC%94%E7%AE%97%E5%AD%90%E7%A9%BA%E9%96%93\"><\/span>\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593\u3092\u8003\u3048\u308b\u306b\u3042\u305f\u3063\u3066\u3001\u5bc6\u5ea6\u6f14\u7b97\u5b50\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u3067\u3042\u308b\u305f\u3081\u3001\u307e\u305a$2\\times2$\u306e\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u5168\u4f53\u304c\u5f35\u308b\u7a7a\u9593\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$2\\times2$\u306e\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217$A$\u306f$A^\u2020=A$\u306a\u306e\u3067\u3001\u5b9f\u6570$r_1,r_2$\u3001\u8907\u7d20\u6570$\\alpha$\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u305b\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$A=\\left(\\begin{matrix}a&amp;b\\\\c&amp;d\\end{matrix}\\right)=\\left(\\begin{matrix}a^*&amp;c^*\\\\b^*&amp;d^*\\end{matrix}\\right)=\\left(\\begin{matrix}r_1&amp;\\alpha\\\\\\alpha^*&amp;r_2\\end{matrix}\\right)\\tag{22}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$a=a^*,d=d^*$\u3088\u308a$a,d$\u306f\u5b9f\u6570\u3001$b=c^*$\u3088\u308a$c$\u3068$b$\u306f\u305d\u308c\u305e\u308c\u306e\u8907\u7d20\u5171\u5f79\u306a\u8907\u7d20\u6570\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u8907\u7d20\u6570\u306e\u81ea\u7531\u5ea6\u306f$2$\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3001$2\\times2$\u306e\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306e\u81ea\u7531\u5ea6\u306f$4$\u3067\u3042\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u7a7a\u9593\u306b\u5bfe\u3057\u3066\u4e0a\u8a18\u306e\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50+\u5358\u4f4d\u884c\u5217$I$\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$I=\\left(\\begin{matrix}1&amp;0\\\\0&amp;1\\end{matrix}\\right), X=\\left(\\begin{matrix}0&amp;1\\\\1&amp;0\\end{matrix}\\right), Y=\\left(\\begin{matrix}0&amp;-i\\\\i&amp;0\\end{matrix}\\right), Z=\\left(\\begin{matrix}1&amp;0\\\\0&amp;-1\\end{matrix}\\right)\\tag{23}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$I$\u3068$Z$\u306e\u5b9a\u6570\u500d($r_II+r_ZZ$)\u306b\u3088\u3063\u3066\u5bfe\u89d2\u6210\u5206\u306e\u5b9f\u6570$r_1,r_2$\u3092\u3001$X$\u3068$Y$\u306e\u5b9a\u6570\u500d($r_XX+r_YY$)\u306b\u3088\u3063\u3066\u5bfe\u89d2\u6210\u5206\u4ee5\u5916\u306e\u8907\u7d20\u6570$\\alpha,\\alpha^*$\u3092\u8868\u73fe\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50+\u5358\u4f4d\u884c\u5217$I$\u306f$2\\times2$\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u7a7a\u9593\u306e\u57fa\u5e95\u306b\u306a\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$r_II+r_XX+r_YY+r_ZZ=\\left(\\begin{matrix}r_I&amp;0\\\\0&amp;r_I\\end{matrix}\\right)+\\left(\\begin{matrix}0&amp;r_X\\\\r_X&amp;0\\end{matrix}\\right)+\\left(\\begin{matrix}0&amp;-ir_Y\\\\ir_Y&amp;0\\end{matrix}\\right)+\\left(\\begin{matrix}r_Z&amp;0\\\\0&amp;-r_Z\\end{matrix}\\right)\\tag{24}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$=\\left(\\begin{matrix}r_I+r_Z&amp;r_X-ir_Y\\\\r_X+ir_Y&amp;r_I-r_Z\\end{matrix}\\right)\\tag{25}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$r_I=\\frac{r_1+r_2}{2}$,$r_Z=\\frac{r_1-r_2}{2}$\u3068\u3059\u308b\u3068<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$=\\left(\\begin{matrix}r_1&amp;r_X-ir_Y\\\\r_X+ir_Y&amp;r_2\\end{matrix}\\right)\\tag{26}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u3089\u306e\u57fa\u5e95\u304c\u76f4\u4ea4\u3057\u3066\u3044\u308b\u3053\u3068\u3082\u7c21\u5358\u306b\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u884c\u5217\u7a7a\u9593\u306e\u5185\u7a4d\u306b\u306f\u30d2\u30eb\u30d9\u30eb\u30c8\u30fb\u30b7\u30e5\u30df\u30c3\u30c8\u5185\u7a4d<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\langle A,B\\rangle=Tr(A^\\dagger B)\\tag{27}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3092\u7528\u3044\u307e\u3059\u3002$I,X,Y,Z$\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306a\u306e\u3067\u3001\u3053\u308c\u3089\u306b\u3064\u3044\u3066\u306f$A^\\dagger=A$\u3068\u306a\u308a\u3001$\\langle A,B\\rangle=Tr(AB)$\u3068\u66f8\u3051\u307e\u3059\u3002\u4ee5\u4e0b\u306b$X$\u3068$Y$\u306e\u5185\u7a4d\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\langle X,Y\\rangle=Tr(X^\\dagger Y)=Tr(XY)=Tr\\left(\\left(\\begin{matrix}0&amp;1\\\\1&amp;0\\end{matrix}\\right)\\left(\\begin{matrix}0&amp;-i\\\\i&amp;0\\end{matrix}\\right)\\right)=Tr\\left(\\left(\\begin{matrix}i&amp;0\\\\0&amp;-i\\end{matrix}\\right)\\right)=0\\tag{28}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u81ea\u8eab\u3068\u306e\u5185\u7a4d\u306f$I^2=I, X^2=I, Y^2=I, Z^2=I$\u3088\u308a$Tr(I)=2$\u3068\u306a\u308a\u3001\u5168\u57fa\u5e95\u306b\u304a\u3044\u3066$2$\u306b\u306a\u308b\u305f\u3081\u3001\u81ea\u8eab\u3068\u306e\u5185\u7a4d\u304c$1$\u306b\u306a\u308b\u3088\u3046\u306b\u5927\u304d\u3055\u3092\u305d\u308d\u3048\u3066\u4ee5\u4e0b\u306e\u5f0f\u3067\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u7a7a\u9593\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$A=\\frac{1}{2}(r_II+r_XX+r_YY+r_ZZ)\\tag{29}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u306e\u5bc6\u5ea6\u6f14\u7b97\u5b50\u8868\u73fe\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u3068\u306a\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u3059\u3068\u3001\u4e0a\u8a18\u306e\u57fa\u5e95\u3092\u7528\u3044\u3066\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593\u3092\u8868\u305b\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u5bc6\u5ea6\u6f14\u7b97\u5b50\u306e\u5b9a\u7fa9\u3092\u6539\u3081\u3066\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u3053\u3067\u306f\u7c21\u5358\u306e\u305f\u3081\u306b\u7d14\u7c8b\u72b6\u614b\u306e\u5bc6\u5ea6\u6f14\u7b97\u5b50\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho=\\binom{\\alpha}{\\beta}\\left(\\begin{matrix}\\alpha^\\ast&amp;\\beta^\\ast\\end{matrix}\\right)=\\left(\\begin{matrix}{|\\alpha|}^2&amp;\\alpha\\beta^\\ast\\\\\\alpha^\\ast\\beta&amp;{|\\beta|}^2\\end{matrix}\\right)\\tag{30}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u884c\u5217\u304c\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306b\u306a\u308b\u3053\u3068\u306f\u81ea\u660e\u3067\u3059\u3002\u307e\u305f\u3001\u5bfe\u89d2\u6210\u5206\u306e\u548c\u304c\u78ba\u7387\u306e\u7dcf\u548c\u306b\u306a\u308b\u305f\u3081\u3001\u30c8\u30ec\u30fc\u30b9\u304c$1$\u3068\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5bc6\u5ea6\u6f14\u7b97\u5b50\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u6027\u3068\u30c8\u30ec\u30fc\u30b9$1$\u3092\u6e80\u305f\u3059\u884c\u5217\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3088\u3063\u3066$r_I=1$\u3067\u56fa\u5b9a\u3057\u305f\u4ee5\u4e0b\u306e\u5f0f\u306b\u3088\u3063\u3066\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho=\\frac{1}{2}(I+r_XX+r_YY+r_ZZ)\\tag{31}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u5f0f(31)\u3092\u884c\u5217\u3067\u66f8\u304f\u3068\u3001<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho=\\frac{1}{2}\\left(\\begin{matrix}1+r_Z&amp;r_X-ir_Y\\\\r_X+ir_Y&amp;1-r_Z\\end{matrix}\\right)\\tag{32}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u884c\u5217\u306e\u56fa\u6709\u5024\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\lambda_\\pm=\\frac{1}{2}\\left(1\\pm\\sqrt{r_X^2+r_Y^2+r_Z^2}\\right)\\tag{33}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u5bc6\u5ea6\u6f14\u7b97\u5b50\u306e\u56fa\u6709\u5024\u306f\u78ba\u7387\u3068\u3057\u3066\u89e3\u91c8\u3067\u304d\u308b\u305f\u3081\u3001\u8ca0\u306e\u5024\u306b\u306a\u3063\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002\u7279\u306b\u5c0f\u3055\u3044\u65b9\u306e\u56fa\u6709\u5024<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\lambda_-=\\frac{1}{2}\\left(1-\\sqrt{r_X^2+r_Y^2+r_Z^2}\\right)\\tag{34}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u304c$0$\u4ee5\u4e0a\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$r_X^2+r_Y^2+r_Z^2\\leq1\\tag{35}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3068\u3044\u3046\u5236\u7d04\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u6e2c\u5b9a\u78ba\u7387\u304c\u8ca0\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306b\u3059\u308b\u305f\u3081\u306b\u5bc6\u5ea6\u6f14\u7b97\u5b50\u306b\u306f\u534a\u6b63\u5b9a\u5024\u6027\u3068\u3044\u3046\u5236\u7d04\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u305d\u3057\u3066\u3001\u3053\u306e\u5236\u7d04\u306f$(r_X,r_Y,r_Z)$\u304c\u534a\u5f84$1$\u306e\u7403\u9762\u3068\u305d\u306e\u5185\u5074\u306b\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4ee5\u4e0a\u3088\u308a\u3001\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u7a7a\u9593\u306e\u81ea\u7531\u5ea6\u306f$4$\u3067\u3057\u305f\u306e\u3067\u3001\u30c8\u30ec\u30fc\u30b9$1$\u3068\u3044\u3046\u5236\u7d04\u306b\u3088\u3063\u3066\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593\u306e\u81ea\u7531\u5ea6\u306f$3$\u306b\u4e0b\u304c\u308a\u3001\u534a\u6b63\u5b9a\u5024\u6027\u306b\u3088\u3063\u3066$(r_X,r_Y,r_Z)$\u304c\u534a\u5f84$1$\u306e\u7403\u9762\u3068\u305d\u306e\u5185\u5074\u306b\u5236\u9650\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u305d\u3057\u3066\u3053\u306e\u7a7a\u9593\u306f\u524d\u8ff0\u3057\u305f\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u5c11\u3057\u4f8b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$\\ket{\\psi}=\\left(\\begin{matrix}1\\\\0\\\\\\end{matrix}\\right)$\u306e\u3068\u304d\u3001\u5bc6\u5ea6\u6f14\u7b97\u5b50\u8868\u73fe\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u73fe\u3067\u304d\u3001\u56f38\u306e\u70b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho=\\binom{1}{0}\\left(\\begin{matrix}1&amp;0\\end{matrix}\\right)=\\left(\\begin{matrix}{1}&amp;0\\\\0&amp;{0}\\end{matrix}\\right)=\\frac{1}{2}\\left(\\left(\\begin{matrix}1&amp;0\\\\0&amp;1\\end{matrix}\\right)+\\left(\\begin{matrix}1&amp;0\\\\0&amp;-1\\end{matrix}\\right)\\right)=\\frac{1}{2}(I+1\\cdot Z)\\tag{36}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":8901,\"width\":\"296px\",\"height\":\"auto\",\"aspectRatio\":\"0.9949475320637389\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"982\" height=\"987\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5.png\" alt=\"\" class=\"wp-image-8901\" style=\"aspect-ratio: 0.9949475320637389; width: 296px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5.png 982w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5-298x300.png 298w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5-150x150.png 150w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/04\/image-5-768x772.png 768w\" sizes=\"auto, (max-width: 982px) 100vw, 982px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f38: $\\rho=\\frac{1}{2}(I+Z)$\u306b\u5bfe\u5fdc\u3059\u308b\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u306e\u70b9(\u56f33\u306e\u518d\u63b2)<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>$\\ket{\\psi}=\\frac{1}{\\sqrt{2}}\\binom{1}{e^{i\\pi\/4}}$($\\theta=\\frac{\\pi}{2}\u3001\\phi=\\frac{\\pi}{4}$)\u306e\u3068\u304d\u3001$e^{-i\\pi\/4}=\\frac{1-i}{\\sqrt{2}}$\u306a\u306e\u3067\u5bc6\u5ea6\u6f14\u7b97\u5b50\u8868\u73fe\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u73fe\u3067\u304d\u3001\u56f39\u306e\u70b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho=\\frac{1}{2}\\binom{1}{e^{i\\pi\/4}}\\left(\\begin{matrix}1&amp;e^{-i\\pi\/4}\\end{matrix}\\right)=\\frac{1}{2}\\left(\\begin{matrix}1&amp;\\frac{1-i}{\\sqrt{2}}\\\\\\frac{1+i}{\\sqrt{2}}&amp;1\\end{matrix}\\right)=\\frac{1}{2}\\left(\\left(\\begin{matrix}1&amp;0\\\\0&amp;1\\end{matrix}\\right)+\\frac{1}{\\sqrt{2}}\\left(\\begin{matrix}0&amp;1\\\\1&amp;0\\end{matrix}\\right)+\\frac{1}{\\sqrt{2}}\\left(\\begin{matrix}0&amp;-i\\\\i&amp;0\\end{matrix}\\right)\\right)=\\frac{1}{2}(I+\\frac{1}{\\sqrt{2}}X+\\frac{1}{\\sqrt{2}}Y)\\tag{37}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9162,\"width\":\"290px\",\"height\":\"auto\",\"aspectRatio\":\"1.0148757834327569\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1009\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/35957d0c8009435a6e91cf68f206c762-1024x1009.png\" alt=\"\" class=\"wp-image-9162\" style=\"aspect-ratio: 1.0148757834327569; width: 290px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/35957d0c8009435a6e91cf68f206c762-1024x1009.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/35957d0c8009435a6e91cf68f206c762-300x296.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/35957d0c8009435a6e91cf68f206c762-768x757.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/35957d0c8009435a6e91cf68f206c762-1536x1514.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/35957d0c8009435a6e91cf68f206c762.png 1542w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f39: $\\rho=\\frac{1}{2}\\left(I+\\frac{1}{\\sqrt{2}}X+\\frac{1}{\\sqrt{2}}Y\\right)$\u306b\u5bfe\u5fdc\u3059\u308b\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u306e\u70b9<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u56f38\u3001\u56f39\u306e\u3088\u3046\u306b\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u306e\u5ea7\u6a19\u3068\u4e00\u81f4\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001$N$\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306b\u304a\u3044\u3066\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593\u306e\u57fa\u5e95\u306f$\\{I,X,Y,Z\\}^{\\bigotimes N}$(\u30c6\u30f3\u30bd\u30eb\u7a4d\u4e57)\u3067\u8868\u305b\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$N=2$\u306e\u3068\u304d\u306e\u4f8b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$<br \/>\\rho<br \/>=<br \/>\\frac{1}{2^2}<br \/>\\Bigl(<br \/>I\\otimes I<br \/>+ r_{XI}\\, X\\otimes I<br \/>+ r_{YI}\\, Y\\otimes I<br \/>+ r_{ZI}\\, Z\\otimes I<br \/>+ r_{IX}\\, I\\otimes X<br \/>+ r_{IY}\\, I\\otimes Y<br \/>+ r_{IZ}\\, I\\otimes Z<br \/>+ r_{XX}\\, X\\otimes X<br \/>+ r_{XY}\\, X\\otimes Y<br \/>+ r_{XZ}\\, X\\otimes Z<br \/>+ r_{YX}\\, Y\\otimes X<br \/>+ r_{YY}\\, Y\\otimes Y<br \/>+ r_{YZ}\\, Y\\otimes Z<br \/>+ r_{ZX}\\, Z\\otimes X<br \/>+ r_{ZY}\\, Z\\otimes Y<br \/>+ r_{ZZ}\\, Z\\otimes Z<br \/>\\Bigr)\\tag{38}<br \/>$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3068\u304d\u3001\u81ea\u7531\u5ea6\u306f$4^N-1$\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u72b6\u614b\u30d9\u30af\u30c8\u30eb\u8868\u8a18\u306e\u3068\u304d\u306e$\\ket{\\psi}=C_{00}\\ket{00}+C_{01}\\ket{01}+C_{10}\\ket{10}+C_{11}\\ket{11}$\u306e\u81ea\u7531\u5ea6$2^N\u00d72(\u8907\u7d20\u6570)-1(\u78ba\u7387\u304c1)-1(\u30b0\u30ed\u30fc\u30d0\u30eb\u4f4d\u76f8)$\u3088\u308a\u3082\u30aa\u30fc\u30c0\u30fc\u304c\u304b\u306a\u308a\u5927\u304d\u304f\u306a\u3063\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u5bc6\u5ea6\u6f14\u7b97\u5b50\u8868\u73fe\u306b\u3088\u3063\u3066\u6df7\u5408\u72b6\u614b\u3082\u8868\u73fe\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6df7\u5408\u72b6\u614b\u306f\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u306e\u5185\u90e8\u3092\u542b\u3080\u7403\u5168\u4f53\u306e\u70b9\u3092\u53d6\u308c\u307e\u3059\u304c\u3001\u7d14\u7c8b\u72b6\u614b\u306f\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u306e\u7403\u9762\u4e0a\u306e\u70b9\u3057\u304b\u53d6\u308c\u306a\u3044\u305f\u3081\u3001\u6df7\u5408\u72b6\u614b\u3082\u8868\u73fe\u3067\u304d\u308b\u5bc6\u5ea6\u6f14\u7b97\u5b50\u8868\u73fe\u306e\u65b9\u304c\u81ea\u7531\u5ea6\u304c\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%91%E3%83%A9%E3%83%A1%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF%E3%82%B2%E3%83%BC%E3%83%88\"><\/span>\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8\u306f\u3001\u30b2\u30fc\u30c8\u306e\u884c\u5217\u304c\u9023\u7d9a\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u4f9d\u5b58\u3059\u308b\u91cf\u5b50\u30b2\u30fc\u30c8\u306e\u3053\u3068\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30b2\u30fc\u30c8\u3068\u306a\u308b\u6761\u4ef6\u306f\u30e6\u30cb\u30bf\u30ea\u6027\u3067\u3042\u308b\u305f\u3081\u3001\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8\u306f\u4efb\u610f\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u5024\u306b\u304a\u3044\u3066\u30e6\u30cb\u30bf\u30ea\u6027\u3092\u4fdd\u8a3c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u3092\u6e80\u305f\u3059\u30e6\u30cb\u30bf\u30ea\u884c\u5217\u306f$A$\u3092\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u3001$\\theta$\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u305b\u307e\u3059\u3002<\/p>\n<p>$$U(\\theta)=e^{-iA(\\theta)}\\tag{39}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u672c\u8ad6\u6587\u3067\u306f$A(\\theta)=\\theta H$\u3068\u306a\u308b$\\theta$\u306b\u4f9d\u5b58\u3057\u306a\u3044\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217$H$\u3092\u7528\u3044\u305f\u4ee5\u4e0b\u306e\u5f62\u3092\u6271\u3044\u307e\u3059\u3002(\u5c0e\u51fa\u306fAppendix\u306b\u8a18\u8f09\u3057\u307e\u3057\u305f)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$U(\\theta)=e^{-i\\theta H}\\tag{40}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306a$H$\u3092\u751f\u6210\u5b50\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$e$\u306e\u6307\u6570\u306b\u884c\u5217\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u306e\u3088\u3046\u306a\u6570\u306e\u884c\u5217\u4e57\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b\u3055\u308c\u305f\u5f62\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$e^{-i\\theta H}=\\sum_{n=0}^{\\infty}{\\frac{1}{n!}{(-i\\theta H)}^n}\\tag{41}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066$R_Y\\left(\\theta\\right)=e^{-i\\frac{\\theta}{2}Y}$\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b\u3067\u8868\u3057\u305f\u5f62\u3092\u5947\u6570\u4e57\u3001\u5076\u6570\u4e57\u3067\u5206\u3051\u308b\u3068\u3001$Y^2=I$\u306a\u306e\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$${R_Y(\\theta)=e}^{-\\frac{i\\theta}{2}Y}=\\sum_{n=0}^{\\infty}{\\frac{1}{n!}{(-\\frac{i\\theta}{2}Y)}^n}\\ =\\left(\\sum_{k=0}^{\\infty}{\\frac{{(-1)}^k}{(2k)!}{(\\frac{\\theta}{2})}^{2k}}\\right)I-i\\left(\\sum_{k=0}^{\\infty}{\\frac{\\left(-1\\right)^k}{\\left(2k+1\\right)!}\\left(\\frac{\\theta}{2}\\right)^{2k+1}}\\right)Y\\tag{42}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001$\\sin(\\frac{\\theta}{2})=\\sum_{k=0}^{\\infty}{\\frac{{(-1)}^k}{(2k+1)!}{(\\frac{\\theta}{2})}^{2k+1}}$\u3001$\\cos(\\frac{\\theta}{2})=\\sum_{k=0}^{\\infty}{\\frac{{(-1)}^k}{(2k)!}{(\\frac{\\theta}{2})}^{2k}}$\u306a\u306e\u3067<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$=\\cos{\\left(\\frac{\\theta}{2}\\right)}I-i\\sin\\left(\\frac{\\theta}{2}\\right)Y=\\cos{\\left(\\frac{\\theta}{2}\\right)}\\left(\\begin{matrix}1&amp;0\\\\0&amp;1\\end{matrix}\\right)-i\\sin\\left(\\frac{\\theta}{2}\\right)\\left(\\begin{matrix}0&amp;-i\\\\i&amp;0\\end{matrix}\\right)=\\left(\\begin{matrix}\\cos{\\left(\\frac{\\theta}{2}\\right)}&amp;-\\sin\\left(\\frac{\\theta}{2}\\right)\\\\\\sin\\left(\\frac{\\theta}{2}\\right)&amp;\\cos{\\left(\\frac{\\theta}{2}\\right)}\\end{matrix}\\right)\\tag{43}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u5f97\u3089\u308c\u305f\u884c\u5217\u306f$2$\u6b21\u5143\u56de\u8ee2\u884c\u5217\u306e\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u5b9f\u306f\u3053\u308c\u306f\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u3067$Y$\u8ef8\u307e\u308f\u308a\u89d2\u5ea6$\\theta$\u306e\u56de\u8ee2\u3068\u3057\u3066\u89e3\u91c8\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3088\u308a\u4e00\u822c\u306b\u3001\u751f\u6210\u5b50\u3068\u3057\u3066$\\frac{r_XX+r_YY+r_ZZ}{2}$\u3092\u9078\u3093\u3060\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8\u306f\u3001\u30d9\u30af\u30c8\u30eb$(r_X,r_Y,r_Z)$\u306e\u5927\u304d\u3055\u304c$1$\u306e\u3068\u304d\u3001\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u306e$(r_X,r_Y,r_Z)$\u3092\u8ef8\u3068\u3057\u305f\u89d2\u5ea6$\\theta$\u306e\u56de\u8ee2\u30b2\u30fc\u30c8\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%AA%E3%83%96%E3%82%B6%E3%83%BC%E3%83%90%E3%83%96%E3%83%AB\"><\/span>\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u3068\u306f\u91cf\u5b50\u7cfb\u304b\u3089\u89b3\u6e2c\u3067\u304d\u308b\u60c5\u5831\u306e\u3053\u3068\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u76f4\u63a5\u89b3\u6e2c\u3067\u304d\u308b\u306e\u306f$|0\\rangle$\u3068$|1\\rangle$\u306e\u78ba\u7387\u306e\u307f\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u306e$Z$\u3092\u6e2c\u5b9a\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3064\u307e\u308a\u3001$Z$\u6e2c\u5b9a\u306b\u5e30\u7740\u3067\u304d\u308b\u3082\u306e\u5168\u3066\u304c\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u3067\u3042\u308b\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066$X$\u6e2c\u5b9a\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u56f310\u306e\u3088\u3046\u306b$Y$\u8ef8\u56de\u8ee2\u30b2\u30fc\u30c8$R_Y(\\theta)$\u3092$\\theta = -\\frac{\\pi}{2}$\u3067\u9069\u7528\u3059\u308b\u3068$X$\u8ef8\u65b9\u5411\u3092$Z$\u8ef8\u65b9\u5411\u306b\u56de\u8ee2\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u305d\u306e\u5f8c$Z$\u6e2c\u5b9a\u3092\u884c\u3046\u3053\u3068\u3067\u30b2\u30fc\u30c8\u9069\u7528\u524d\u306e$X$\u3092\u6e2c\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9039,\"width\":\"459px\",\"height\":\"auto\",\"aspectRatio\":\"0.9908398916268869\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"864\" height=\"872\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/185bbedac94d9fd4779ad91f4cfe2749.png\" alt=\"\" class=\"wp-image-9039\" style=\"aspect-ratio: 0.9908398916268869; width: 459px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/185bbedac94d9fd4779ad91f4cfe2749.png 864w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/185bbedac94d9fd4779ad91f4cfe2749-297x300.png 297w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/185bbedac94d9fd4779ad91f4cfe2749-150x150.png 150w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/185bbedac94d9fd4779ad91f4cfe2749-768x775.png 768w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f310: $R_Y\\left(-\\frac{\\pi}{2}\\right)$\u306b\u3088\u308b$X$\u6e2c\u5b9a\u306e$Z$\u6e2c\u5b9a\u3078\u306e\u5e30\u7740<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u4efb\u610f\u306e\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306f\u30e6\u30cb\u30bf\u30ea\u5909\u63db\u3067\u5bfe\u89d2\u5316\u3067\u304d\u308b\u305f\u3081\u3001\u540c\u69d8\u306b\u57fa\u5e95\u5909\u63db\u30b2\u30fc\u30c8\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067$Z$\u6e2c\u5b9a\u306b\u5e30\u7740\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3064\u307e\u308a\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u3068\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u3067\u3042\u308a\u3001${I,X,Y,Z}$\u3067\u8868\u305b\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002(\u591a\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u3067\u306f$\\{I,X,Y,Z\\}^{\\bigotimes N}$)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9C%9F%E5%BE%85%E5%80%A4\"><\/span>\u671f\u5f85\u5024<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u3042\u308b\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb$B$\u306b\u95a2\u3057\u3066\u72b6\u614b$\\rho$\u3092\u6e2c\u5b9a\u3092\u3057\u305f\u3068\u304d\u306e\u671f\u5f85\u5024$\\left\\langle B\\right\\rangle$\u306f\u3001$\\rho$\u3068$B$\u306e\u5185\u7a4d\u3067\u8a18\u8ff0\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\left\\langle B\\right\\rangle_\\rho=Tr(B\\rho)\\tag{44}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066$XZ$\u5e73\u9762\u4e0a\u306e\u7d14\u7c8b\u72b6\u614b$\\rho=\\frac{1}{2}(I+\\sin(\\theta)X+\\cos(\\theta)Z)$\u306b\u5bfe\u3057\u3066$Z$\u6e2c\u5b9a\u3092\u884c\u3046\u3068\u304d\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$\\left\\langle Z\\right\\rangle_\\rho=Tr(Z\\rho)=Tr(\\frac{1}{2}(ZI+\\sin(\\theta)ZX+\\cos(\\theta)ZZ))=\\frac{1}{2}(Tr(ZI)+\\sin(\\theta)Tr(ZX)+\\cos(\\theta)Tr(ZZ))$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$Z$\u306b\u5bfe\u3057\u3066$I,X$\u306f\u76f4\u4ea4\u3059\u308b\u305f\u3081\u5185\u7a4d\u306f$0$\u3001\u81ea\u8eab\u3068\u306e\u5185\u7a4d\u306f$1$\u306a\u306e\u3067<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\left\\langle Z\\right\\rangle_\\rho=\\cos(\\theta)\\tag{45}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9041,\"width\":\"490px\",\"height\":\"auto\",\"aspectRatio\":\"0.9921931233043575\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1016\" height=\"1024\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/008bc99633c52b3e6b1271ca39b5d2d5-1016x1024.png\" alt=\"\" class=\"wp-image-9041\" style=\"aspect-ratio: 0.9921931233043575; width: 490px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/008bc99633c52b3e6b1271ca39b5d2d5-1016x1024.png 1016w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/008bc99633c52b3e6b1271ca39b5d2d5-298x300.png 298w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/008bc99633c52b3e6b1271ca39b5d2d5-150x150.png 150w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/008bc99633c52b3e6b1271ca39b5d2d5-768x774.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/05\/008bc99633c52b3e6b1271ca39b5d2d5.png 1070w\" sizes=\"auto, (max-width: 1016px) 100vw, 1016px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f311: \u671f\u5f85\u5024\u3068\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u306b\u5bfe\u3059\u308b\u72b6\u614b$\\rho$\u306e\u5c04\u5f71\u306e\u5bfe\u5fdc<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u56f311\u306e\u3088\u3046\u306b\u3001\u30d9\u30af\u30c8\u30eb$(r_X,r_Y,r_Z)$\u306e\u5927\u304d\u3055\u304c$1$\u306e\u3068\u304d\u3001\u305d\u306e\u72b6\u614b\u306e\u671f\u5f85\u5024\u3092\u5f97\u308b\u64cd\u4f5c\u306f\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u306b\u5bfe\u3059\u308b\u72b6\u614b$\\rho$\u306e\u5c04\u5f71\u3092\u3068\u308b\u64cd\u4f5c\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%91%E3%83%A9%E3%83%A1%E3%83%BC%E3%82%BF%E3%82%B7%E3%83%95%E3%83%88%E3%83%AB%E3%83%BC%E3%83%AB\"><\/span>\u30d1\u30e9\u30e1\u30fc\u30bf\u30b7\u30d5\u30c8\u30eb\u30fc\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u30d1\u30e9\u30e1\u30fc\u30bf\u30b7\u30d5\u30c8\u30eb\u30fc\u30eb\u3068\u306f\u3001\u91cf\u5b50\u6a5f\u68b0\u5b66\u7fd2\u306b\u304a\u3044\u3066\u3001\u4e09\u89d2\u95a2\u6570\u306e\u7279\u6027\u3092\u5229\u7528\u3057\u3066\u52fe\u914d\u3092\u5f97\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u751f\u6210\u5b50$P$\u304c\u30d1\u30a6\u30ea\u578b(\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u5b9a\u6570\u500d\u307e\u305f\u306f\u30c6\u30f3\u30bd\u30eb\u7a4d)\u306e\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8$U(\\theta)$\u306e$\\theta$\u5fae\u5206\u306b\u4f7f\u3048\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{\\partial\\left\\langle B\\right\\rangle_\\rho\\left(\\theta\\right)}{\\partial\\theta}=\\frac{1}{2}\\left\\{\\left\\langle B\\right\\rangle_\\rho\\left(\\theta+\\frac{\\pi}{2}\\right)-\\left\\langle B\\right\\rangle_\\rho\\left(\\theta-\\frac{\\pi}{2}\\right)\\right\\}\\tag{46}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067\u3001$B$\u306f\u9078\u629e\u3057\u305f\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u3001$\\left\\langle B\\right\\rangle_\\rho$\u306f$\\rho$\u306b\u304a\u3051\u308b$B$\u306e\u671f\u5f85\u5024\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\left\\langle B\\right\\rangle_\\rho(\\theta)=Tr(B\\rho(\\theta))\\tag{47}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$\\rho(\\theta)$\u306f\u5165\u529b\u72b6\u614b$\\rho_{in}$\u306b\u30d1\u30e9\u30e1\u30fc\u30bf$\\theta$\u3092\u6301\u3064\u30b2\u30fc\u30c8$U(\\theta)$\u3092\u4f5c\u7528\u3055\u305b\u3066\u5f97\u3089\u308c\u305f\u72b6\u614b\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho\\left(\\theta\\right)=U(\\theta)\\rho_{in}U^\\dagger(\\theta)\\tag{48}$$<\/p>\n<p>\u305d\u3082\u305d\u3082\u306a\u305c\u3053\u306e\u3088\u3046\u306a\u624b\u7d9a\u304d\u304c\u5fc5\u8981\u306a\u306e\u304b\u3092\u78ba\u8a8d\u3057\u3066\u304a\u304d\u307e\u3059\u3002\u6c42\u3081\u305f\u3044\u91cf\u306f<\/p>\n<p>$$\\frac{\\partial\\left\\langle B\\right\\rangle_\\rho\\left(\\theta\\right)}{\\partial\\theta}=Tr\\left(B\\frac{\\partial\\rho\\left(\\theta\\right)}{\\partial\\theta}\\right)\\tag{49}$$<\/p>\n<p>\u3067\u3059\u304c\u3001$\\partial\\rho(\\theta)\/\\partial\\theta$ \u306f\u91cf\u5b50\u72b6\u614b\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5bc6\u5ea6\u6f14\u7b97\u5b50\u7a7a\u9593\u306f $Tr(\\rho)=1$\u3001\u3059\u306a\u308f\u3061\u30d1\u30a6\u30ea\u57fa\u5e95\u3067\u66f8\u3044\u305f\u3068\u304d\u306e $I$ \u306e\u4fc2\u6570\u304c $1$ \u306b\u56fa\u5b9a\u3055\u308c\u305f\u7a7a\u9593\u3067\u3057\u305f\u304c\u3001\u3053\u306e\u4fc2\u6570\u306f $\\theta$ \u306b\u3088\u3089\u306a\u3044\u5b9a\u6570\u306a\u306e\u3067\u3001\u5fae\u5206\u3059\u308b\u3068\u6d88\u3048\u3066\u3057\u307e\u3046\u305f\u3081\u3067\u3059\u3002\u5b9f\u969b\u3001$\\rho(\\theta)=\\frac{1}{2^N}\\left(I+\\sum_{P\\neq I}r_P(\\theta)P\\right)$ \u3068\u66f8\u3051\u3070<\/p>\n<p>$$\\frac{\\partial\\rho\\left(\\theta\\right)}{\\partial\\theta}=\\frac{1}{2^N}\\sum_{P\\neq I}\\frac{\\partial r_P\\left(\\theta\\right)}{\\partial\\theta}P\\tag{50}$$<\/p>\n<p>\u3068\u306a\u308a\u3001$I$ \u6210\u5206\u3092\u6301\u3061\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u30d6\u30ed\u30c3\u30db\u7403\u4e0a\u3092\u52d5\u304f\u70b9\u306b\u5bfe\u3059\u308b\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u3067\u3042\u3063\u3066\u3001\u70b9\u305d\u306e\u3082\u306e\u3067\u306f\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306b\u3067\u304d\u308b\u306e\u306f\u72b6\u614b\u3092\u7528\u610f\u3057\u3066\u305d\u306e\u4e0a\u3067\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u306e\u671f\u5f85\u5024\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u3060\u3051\u306a\u306e\u3067\u3001\u72b6\u614b\u3067\u306a\u3044\u3082\u306e\u306b\u5bfe\u3059\u308b\u671f\u5f85\u5024\u3092\u76f4\u63a5\u6e2c\u308b\u56de\u8def\u306f\u4f5c\u308c\u307e\u305b\u3093\u3002\u30d1\u30e9\u30e1\u30fc\u30bf\u30b7\u30d5\u30c8\u30eb\u30fc\u30eb\u306f\u3001\u3053\u306e\u5fae\u5206\u3092\u5b9f\u969b\u306b\u7528\u610f\u3067\u304d\u308b $2$ \u3064\u306e\u72b6\u614b $\\rho\\left(\\theta\\pm\\frac{\\pi}{2}\\right)$ \u4e0a\u306e\u671f\u5f85\u5024\u306e\u5dee\u3068\u3057\u3066\u66f8\u304d\u76f4\u3059\u624b\u7d9a\u304d\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u624b\u6cd5\u3067\u5f97\u3089\u308c\u305f\u52fe\u914d\u306f\u3001\u5fae\u5206\u306e\u6975\u9650\u64cd\u4f5c\u3092\u8fd1\u4f3c\u3067\u8a08\u7b97\u3059\u308b\u6570\u5024\u5dee\u5206\u3068\u306f\u7570\u306a\u308a\u3001\u89e3\u6790\u7684\u306b\u6b63\u3057\u3044\u5024\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u751f\u6210\u5b50$P$\u304c\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u305d\u306e\u3082\u306e\u306e\u5834\u5408\u3092\u8003\u3048\u3066\u4e0a\u8a18\u306e\u5f0f\u304c\u6b63\u3057\u3044\u304b\u3092\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u30b2\u30fc\u30c8$U(\\theta)$\u306f\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u6027\u8cea$P^2=I$\u304b\u3089\u3001\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b\u3067\u8868\u3057\u305f\u5f62\u3092\u5947\u6570\u4e57\u3001\u5076\u6570\u4e57\u3067\u5206\u3051\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$U\\left(\\theta\\right)=e^{-\\frac{i\\theta}{2}P}=\\sum_{n=0}^{\\infty}{\\frac{1}{n!}{(-\\frac{i\\theta}{2}P)}^n}=\\left(\\sum_{k=0}^{\\infty}{\\frac{{(-1)}^k}{(2k)!}{(\\frac{\\theta}{2})}^{2k}}\\right)I-i\\left(\\sum_{k=0}^{\\infty}{\\frac{\\left(-1\\right)^k}{\\left(2k+1\\right)!}\\left(\\frac{\\theta}{2}\\right)^{2k+1}}\\right)P\\tag{51}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$\\sin(\\frac{\\theta}{2})=\\sum_{k=0}^{\\infty}{\\frac{{(-1)}^k}{(2k+1)!}{(\\frac{\\theta}{2})}^{2k+1}}$\u3001$\\cos(\\frac{\\theta}{2})=\\sum_{k=0}^{\\infty}{\\frac{{(-1)}^k}{(2k)!}{(\\frac{\\theta}{2})}^{2k}}$\u306a\u306e\u3067<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$=\\cos{\\left(\\frac{\\theta}{2}\\right)}I-i\\sin\\left(\\frac{\\theta}{2}\\right)P\\tag{52}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6b21\u306b\u5165\u529b\u72b6\u614b$\\rho_{in}$\u306b$U(\\theta)$\u3092\u4f5c\u7528\u3055\u305b\u305f\u72b6\u614b$\\rho$\u3092\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3059\u3002(\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50$P$\u3068$I$\u306f\u5171\u5f79\u8ee2\u7f6e\u304c\u81ea\u8eab\u306b\u4e00\u81f4\u3059\u308b\u305f\u3081\u3001\u4fc2\u6570\u306b$i$\u304c\u3042\u308b$\\sin$\u306e\u9805\u3060\u3051\u7b26\u53f7\u304c\u53cd\u8ee2)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho\\left(\\theta\\right)=U\\left(\\theta\\right)\\rho_{in}U^\\dagger\\left(\\theta\\right)=\\left(\\cos{\\left(\\frac{\\theta}{2}\\right)}I-i\\sin\\left(\\frac{\\theta}{2}\\right)P\\right)\\rho_{in}\\left(\\cos{\\left(\\frac{\\theta}{2}\\right)}I+i\\sin\\left(\\frac{\\theta}{2}\\right)P\\right)\\tag{53}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ =\\rho_{in}\\cos^2{\\left(\\frac{\\theta}{2}\\right)}+P\\rho_{in}P\\sin^2{\\left(\\frac{\\theta}{2}\\right)}+\\left(\\rho_{in}P-P\\rho_{in}\\right)i\\sin\\left(\\frac{\\theta}{2}\\right)\\cos\\left(\\frac{\\theta}{2}\\right)\\tag{54}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u5404\u9805\u3092\u4e09\u89d2\u95a2\u6570\u306e\u500d\u89d2\u306e\u516c\u5f0f\u3067\u5909\u5f62\u3057\u3066\u6574\u7406\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ =\\rho_{in}\\frac{1+\\cos(\\theta)}{2}+P\\rho_{in}P\\frac{1-\\cos(\\theta)}{2}+\\left(\\rho_{in}P-P\\rho_{in}\\right)i\\frac{\\sin\\left(\\theta\\right)}{2}\\tag{55}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\ =\\left(\\frac{\\rho_{in}+P\\rho_{in}P}{2}\\right)+\\left(\\frac{\\rho_{in}-P\\rho_{in}P}{2}\\right)\\cos{\\left(\\theta\\right)}+\\left(\\frac{\\rho_{in}P-P\\rho_{in}}{2}i\\right)\\sin(\\theta)\\tag{56}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e$\\rho$\u306b\u304a\u3051\u308b$B$\u306e\u671f\u5f85\u5024\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u3001\u30c8\u30ec\u30fc\u30b9\u3092\u3068\u3063\u3066\u3044\u308b\u5404\u4fc2\u6570\u306b\u306f\u30d1\u30e9\u30e1\u30fc\u30bf$\\theta$\u304c\u542b\u307e\u308c\u305a\u3001\u5468\u671f\u306e\u63c3\u3063\u305f\u4e09\u89d2\u95a2\u6570\u306e\u7dda\u578b\u7d50\u5408\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\left\\langle B\\right\\rangle_\\rho\\left(\\theta\\right)=Tr\\left(B\\rho\\left(\\theta\\right)\\right)=Tr\\left(B\\left(\\frac{\\rho_{in}+P\\rho_{in}P}{2}\\right)\\right)\\tag{57}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$+Tr\\left(B\\left(\\frac{\\rho_{in}-P\\rho_{in}P}{2}\\right)\\right)\\cos{\\left(\\theta\\right)}+Tr\\left(B\\left(\\frac{\\rho_{in}P-P\\rho_{in}}{2}i\\right)\\right)\\sin(\\theta)\\tag{58}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u5468\u671f\u304c\u63c3\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30d1\u30e9\u30e1\u30fc\u30bf$\\theta$\u3092$\\frac{\\pi}{2}$\u305a\u3089\u305b\u3070$\\sin$\u3001$\\cos$\u306e\u9805\u306f\u5fae\u7a4d\u5206\u304c\u8868\u73fe\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\cos{\\left(\\theta\\pm\\frac{\\pi}{2}\\right)}=\\mp\\sin{\\left(\\theta\\right)},\\hspace{5pt}\\sin{\\left(\\theta\\pm\\frac{\\pi}{2}\\right)}=\\pm\\cos\\left(\\theta\\right)\\tag{59}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3088\u3063\u3066\u5f0f(60)\u306e\u3088\u3046\u306b$\\theta+\\frac{\\pi}{2}$\u3057\u305f\u3082\u306e\u304b\u3089$\\theta-\\frac{\\pi}{2}$\u3057\u305f\u3082\u306e\u3092\u5f15\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u5b9a\u6570\u9805\u306e\u307f\u304c\u6253\u3061\u6d88\u3055\u308c\u3001$\\sin$\u3001$\\cos$\u306e\u9805\u306f\u5fae\u5206\u3055\u308c\u305f\u72b6\u614b\u3067$2$\u500d\u306b\u306a\u3063\u3066\u6b8b\u308b\u305f\u3081\u3001$\\frac{1}{2}$\u3092\u304b\u3051\u308b\u3053\u3068\u3067$\\left\\langle B\\right\\rangle_\\rho(\\theta)$\u306b\u304a\u3051\u308b$\\theta$\u5fae\u5206\u304c\u8868\u73fe\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{\\partial\\left\\langle B\\right\\rangle_\\rho\\left(\\theta\\right)}{\\partial\\theta}=\\frac{1}{2}\\left\\{\\left\\langle B\\right\\rangle_\\rho\\left(\\theta+\\frac{\\pi}{2}\\right)-\\left\\langle B\\right\\rangle_\\rho\\left(\\theta-\\frac{\\pi}{2}\\right)\\right\\}\\tag{60}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%8F%90%E6%A1%88%E6%89%8B%E6%B3%95\"><\/span>\u63d0\u6848\u624b\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u672c\u8ad6\u6587\u3067\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6301\u3063\u305f\u91cf\u5b50\u56de\u8def\u5168\u4f53\u3092\u5b66\u7fd2\u30e2\u30c7\u30eb\u3068\u3057\u3066\u6271\u3044\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u53cd\u5fa9\u7684\u306a\u66f4\u65b0\u306b\u3088\u308a\u4e0e\u3048\u3089\u308c\u305f\u30bf\u30b9\u30af\u3092\u5b66\u7fd2\u3059\u308b\u67a0\u7d44\u307f\u3092\u63d0\u6848\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6700\u9069\u5316\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:list {\"ordered\":true} -->\n<ol class=\"wp-block-list\"><!-- wp:list-item -->\n<li>\u5165\u529b\u30c7\u30fc\u30bf$\\bm{x_i}$(\u53e4\u5178\u30c7\u30fc\u30bf)\u3092\u5165\u529b\u30b2\u30fc\u30c8$U_{in}(\\bm{x_i})$\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3001\u521d\u671f\u72b6\u614b\u306b\u4f5c\u7528\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u308a\u91cf\u5b50\u72b6\u614b$\\ket{\\psi_{in}(\\bm{x_i})}$\u306b$\\bm{x_i}$\u306e\u60c5\u5831\u3092\u843d\u3068\u3057\u8fbc\u3080<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>\u72b6\u614b$\\ket{\\psi_{in}(\\bm{x_i})}$\u306b\u30d1\u30e9\u30e1\u30fc\u30bf$\\bm{\\theta}$\u306b\u4f9d\u5b58\u3057\u305f\u30b2\u30fc\u30c8$U(\\bm{\\theta})$\u3092\u4f5c\u7528\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u308a\u51fa\u529b\u72b6\u614b$\\ket{\\psi_{out}(\\bm{x_i},\\bm{\\theta})}$\u3092\u5f97\u308b<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>\u51fa\u529b\u72b6\u614b$\\ket{\\psi_{out}(\\bm{x_i},\\bm{\\theta})}$\u304b\u3089\u671f\u5f85\u5024$\\left\\langle B\\right\\rangle(\\bm{x_i},\\bm{\\theta})$\u3092\u6e2c\u5b9a\u3057\u3001\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u5b9a\u7fa9\u57df\u3084\u5024\u57df\u306e\u8abf\u6574\u3001\u78ba\u7387\u554f\u984c\u306a\u3089\u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u3084\u30b7\u30b0\u30e2\u30a4\u30c9\u3092\u901a\u3057\u3066\u6700\u7d42\u7684\u306a\u30e2\u30c7\u30eb\u306e\u51fa\u529b$y(\\bm{x_i},\\bm{\\theta})=F(\u27e8B\u27e9(\\bm{x_i},\\bm{\\theta}))$\u3092\u5f97\u308b<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>\u6b63\u89e3\u30c7\u30fc\u30bf$f(\\bm{x_i})$\u3068\u30e2\u30c7\u30eb\u306e\u51fa\u529b$y(\\bm{x_i},\\bm{\\theta})$\u304b\u3089\u5b9a\u7fa9\u3055\u308c\u308b\u30b3\u30b9\u30c8\u95a2\u6570$L(\\theta)$\u3092\u6700\u5c0f\u5316\u3059\u308b$\\theta=\\theta^{\\prime}$\u3092\u6c42\u3081\u3066\u66f4\u65b0<\/li>\n<!-- \/wp:list-item --><\/ol>\n<!-- \/wp:list -->\n\n<!-- wp:image {\"id\":9104,\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"362\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1024x362.png\" alt=\"\" class=\"wp-image-9104\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1024x362.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-300x106.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-768x271.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1536x543.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image.png 1828w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f312: \u91cf\u5b50\u56de\u8def\u5b66\u7fd2\u306e\u5168\u4f53\u306e\u6d41\u308c<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u5168\u4f53\u306e\u6d41\u308c\u306f\u56f312\u306e\u3068\u304a\u308a\u3067\u3059\u3002\u4ee5\u4e0b\u3067\u5404\u624b\u9806\u3092\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%AC%A6%E5%8F%B7%E5%8C%96\"><\/span>\u7b26\u53f7\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u3001\u5165\u529b\u53e4\u5178\u30c7\u30fc\u30bf\u3092\u91cf\u5b50\u30c7\u30fc\u30bf\u306b\u5909\u63db\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u521d\u671f\u5316\u3055\u308c\u305f\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u5165\u529b\u30c7\u30fc\u30bf$x_i$\u306e\u60c5\u5831\u3092\u6301\u3064\u3088\u3046\u306b\u91cf\u5b50\u56de\u8def$U_{in}(\\theta_{in})$\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6c7a\u3081\u3001\u521d\u671f\u72b6\u614b(\u56fa\u5b9a)\u3092\u305d\u306e\u91cf\u5b50\u56de\u8def\u306b\u901a\u3059\u3053\u3068\u3067\u5165\u529b\u72b6\u614b$\\ket{\\psi_{in}}(x_i)$\u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066${U_{in}=R}_y\\left({\\sin}^{-1}x_i\\right)$\u3067\u5b9a\u7fa9\u3055\u308c\u308b$Y$\u8ef8\u56de\u8ee2\u30b2\u30fc\u30c8\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002(\u3053\u3053\u3067\u306f$\\theta_{in}={\\sin}^{-1}x_i$)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u521d\u671f\u72b6\u614b$\\ket{0}$\u306b\u5bfe\u3057\u3066\u4f5c\u7528\u3055\u305b\u308b\u3068\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u3067\u306f\u56f313\u306e\u3088\u3046\u306b$Y$\u8ef8\u3092\u8ef8\u3068\u3057\u3066\u89d2\u5ea6$\\sin^{-1}x_i$\u56de\u8ee2\u3057\u3001$(r_X,r_Y,r_Z)=(x_i,0,\\sqrt{1-x_i^2})$\u306b\u4f4d\u7f6e\u3059\u308b\u72b6\u614b\u3078\u3068\u9077\u79fb\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9112,\"width\":\"500px\",\"height\":\"auto\",\"aspectRatio\":\"1.6228454131071333\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"631\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/795316b92fc766b0181f6fef074f03fa-2-1024x631.png\" alt=\"\" class=\"wp-image-9112\" style=\"aspect-ratio: 1.6228454131071333; width: 500px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/795316b92fc766b0181f6fef074f03fa-2-1024x631.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/795316b92fc766b0181f6fef074f03fa-2-300x185.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/795316b92fc766b0181f6fef074f03fa-2-768x473.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/795316b92fc766b0181f6fef074f03fa-2.png 1196w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f313: $R_y\\left(\\sin^{-1}x_i\\right)$\u306b\u3088\u308b\u5165\u529b\u30c7\u30fc\u30bf\u306e\u57cb\u3081\u8fbc\u307f<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306b$r_X$\u3068$r_Z$\u306b\u5165\u529b\u53e4\u5178\u30c7\u30fc\u30bf$x_i$\u306b\u4f9d\u5b58\u3057\u305f\u91cf\u304c\u53cd\u6620\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"1%E3%81%A4%E3%81%AE%E5%85%A5%E5%8A%9B%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E8%A4%87%E6%95%B0%E3%81%AE%E9%87%8F%E5%AD%90%E3%83%93%E3%83%83%E3%83%88%E3%81%B8%E3%81%AE%E5%9F%8B%E3%82%81%E8%BE%BC%E3%81%BF\"><\/span>1\u3064\u306e\u5165\u529b\u30c7\u30fc\u30bf\u306e\u8907\u6570\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u3078\u306e\u57cb\u3081\u8fbc\u307f<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u6b21\u306b\u975e\u7dda\u5f62\u9805\u3092\u751f\u307f\u51fa\u3059\u305f\u3081\u306b$1$\u3064\u306e\u5165\u529b\u53e4\u5178\u30c7\u30fc\u30bf\u306e\u60c5\u5831\u3092\u8907\u6570\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u57cb\u3081\u8fbc\u3080\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4e0a\u8a18\u306e$Y$\u8ef8\u56de\u8ee2\u30b2\u30fc\u30c8\u3067$N$\u91cf\u5b50\u30d3\u30c3\u30c8\u306b$x_i$\u3092\u57cb\u3081\u8fbc\u3080\u3068\u304d\u3001\u305d\u306e$N$\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306e\u72b6\u614b$\\rho_{in}(=\\ket{\\psi_{in}}\\bra{\\psi_{in}})$\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u305b\u307e\u3059\u3002\u3053\u3053\u3067$j$\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u756a\u53f7\u3067\u3059\u3002(\u521d\u671f\u72b6\u614b$\\ket{0}$)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho_{in}\\left(x_i\\right)=\\bigotimes_{j=1}^{N}{R_y\\left({\\sin}^{-1}x_i\\right)\\left|0\\right\\rangle\\left\\langle0\\right|}R_y\\left({\\sin}^{-1}x_i\\right)^\\dagger=\\frac{1}{2^N}\\bigotimes_{j=1}^{N}\\left[I+x_iX_j+\\sqrt{1-{x_i}^2}Z_j\\right]\\tag{61}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u3092\u5c55\u958b\u3059\u308b\u3068\u975e\u7dda\u5f62\u9805\u304c$x_i^N$\u307e\u3067\u73fe\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3068\u3057\u3066$N=2$\u306e\u3068\u304d\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\begin{align}\\rho_{in}\\left(x_i\\right)=\\frac{1}{4}(I\\otimes I+x_iI\\otimes X_2+\\sqrt{1-{x_i}^2}I\\otimes Z_2\\\\+x_iX_1\\otimes I+{\\color{red}{x_i}^2X_1\\otimes X_2}+{\\color{red}x_i\\sqrt{1-{x_i}^2}X_1\\otimes Z_2}\\\\+\\sqrt{1-{x_i}^2}Z_1\\otimes I+{\\color{red}x_i\\sqrt{1-{x_i}^2}Z_1\\otimes X_2}+{\\color{red}{\\sqrt{1-{x_i}^2}}^2Z_1\\otimes Z_2})\\tag{62}\\end{align}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u8d64\u6587\u5b57\u3067\u793a\u3057\u305f\u9805\u304c\u975e\u7dda\u5f62\u9805\u3067\u3059\u3002$2$\u6b21\u306e\u9805\u307e\u3067\u73fe\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u975e\u7dda\u5f62\u9805\u306f\u30e2\u30c7\u30eb\u306e\u8868\u73fe\u529b\u3092\u5927\u304d\u304f\u5de6\u53f3\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3048\u3070$f(x)=x^2$\u3068\u3044\u3046\u95a2\u6570\u306e\u30c7\u30fc\u30bf$(x,f(x))$\u304c$(0.5,0.25)$\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001$X_1\\otimes X_2$\u8ef8\u306b$x^2$\u306e\u5024\u304c\u5165\u308b\u3053\u3068\u306b\u306a\u308b\u306e\u3067\u3001$X_1\\otimes X_2$\u8ef8\u3092\u6e2c\u5b9a\u3059\u308b\u8ef8($Z_1$\u8ef8)\u306b\u56de\u8ee2\u3055\u305b\u308b\u3088\u3046\u306b\u30d1\u30e9\u30e1\u30fc\u30bf$\\theta$\u3092\u8abf\u6574\u3059\u308b\u3053\u3068\u3067\u6700\u9069\u5316\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002(\u56f314\u306f$3$\u6b21\u5143\u7a7a\u9593\u306b$X_1\\otimes X_2$\u8ef8\u3001$X_1$\u8ef8\u3001$Z_1$\u8ef8\u3092\u7121\u7406\u3084\u308a\u8868\u73fe\u3057\u305f\u3082\u306e\u3067\u3042\u308a\u3001\u56de\u8ee2\u8ef8\u7b49\u306f\u6b63\u78ba\u3067\u306f\u3042\u308a\u307e\u305b\u3093)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9629,\"sizeSlug\":\"medium\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-medium\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/08\/1b9def0066ab4fc321c9cca2ffdbe278-300x281.png\" alt=\"\" width=\"300\" height=\"281\" class=\"wp-image-9629 aligncenter\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/08\/1b9def0066ab4fc321c9cca2ffdbe278-300x281.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/08\/1b9def0066ab4fc321c9cca2ffdbe278-1024x958.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/08\/1b9def0066ab4fc321c9cca2ffdbe278-768x718.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/08\/1b9def0066ab4fc321c9cca2ffdbe278-1536x1437.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/08\/1b9def0066ab4fc321c9cca2ffdbe278.png 1582w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f314: $X_1\\otimes X_2$\u8ef8\u3001$X_1$\u8ef8\u3001$Z_1$\u8ef8\u306e\u6a21\u5f0f\u56f3<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>$f(x)=x^3$\u306e\u3068\u304d\u306f\u57cb\u3081\u8fbc\u307f\u30d3\u30c3\u30c8\u6570$N=2$\u3067\u306f\u5b8c\u5168\u306b\u8868\u73fe\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u52a0\u3048\u3066$\\sin$\u306a\u3069\u306e\u95a2\u6570\u306f\u3001\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b\u3092\u8003\u3048\u3066\u3082\u308f\u304b\u308b\u3088\u3046\u306b\u3001\u6271\u3048\u308b\u975e\u7dda\u5f62\u9805\u306e\u6b21\u6570\u304c\u4e0a\u304c\u308c\u3070\u4e0a\u304c\u308b\u307b\u3069\u9ad8\u3044\u7cbe\u5ea6\u3067\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b<span>\u5404\u8ef8\u306e\u5bc4\u4e0e\u3092\u3069\u308c\u3060\u3051\u6e2c\u5b9a\u8ef8\u65b9\u5411\u306b\u4e57\u305b\u308b\u304b\u3092\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u64cd\u4f5c\u3059\u308b\u3053\u3068\u3067\u6700\u9069\u5316\u304c\u884c\u3048\u3001\u5404\u8ef8\u306b$x^N$\u306e\u5024\u304c\u8f09\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u8003\u3048\u308b\u3068$N$\u304c\u5341\u5206\u306a\u5927\u304d\u3055\u3067\u3042\u308c\u3070\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b\u3067\u304d\u308b\u3088\u3046\u306a\u95a2\u6570\u306e\u8fd1\u4f3c\u306f\u3046\u307e\u304f\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u60f3\u50cf\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001$2$\u6b21\u4ee5\u4e0a\u306e\u4fc2\u6570\u3092\u6301\u3064\u9805(\u8d64\u6587\u5b57\u306e\u9805)\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u3055\u308c\u3066\u3044\u306a\u3044\u3068\u6271\u3048\u306a\u3044\u3053\u3068\u304c\u8aad\u307f\u53d6\u308c\u3001\u9069\u5207\u306b\u91cf\u5b50\u30d3\u30c3\u30c8\u3092\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u3059\u308b\u3053\u3068\u3082\u30e2\u30c7\u30eb\u306e\u8868\u73fe\u529b\u3092\u640d\u306a\u308f\u306a\u3044\u305f\u3081\u306b\u91cd\u8981\u3067\u3042\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":4} -->\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%A4%9A%E6%AC%A1%E5%85%83%E3%83%87%E3%83%BC%E3%82%BF%E3%81%AE%E5%9F%8B%E3%82%81%E8%BE%BC%E3%81%BF\"><\/span>\u591a\u6b21\u5143\u30c7\u30fc\u30bf\u306e\u57cb\u3081\u8fbc\u307f<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u6b21\u306b$d$\u6b21\u5143\u306e\u30c7\u30fc\u30bf$\\bm{x_i}=\\left(x_1,x_2,\\ldots,x_d\\right)$\u3092\u6271\u3046\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4ee5\u4e0b\u306e\u5f0f\u3067\u5404\u6210\u5206\u3092\u305d\u308c\u305e\u308c\u8907\u6570\u30d3\u30c3\u30c8\u306b\u57cb\u3081\u8fbc\u307f\u307e\u3059\u3002\u3053\u3053\u3067\u3082$j$\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u756a\u53f7\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\rho_{in}\\left(\\bm{x}_\\bm{i}\\right)=\\frac{1}{2^N}\\bigotimes_{k=1}^{d}\\left(\\bigotimes_{j=1}^{n_k}\\left[I+x_kX_j+\\sqrt{1-x_k^2} Z_j\\right]\\right)\\tag{63}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067$n_k$\u306f$k$\u756a\u76ee\u306e\u6210\u5206\u3092\u57cb\u3081\u8fbc\u3080\u30d3\u30c3\u30c8\u6570\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u3092\u5c55\u958b\u3059\u308b\u3068\u5404\u6210\u5206\u306e\u7a4d\u306e\u9805\u304c$x_1^{n_1}x_2^{n_2}&#8230;x_k^{n_k}$\u307e\u3067\u73fe\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3048\u3070$3$\u6b21\u5143\u306e\u30c7\u30fc\u30bf$\\bm{x_i}=\\left(x_1,x_2,x_3\\right)$\u3092\u305d\u308c\u305e\u308c\u3092\u57cb\u3081\u8fbc\u3080\u30d3\u30c3\u30c8\u6570$\\bm{n}=\\left(3,1,2\\right)$\u3067\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u57cb\u3081\u8fbc\u3080\u3068\u304d\u3001\u5fc5\u8981\u306a\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u306f$3+1+2=6$\u3068\u306a\u308a\u3001\u975e\u7dda\u5f62\u9805\u3068\u3057\u3066$x_1^3x_2^1x_3^2$\u307e\u3067\u73fe\u308c\u307e\u3059\u3002\u3053\u306e\u69d8\u5b50\u3092\u56f315\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9130,\"width\":\"739px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"264\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/2b530e80c7d0de90885e285c5d798063-1024x264.png\" alt=\"\" class=\"wp-image-9130\" style=\"width: 739px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/2b530e80c7d0de90885e285c5d798063-1024x264.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/2b530e80c7d0de90885e285c5d798063-300x77.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/2b530e80c7d0de90885e285c5d798063-768x198.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/2b530e80c7d0de90885e285c5d798063-1536x397.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/2b530e80c7d0de90885e285c5d798063-2048x529.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f315: \u591a\u6b21\u5143\u30c7\u30fc\u30bf\u306e\u8907\u6570\u91cf\u5b50\u30d3\u30c3\u30c8\u3078\u306e\u57cb\u3081\u8fbc\u307f<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067\u3082\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u304c\u9069\u5207\u306b\u3055\u308c\u3066\u3044\u306a\u3044\u3068\u5404\u6b21\u5143\u306e\u30c7\u30fc\u30bf\u304c\u72ec\u7acb\u306b\u3057\u304b\u6271\u3048\u306a\u3044\u305f\u3081\u3001\u4f8b\u3048\u3070\u753b\u50cf\u30c7\u30fc\u30bf\u306a\u3069\u306e\u5404\u30d4\u30af\u30bb\u30eb\u306e\u63a5\u7d9a\u60c5\u5831\u306a\u3069\u304c\u9069\u5207\u306b\u6271\u3048\u306a\u3044\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3053\u3068\u304b\u3089\u3082\u3084\u306f\u308a\u30e2\u30c7\u30eb\u306e\u8868\u73fe\u529b\u3092\u640d\u306a\u308f\u306a\u3044\u305f\u3081\u306b\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3092\u4f5c\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3042\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%91%E3%83%A9%E3%83%A1%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF%E3%82%B2%E3%83%BC%E3%83%88%E3%81%AE%E9%81%A9%E7%94%A8\"><\/span>\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8\u306e\u9069\u7528<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u8abf\u6574\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf$\\theta$\u3092\u6301\u3063\u305f\u30b2\u30fc\u30c8$U(\\bm{\\theta})$\u3092\u5165\u529b\u72b6\u614b$\\ket{\\psi_{in}}$\u306b\u9069\u7528\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067$U(\\bm{\\theta})$\u306e\u8a2d\u8a08\u306f\u69d8\u3005\u306a\u3082\u306e\u304c\u8003\u3048\u3089\u308c\u307e\u3059\u304c\u3001\u5148\u8ff0\u3057\u305f\u901a\u308a\u30e2\u30c7\u30eb\u306e\u8868\u73fe\u529b\u3092\u640d\u306a\u308f\u306a\u3044\u305f\u3081\u306b\u3082\u3001\u3044\u304b\u306b\u3057\u3066\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3092\u4f5c\u308b\u304b\u304c\u91cd\u8981\u3067\u3042\u308b\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u306f\u74b0\u5883\u3068\u306e\u76f8\u4e92\u4f5c\u7528\u306b\u3088\u3063\u3066\u72b6\u614b\u306e\u60c5\u5831\u3092\u5931\u3063\u3066\u3044\u304f\u305f\u3081\uff08\u30c7\u30b3\u30d2\u30fc\u30ec\u30f3\u30b9\uff09\u3001\u56de\u8def\u306e\u5b9f\u884c\u6642\u9593\u306f\u30b3\u30d2\u30fc\u30ec\u30f3\u30b9\u6642\u9593\u3068\u547c\u3070\u308c\u308b\u6642\u9593\u30b9\u30b1\u30fc\u30eb\u3067\u5236\u9650\u3055\u308c\u307e\u3059\u3002\u3055\u3089\u306b\u5404\u30b2\u30fc\u30c8\u306b\u306f\u6709\u9650\u306e\u8aa4\u308a\u7387 $\\epsilon$ \u304c\u3042\u308a\u3001\u30b2\u30fc\u30c8\u6570\u3092 $G$ \u3068\u3059\u308b\u3068\u56de\u8def\u5168\u4f53\u304c\u8aa4\u308a\u306a\u304f\u5b9f\u884c\u3055\u308c\u308b\u78ba\u7387\u306f\u304a\u3088\u305d $(1-\\epsilon)^G\\simeq e^{-\\epsilon G}$ \u3068\u6307\u6570\u7684\u306b\u6e1b\u8870\u3057\u307e\u3059\u3002\u73fe\u5728\u306e\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u8aa4\u308a\u8a02\u6b63\u3092\u5b9f\u88c5\u3067\u304d\u308b\u898f\u6a21\u306b\u9054\u3057\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u3053\u308c\u3089\u306e\u8aa4\u308a\u306f\u305d\u306e\u307e\u307e\u6e2c\u5b9a\u7d50\u679c\u306b\u6b8b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u56de\u8def\u306e\u6d45\u3055\u3082\u91cd\u8981\u3067\u3042\u308b\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4f8b\u3048\u3070\u56f316\u306e\u3088\u3046\u306a$U(\\bm{\\theta})$\u304c\u8003\u3048\u3089\u308c\u307e\u3059\u3002$7$\u6b21\u5143\u306e\u30d1\u30e9\u30e1\u30fc\u30bf$\\bm{\\theta}=\\left(\\theta_1,\\theta_2,\\ldots,\\theta_7\\right)$\u3092\u6301\u3061\u3001$2$\u8ef8\u306e\u56de\u8ee2\u30b2\u30fc\u30c8\u306b\u3088\u308a\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u5168\u4f53\u3092\u4f7f\u7528\u3067\u304d\u3001$CNOT$\u30b2\u30fc\u30c8\u306b\u3088\u308a\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u3055\u308c\u305f\u6df1\u3055$6$\u306e\u56de\u8def\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9132,\"width\":\"766px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"260\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1-1024x260.png\" alt=\"\" class=\"wp-image-9132\" style=\"width: 766px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1-1024x260.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1-300x76.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1-768x195.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1-1536x390.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-1.png 1668w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f316: \u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8$U(\\bm{\\theta})$\u306e\u4f8b<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%87%BA%E5%8A%9B%E3%81%AE%E6%B1%BA%E5%AE%9A\"><\/span>\u51fa\u529b\u306e\u6c7a\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u51fa\u529b\u72b6\u614b$\\ket{\\psi_{out}(\\bm{x_i},\\bm{\\theta})}$\u306b\u5bfe\u3057\u3066\u4efb\u610f\u306e\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb$B$\u306e\u671f\u5f85\u5024$\\left\\langle B\\right\\rangle(\\bm{x_i},\\bm{\\theta})$\u3092\u6e2c\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3068\u304d\u306e\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb$B$\u306b\u5236\u9650\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u56de\u8def\u306e\u6d45\u3055\u306a\u3069\u3092\u8003\u3048\u308b\u3068\u5358\u4e00\u91cf\u5b50\u30d3\u30c3\u30c8\u306e$Z$\u6e2c\u5b9a\u304c\u9069\u5207\u3068\u3044\u3048\u307e\u3059\u3002\u3069\u306e\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u3082\u6700\u7d42\u7684\u306b\u5358\u4e00\u91cf\u5b50\u30d3\u30c3\u30c8\u306e$Z$\u6e2c\u5b9a\u306b\u5e30\u7740\u3055\u305b\u3066\u6e2c\u5b9a\u3059\u308b\u305f\u3081\u3001\u5e30\u7740\u3059\u308b\u305f\u3081\u306e\u56de\u8ee2\u30b2\u30fc\u30c8\u304c\u5fc5\u8981\u306b\u306a\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001\u9069\u5207\u306b\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u3055\u308c\u3066\u3044\u308c\u3070\u4ed6\u306e\u30d3\u30c3\u30c8\u306e\u60c5\u5831\u3092\u542b\u3093\u3060\u30d3\u30c3\u30c8\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u5168\u3066\u306e\u30d3\u30c3\u30c8\u3092\u6e2c\u5b9a\u3059\u308b\u5fc5\u8981\u3082\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u305f\u3060\u3057\u6e2c\u5b9a\u3067\u5f97\u3089\u308c\u308b\u5024\u306f$-1$\u304b\u3089$1$\u306e\u9593\u306e\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u5b9a\u7fa9\u57df\u3084\u5024\u57df\u306e\u8abf\u6574\u3001\u78ba\u7387\u554f\u984c\u306a\u3089\u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u3084\u30b7\u30b0\u30e2\u30a4\u30c9\u3092\u901a\u3057\u3066\u6700\u7d42\u7684\u306a\u30e2\u30c7\u30eb\u306e\u51fa\u529b$y(\\bm{x_i},\\bm{\\theta})=F(\u27e8B\u27e9(\\bm{x_i},\\bm{\\theta}))$\u3068\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%B3%E3%82%B9%E3%83%88%E9%96%A2%E6%95%B0%E3%81%AE%E6%9C%80%E9%81%A9%E5%8C%96\"><\/span>\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u6700\u9069\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u3001\u6b63\u89e3\u30c7\u30fc\u30bf$f(\\bm{x_i})$\u3068\u30e2\u30c7\u30eb\u306e\u51fa\u529b$y(\\bm{x_i},\\bm{\\theta})$\u304b\u3089\u30b3\u30b9\u30c8\u95a2\u6570$L(\\theta)$\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3068\u304d\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u306f\u554f\u984c\u3054\u3068\u306b\u9069\u5207\u306a\u3082\u306e\u3092\u9078\u3076\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u4f8b\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306a$2$\u4e57\u8aa4\u5dee\u304c\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$L\\left(\\bm{\\theta}\\right)={\\sum_{\\operatorname{i}}\\left|\\left|f\\left(\\bm{x}_\\bm{i}\\right)-y\\left(\\bm{x}_\\bm{i},\\bm{\\theta}\\right)\\right|\\right|}^2\\tag{64}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u3088\u3046\u306a\u30b3\u30b9\u30c8\u95a2\u6570\u306e$\\theta_j$\u5fae\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30c1\u30a7\u30a4\u30f3\u30eb\u30fc\u30eb\u3067\u8868\u305b\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{\\partial L}{\\partial\\theta_j}=\\sum_{i}{\\frac{\\partial L}{\\partial y\\left(\\bm{x}_\\bm{i},\\bm{\\theta}\\right)}\\frac{\\partial y\\left(\\bm{x}_\\bm{i},\\bm{\\theta}\\right)}{\\partial\\left\\langle B\\left(\\bm{x}_\\bm{i},\\bm{\\theta}\\right)\\right\\rangle}{\\color{red}\\frac{\\partial\\left\\langle B\\left(\\bm{x}_\\bm{i},\\theta\\right)\\right\\rangle}{\\partial\\theta_j}}}\\tag{65}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u8d64\u6587\u5b57\u306e\u90e8\u5206\u306f\u91cf\u5b50\u56de\u8def\u3092\u7d4c\u7531\u3059\u308b\u56e0\u5b50\u306a\u306e\u3067\u3001\u5148\u8ff0\u3057\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u30b7\u30d5\u30c8\u30eb\u30fc\u30eb\u3067\u8a08\u7b97\u3057\u307e\u3059\u3002\u6b8b\u308a\u306e $2$ \u3064\u306e\u56e0\u5b50\u306f\u3001\u81ea\u5206\u3067\u95a2\u6570\u5f62\u3092\u9078\u3093\u3067\u5b9a\u7fa9\u3057\u305f\u53e4\u5178\u7684\u306a\u95a2\u6570\u3067\u3042\u308b\u30b3\u30b9\u30c8\u95a2\u6570 $L$ \u3068\u5f8c\u51e6\u7406 $F$ \u306e\u5fae\u5206\u306a\u306e\u3067\u3001\u89e3\u6790\u7684\u306b\u5fae\u5206\u3057\u3066\u53e4\u5178\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u8a55\u4fa1\u3067\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u5fae\u5206\u306e\u8a08\u7b97\u7d50\u679c\u3092\u4f7f\u3063\u3066\u52fe\u914d\u964d\u4e0b\u6cd5\u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3057\u3066\u6700\u9069\u5316\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E9%A8%93%E8%A8%AD%E5%AE%9A\"><\/span>\u5b9f\u9a13\u8a2d\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u672c\u8ad6\u6587\u3067\u306f\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u5b9f\u6a5f\u3092\u7528\u3044\u305f\u691c\u8a3c\u306f\u884c\u308f\u308c\u3066\u304a\u3089\u305a\u3001\u53e4\u5178\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u306e\u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u304c\u884c\u308f\u308c\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9B%9E%E8%B7%AF%E8%A8%AD%E8%A8%88\"><\/span>\u56de\u8def\u8a2d\u8a08<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u56f317\u306b\u793a\u3059\u3088\u3046\u306a\u91cf\u5b50\u30d3\u30c3\u30c8\u6570$N=6$\u3001\u56de\u8def\u6df1\u3055$D=6$\u306e\u56de\u8def\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u53e4\u5178\u5165\u529b\u30c7\u30fc\u30bf\u304b\u3089\u5165\u529b\u72b6\u614b$\\rho_{in}$\u3092\u4f5c\u308b\u56de\u8def$U_{in}$\u306f\u305d\u308c\u305e\u308c\u306e\u554f\u984c\u3054\u3068\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u305f\u3081\u3001\u3053\u3053\u3067\u306f\u5b9a\u7fa9\u3057\u307e\u305b\u3093\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9138,\"width\":\"495px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"496\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-2-1024x496.png\" alt=\"\" class=\"wp-image-9138\" style=\"width: 495px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-2-1024x496.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-2-300x145.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-2-768x372.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-2.png 1330w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f317: \u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u7528\u3044\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u6570$N=6$\u3001\u56de\u8def\u6df1\u3055$D=6$\u306e\u56de\u8def\uff08\u5f15\u7528\u5143\uff1a<a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.98.032309\">https:\/\/doi.org\/10.1103\/PhysRevA.98.032309<\/a>\uff09<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067\u3001$U\\left(\\theta_j^{\\left(i\\right)}\\right)$\u306f\u4ee5\u4e0b\u3067\u8868\u3055\u308c\u308b\u5358\u4e00\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u4efb\u610f\u56de\u8ee2\u3067\u3059\u3002$2$\u8ef8\u306e\u56de\u8ee2\u30b2\u30fc\u30c8\u306b\u3088\u308a\u30d6\u30ed\u30c3\u30db\u7403\u7a7a\u9593\u5168\u4f53\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<br \/>$i$\u306f\u91cf\u5b50\u56de\u8def\u306e\u5c64\u3092\u8868\u3057\u3001$j$\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u756a\u53f7\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$U\\left(\\theta_j^{\\left(i\\right)}\\right)=R_X^{\\left(j\\right)}\\left(\\theta_{j1}^{\\left(i\\right)}\\right)R_Z^{\\left(j\\right)}\\left(\\theta_{j2}^{\\left(i\\right)}\\right)R_X^{\\left(j\\right)}\\left(\\theta_{j3}^{\\left(i\\right)}\\right)\\tag{66}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$e^{-iHT}$\u306f\u4ee5\u4e0b\u306e\u751f\u6210\u5b50$H$\u3067\u8868\u3055\u308c\u308b\u6a2a\u78c1\u5834\u30a4\u30b8\u30f3\u30b0\u30e2\u30c7\u30eb\u306b\u3088\u308b\u6642\u9593\u767a\u5c55\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u8907\u96d1\u306a\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3092\u751f\u6210\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$H=\\sum_{j=1}^{N}{a_jX_j}+\\sum_{j=1}^{N}\\sum_{k=1}^{j-1}J_{jk}Z_j\\otimes Z_k\\tag{67}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$T=10$\u3001$J_{jk}$\u3001$a_j$\u306f$[-1,1]$\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3055\u308c\u4ee5\u964d\u306e\u5b9f\u9a13\u3092\u901a\u3057\u3066\u56fa\u5b9a\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u7570\u306a\u308b$J_{jk}$\u3001$a_j$\u306e\u5024\u3067\u3082\u540c\u69d8\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u3053\u3068\u306f\u78ba\u8a8d\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001$\\theta_j^{\\left(i\\right)}$\u306e\u521d\u671f\u5024\u306f$[0,2\\pi]$\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3055\u308c\u3001\u6e2c\u5b9a\u3055\u308c\u308b\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u306f$Z$\u306e\u307f\u3068\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%8E%E3%82%A4%E3%82%BA%E3%81%AE%E4%BB%98%E5%8A%A0\"><\/span>\u30ce\u30a4\u30ba\u306e\u4ed8\u52a0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u30aa\u30d6\u30b6\u30fc\u30d0\u30d6\u30eb\u306b\u5bfe\u3059\u308b\u671f\u5f85\u5024$\u27e8Z\u27e9$\u304c\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304b\u3089\u3067\u306f\u306a\u304f\u8a08\u7b97\u3067\u6b63\u78ba\u306a\u5024\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3057\u304b\u3057\u3001\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u5b9f\u6a5f\u3067\u306f\u671f\u5f85\u5024\u3092\u5f97\u308b\u305f\u3081\u306b\u8907\u6570\u56de\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0(\u6e2c\u5b9a)\u3092\u884c\u3044\u3001\u671f\u5f85\u5024\u306b\u53ce\u675f\u3055\u305b\u308b\u3001\u3068\u3044\u3046\u30d7\u30ed\u30bb\u30b9\u304c\u5b58\u5728\u3059\u308b\u305f\u3081\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306b\u3088\u308b\u5206\u6563\u3092\u518d\u73fe\u3059\u308b\u305f\u3081\u306b\u4ee5\u4e0b\u306e\u6a19\u6e96\u504f\u5dee$\\sigma$\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u30ac\u30a6\u30b9\u30ce\u30a4\u30ba\u3092\u8a08\u7b97\u3067\u5f97\u3089\u308c\u305f\u671f\u5f85\u5024$\u27e8Z\u27e9$\u306b\u52a0\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\sigma=\\sqrt{\\frac{2}{N_s}}\\frac{1-\\left\\langle Z\\right\\rangle^2}{4}\\tag{68}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u3053\u3067$N_s$\u306f\u30b5\u30f3\u30d7\u30eb\u6570\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%9D%9E%E7%B7%9A%E5%BD%A2%E9%96%A2%E6%95%B0%E3%81%AE%E8%BF%91%E4%BC%BC\"><\/span>\u975e\u7dda\u5f62\u95a2\u6570\u306e\u8fd1\u4f3c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%95%8F%E9%A1%8C%E5%AE%9A%E7%BE%A9\"><\/span>\u554f\u984c\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>$f\\left(x\\right)=x^2,e^x,\\sin{x},\\left|x\\right|$\u306b\u5bfe\u3057\u3066\u5148\u8ff0\u306e\u91cf\u5b50\u56de\u8def\u3092\u5b66\u7fd2\u30e2\u30c7\u30eb\u3068\u3057\u3066\u8fd1\u4f3c\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u3001\u5165\u529b\u72b6\u614b$\\rho_{in}$\u306f\u521d\u671f\u72b6\u614b$\\ket{0}$\u306b\u5bfe\u3057\u3066\u4ee5\u4e0b\u306e$U_{in}(x_i)$\u3092\u4f5c\u7528\u3055\u305b\u3066\u751f\u6210\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$U_{in}\\left(x_i\\right)=\\bigotimes_{j}{R_Z^{\\left(j\\right)}\\left(cos^{-1}\\left(x_i^2\\right)\\right)R_Y^{\\left(j\\right)}\\left(sin^{-1}(x_i)\\right)}\\tag{69}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u554f\u984c\u306b\u304a\u3044\u3066\u5165\u529b$x_i$\u306f$1$\u6b21\u5143\u306a\u306e\u3067\u5168$6$\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u540c\u3058\u56de\u8ee2\u304c\u4f5c\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6e2c\u5b9a\u3059\u308b\u306e\u306f\u7b2c$1$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u671f\u5f85\u5024$\u27e8Z\u27e9$\u3067\u3042\u308a\u3001\u51fa\u529b\u306f$y=a\u27e8Z\u27e9$\u3068\u3057\u3066\u5024\u57df\u3092\u64cd\u4f5c\u3059\u308b$a$\u3092\u4fc2\u6570\u306b\u52a0\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e$a$\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u3066$\\bm{\\theta}$\u3068\u4e00\u7dd2\u306b\u6700\u9069\u5316\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30b3\u30b9\u30c8\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a$2$\u4e57\u8aa4\u5dee\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$L\\left(\\bm{\\theta}\\right)={\\sum_{\\operatorname{i}}\\left|\\left|f\\left(x_i\\right)-y\\left(x_i,\\bm{\\theta}\\right)\\right|\\right|}^2\\tag{70}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4ee5\u4e0a\u306e\u6761\u4ef6\u3067\u5404\u95a2\u6570\u306e\u6559\u5e2b\u30c7\u30fc\u30bf\u6570\u3092$100$\u3068\u3057\u3066\u8fd1\u4f3c\u3092\u884c\u3044\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 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><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u56f318\u306b\u6a2a\u8ef8\u3092$x$\u3001\u7e26\u8ef8\u3092$y$\u3068\u3057\u305f\u5b9f\u9a13\u7d50\u679c\u306e\u30b0\u30e9\u30d5\u3092\u793a\u3057\u307e\u3059\u3002\u51e1\u4f8b\u306e&#8221;initial&#8221;\u304c\u521d\u671f\u5024\u3001&#8221;final&#8221;\u304c\u6700\u9069\u5316\u5f8c\u306e\u5024\u3001&#8221;teacher&#8221;\u304c\u6559\u5e2b\u30c7\u30fc\u30bf\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9150,\"width\":\"360px\",\"height\":\"auto\",\"aspectRatio\":\"1.0658419080473442\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"842\" height=\"790\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-3.png\" alt=\"\" class=\"wp-image-9150\" style=\"aspect-ratio: 1.0658419080473442; width: 360px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-3.png 842w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-3-300x281.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-3-768x721.png 768w\" sizes=\"auto, (max-width: 842px) 100vw, 842px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f318: \u975e\u7dda\u5f62\u95a2\u6570\u306e\u8fd1\u4f3c\u7d50\u679c\uff08\u5f15\u7528\u5143\uff1a<a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.98.032309\">https:\/\/doi.org\/10.1103\/PhysRevA.98.032309<\/a>\uff09<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u4ee5\u4e0a\u306e\u7d50\u679c\u304b\u3089\u3001\u5168\u3066\u306e\u95a2\u6570\u306b\u304a\u3044\u3066\u826f\u597d\u306b\u8fd1\u4f3c\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b\u306b\u3088\u3063\u3066\u7121\u9650\u6b21\u6570\u307e\u3067\u7d9a\u304f$\\sin x$\u306e\u3088\u3046\u306a\u5f37\u3044\u975e\u7dda\u5f62\u95a2\u6570\u3084\u3001$|x|$\u306e\u3088\u3046\u306a\u975e\u89e3\u6790\u7684\u306a\u95a2\u6570\u306e\u8fd1\u4f3c\u304c\u6210\u529f\u3057\u3066\u3044\u308b\u3053\u3068\u304b\u3089\u3001\u975e\u5c40\u6240\u6f14\u7b97\u5b50($X\\otimes X\\otimes&#8230;\\otimes X$\u306e\u3088\u3046\u306a\u6f14\u7b97\u5b50)\u306e\u7a7a\u9593\u306b\u96a0\u308c\u3066\u3044\u305f\u9ad8\u6b21\u9805\u3092\u4f7f\u7528\u3067\u304d\u3066\u3044\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$|x|$\u306e$x=0$\u4ed8\u8fd1\u306b\u304a\u3044\u3066\u8fd1\u4f3c\u304c\u6bd4\u8f03\u7684\u60aa\u3044\u306e\u306f\u305d\u306e\u975e\u89e3\u6790\u7684\u6027\u8cea($x=0$\u306e\u70b9\u3067\u5fae\u5206\u4e0d\u53ef)\u306b\u3088\u308b\u3082\u306e\u3067\u3042\u308a\u3001\u5165\u529b\u95a2\u6570\u3068\u3057\u3066\u5225\u306e\u95a2\u6570\u7cfb(\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f\u306a\u3069)\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u89e3\u6c7a\u3067\u304d\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%88%86%E9%A1%9E%E5%95%8F%E9%A1%8C\"><\/span>\u5206\u985e\u554f\u984c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%95%8F%E9%A1%8C%E5%AE%9A%E7%BE%A9-2\"><\/span>\u554f\u984c\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u56f319\u306e\u3088\u3046\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8(<mark style=\"background-color: rgba(0, 0, 0, 0);\" class=\"has-inline-color has-vivid-cyan-blue-color\">\u9752:\u30af\u30e9\u30b9$1$<\/mark>,<mark style=\"background-color: rgba(0, 0, 0, 0);\" class=\"has-inline-color has-vivid-red-color\">\u8d64:\u30af\u30e9\u30b9$2$<\/mark>)\u306b\u5bfe\u3057\u3066\u5148\u8ff0\u306e\u91cf\u5b50\u56de\u8def\u3092\u5b66\u7fd2\u30e2\u30c7\u30eb\u3068\u3057\u3066\u5206\u985e\u554f\u984c\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9151,\"width\":\"174px\",\"height\":\"auto\",\"sizeSlug\":\"full\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"376\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-4.png\" alt=\"\" class=\"wp-image-9151\" style=\"width: 174px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-4.png 496w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-4-300x227.png 300w\" sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f319: \u5206\u985e\u554f\u984c\u306b\u7528\u3044\u308b\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\uff08\u5f15\u7528\u5143\uff1a<a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.98.032309\">https:\/\/doi.org\/10.1103\/PhysRevA.98.032309<\/a>\uff09<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u5ea7\u6a19$\\bm{x_i}=(x_{i,0},x_{i,1})$\u306b\u5bfe\u3057\u3066\u51fa\u529b$y=(\u30af\u30e9\u30b91\u306e\u78ba\u7387,\u30af\u30e9\u30b92\u306e\u78ba\u7387)$\u3092\u6700\u9069\u5316\u3059\u308b\u554f\u984c\u3068\u3057\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u3001\u5165\u529b\u72b6\u614b$\\rho_{in}$\u306f\u521d\u671f\u72b6\u614b$\\ket{0}$\u306b\u5bfe\u3057\u3066\u4ee5\u4e0b\u306e$U_{in}(x)$\u3092\u4f5c\u7528\u3055\u305b\u3066\u751f\u6210\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$U_{in}\\left(\\bm{x}_\\bm{i}\\right)=\\bigotimes_{j}{R_Z^{\\left(j\\right)}\\left(cos^{-1}\\left({x_{i,jmod2}}^2\\right)\\right)R_Y^{\\left(j\\right)}\\left(sin^{-1}(x_{i,jmod2})\\right)}\\tag{71}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$j$\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u756a\u53f7\u3067\u3042\u308a\u3001\u5076\u6570\u756a\u53f7\u3092\u5ea7\u6a19\u306e\u7b2c$1$\u8981\u7d20\u3001\u5947\u6570\u756a\u53f7\u3092\u7b2c$2$\u8981\u7d20\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u5168\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u304c$6$\u3067\u3042\u308b\u305f\u3081\u3001\u5ea7\u6a19\u306e\u5404\u8981\u7d20\u306e\u6570\u5024\u306f\u305d\u308c\u305e\u308c$3$\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u57cb\u3081\u8fbc\u307e\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6e2c\u5b9a\u3059\u308b\u306e\u306f\u7b2c$1$\u3001\u7b2c$2$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u671f\u5f85\u5024$\u27e8Z_1\u27e9$,$\u27e8Z_2\u27e9$\u3067\u3042\u308a\u3001\u51fa\u529b$\\bm{y_i}=(y_{i,1},y_{i,2})$\u306f\u4ee5\u4e0b\u306e\u30bd\u30d5\u30c8\u30de\u30c3\u30af\u30b9\u95a2\u6570\u3092\u901a\u3057\u305f\u3082\u306e\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3053\u3053\u3067$k$\u306f\u30af\u30e9\u30b9\u306e\u756a\u53f7\u3067\u3042\u308a\u3001$k,j\\in\\{1,2\\}$\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a$y_{i,1},y_{i,2}$\u306e\u548c\u306f$1$\u306b\u306a\u308a\u78ba\u7387\u3068\u3057\u3066\u898f\u683c\u5316\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$y_{i,k}=\\frac{e^{\u27e8Z_k\u27e9}}{\\sum_{j\\in\\{1,2\\}} e^{\u27e8Z_j\u27e9}}\\tag{72}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u30b3\u30b9\u30c8\u95a2\u6570\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u78ba\u7387\u5206\u5e03\u304c\u8fd1\u3044\u307b\u3069$0$\u306b\u8fd1\u3065\u304f\u30af\u30ed\u30b9\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u7528\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$L=-\\sum_i \\sum_{k\\in\\{1,2\\}}f_k(\\mathbf{x}_i)\\log y_{i,k}\\tag{73}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6559\u5e2b\u30c7\u30fc\u30bf$f(\\bm{x_i})$\u306f\u30af\u30e9\u30b9$1$\u306b\u5bfe\u3057\u3066$(1,0)$\u3001\u30af\u30e9\u30b9$2$\u306b\u5bfe\u3057\u3066$(0,1)$\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0a\u306e\u6761\u4ef6\u3067\u6559\u5e2b\u30c7\u30fc\u30bf\u6570\u306f\u5404\u30af\u30e9\u30b9$100$\u305a\u3064\u3068\u3057\u3066\u5206\u985e\u554f\u984c\u3092\u884c\u3044\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C-2\"><\/span>\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u56f320(a)\u306f\u554f\u984c\u5b9a\u7fa9\u3067\u793a\u3057\u305f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3067\u3001\u8272\u306f\u6b63\u89e3\u30e9\u30d9\u30eb\u3092\u8868\u3057\u307e\u3059\u3002\u56f320(b)\u306f\u5b66\u7fd2\u5f8c\u306e\u30e2\u30c7\u30eb\u3092 $[-1,1]^2$ \u4e0a\u306e\u683c\u5b50\u70b9\u3067\u8a55\u4fa1\u3057\u3001\u5f0f(72)\u3067\u5f97\u3089\u308c\u308b\u6240\u5c5e\u78ba\u7387\u3092\u8272\u3067\u8868\u3057\u305f\u3082\u306e\u3067\u3059\u3002\u56f320(a)\u306e\u8272\u304c\u6b63\u89e3\u30e9\u30d9\u30eb\u306e $0$ \u304b $1$ \u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\u3001\u56f320(b)\u306e\u8272\u306f\u9023\u7d9a\u5024\u306e\u78ba\u7387\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9157,\"width\":\"584px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"420\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-5-1024x420.png\" alt=\"\" class=\"wp-image-9157\" style=\"width: 584px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-5-1024x420.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-5-300x123.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-5-768x315.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-5.png 1196w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f320: \u5206\u985e\u554f\u984c\u306e\u7d50\u679c\u3002(a) \u5b66\u7fd2\u306b\u7528\u3044\u305f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3068\u6b63\u89e3\u30e9\u30d9\u30eb\u3001(b) \u5b66\u7fd2\u5f8c\u306e\u30e2\u30c7\u30eb\u304c\u51fa\u529b\u3059\u308b\u6240\u5c5e\u78ba\u7387\uff08\u5f15\u7528\u5143\uff1a<a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.98.032309\">https:\/\/doi.org\/10.1103\/PhysRevA.98.032309<\/a>\uff09<\/figcaption>\n<\/figure>\n<p>\u5224\u5b9a\u306f\u78ba\u7387 $0.5$ \u3092\u5883\u306b\u884c\u308f\u308c\u308b\u305f\u3081\u3001\u9752\u3044\u9818\u57df\u3068\u8d64\u3044\u9818\u57df\u306e\u5883\u76ee\u306b\u3042\u308b $0.5$ \u306e\u7b49\u9ad8\u7dda\u304c\u30e2\u30c7\u30eb\u306e\u6c7a\u5b9a\u5883\u754c\u306b\u3042\u305f\u308a\u307e\u3059\u3002\u9752\u3044\u9818\u57df\u306f\u56f320(a)\u3067\u9752\u3044\u70b9\u304c\u5206\u5e03\u3057\u3066\u3044\u308b\u7bc4\u56f2\u3068\u304a\u304a\u3080\u306d\u4e00\u81f4\u3057\u3001\u8d64\u3044\u9818\u57df\u306f\u8d64\u3044\u74b0\u306e\u4f4d\u7f6e\u3092\u542b\u3093\u3067\u3044\u308b\u305f\u3081\u3001\u5b66\u7fd2\u30c7\u30fc\u30bf\u3092\u6b63\u3057\u304f\u5206\u985e\u3067\u304d\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E5%A4%9A%E4%BD%93%E7%B3%BB%E3%83%80%E3%82%A4%E3%83%8A%E3%83%9F%E3%82%AF%E3%82%B9%E3%81%AE%E8%BF%91%E4%BC%BC\"><\/span>\u91cf\u5b50\u591a\u4f53\u7cfb\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u306e\u8fd1\u4f3c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%95%8F%E9%A1%8C%E5%AE%9A%E7%BE%A9-3\"><\/span>\u554f\u984c\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u6a2a\u78c1\u5834\u30a4\u30b8\u30f3\u30b0\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u4e0b\u3067$10$\u30b9\u30d4\u30f3\u7cfb\u306e\u72b6\u614b\u306e\u6642\u9593\u306b\u3088\u308b\u5909\u5316\u3092\u5148\u8ff0\u306e\u91cf\u5b50\u56de\u8def\u3092\u5b66\u7fd2\u30e2\u30c7\u30eb\u3068\u3057\u3066\u8fd1\u4f3c\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u3001\u4ee5\u4e0b\u306e\u6a2a\u78c1\u5834\u30a4\u30b8\u30f3\u30b0\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u4e0b\u3067$10$\u30b9\u30d4\u30f3\u7cfb\u306e\u72b6\u614b\u306e\u6642\u9593\u306b\u3088\u308b\u5909\u5316\u3092\u4e8b\u524d\u306b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u3001\u6559\u5e2b\u30c7\u30fc\u30bf\u3092\u5f97\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$H=\\sum_{j=1}^{N}{a_jX_j}+\\sum_{j=1}^{N}\\sum_{k=1}^{j-1}J_{jk}Z_jZ_k\\tag{74}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u5f0f\u306e$J_{jk},a_j$\u306f\u56de\u8def\u5185\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3068\u306f\u7121\u95a2\u4fc2\u306b$[-1,1]$\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$10$\u30b9\u30d4\u30f3\u7cfb\u306f\u521d\u671f\u72b6\u614b$\\ket{0}^{\\otimes10}$\u304b\u3089\u958b\u59cb\u3057\u3001\u521d\u671f\u306e\u904e\u6e21\u7684\u306a\u6642\u9593\u533a\u9593($T_{transient}=300$)\u306f\u7834\u68c4\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u305d\u306e\u305f\u3081\u3001\u5b66\u7fd2\u5bfe\u8c61\u306f\u6642\u9593\u533a\u9593$t\\in\\left[T_{transient},T_{transient}+8\\right]$\u306b\u304a\u3051\u308b$3$\u3064\u306e\u30b9\u30d4\u30f3\u306e$Z$\u306e\u671f\u5f85\u5024\u3068\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u5165\u529b\u72b6\u614b\u3092\u4f5c\u308b\u30b2\u30fc\u30c8\u3001\u30b3\u30b9\u30c8\u95a2\u6570\u3001\u6559\u5e2b\u30c7\u30fc\u30bf\u6570\u306a\u3069\u306f\u975e\u7dda\u5f62\u95a2\u6570\u306e\u8fd1\u4f3c\u306e\u3082\u306e\u3068\u540c\u3058\u3082\u306e\u3092\u4f7f\u7528\u3057\u307e\u3059\u304c\u3001\u5024\u57df\u306e\u8abf\u6574\u306e\u5fc5\u8981\u304c\u306a\u3044\u305f\u3081\u3001\u51fa\u529b\u306f\u7b2c$1$\u3001\u7b2c$2$\u3001\u7b2c$3$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u671f\u5f85\u5024$\u27e8Z_1\u27e9,\u27e8Z_2\u27e9, \u27e8Z_3\u27e9$\u3092\u305d\u306e\u307e\u307e\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305f\u3001\u5165\u529b\u30c7\u30fc\u30bf\u306f\u6642\u9593$t$\u3068\u3059\u308b\u306e\u304c\u81ea\u7136\u3067\u3059\u304c\u3001$\\sin ^{-1}(x)$\u306a\u3069\u306b\u5165\u308c\u308b\u305f\u3081\u306b\u5b9a\u7fa9\u57df\u3092\u4ee5\u4e0b\u306e\u5199\u50cf\u3067$[-1,1]$\u306b\u8abf\u6574\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$t=4\\left(x+1\\right)+T_{transient}\\tag{75}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4ee5\u4e0a\u306e\u6761\u4ef6\u3067\u91cf\u5b50\u591a\u4f53\u7cfb\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u306e\u8fd1\u4f3c\u3092\u884c\u3044\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading {\"level\":3} -->\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C-3\"><\/span>\u7d50\u679c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u56f321\u306b\u6a2a\u8ef8\u3092$[-1,1]$\u306b\u5199\u50cf\u3057\u305f\u6642\u9593$t$\u3001\u7e26\u8ef8\u3092\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u671f\u5f85\u5024\u3068\u3057\u305f\u5b9f\u9a13\u7d50\u679c\u306e\u30b0\u30e9\u30d5\u3092\u793a\u3057\u307e\u3059\u3002\u51e1\u4f8b\u306e&#8221;initial&#8221;\u304c\u521d\u671f\u5024\u3001&#8221;final&#8221;\u304c\u6700\u9069\u5316\u5f8c\u306e\u5024\u3001&#8221;teacher&#8221;\u304c\u6559\u5e2b\u30c7\u30fc\u30bf\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:image {\"id\":9160,\"width\":\"566px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"528\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-6-1024x528.png\" alt=\"\" class=\"wp-image-9160\" style=\"width: 566px; height: auto;\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-6-1024x528.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-6-300x155.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-6-768x396.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2026\/06\/image-6.png 1252w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/>\n<figcaption class=\"wp-element-caption\">\u56f321: \u91cf\u5b50\u591a\u4f53\u7cfb\u30c0\u30a4\u30ca\u30df\u30af\u30b9\u306e\u8fd1\u4f3c\u7d50\u679c\uff08\u5f15\u7528\u5143\uff1a<a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.98.032309\">https:\/\/doi.org\/10.1103\/PhysRevA.98.032309<\/a>\uff09<\/figcaption>\n<\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p>\u4ee5\u4e0a\u306e\u7d50\u679c\u304b\u3089\u3001\u5168\u3066\u306e\u30d3\u30c3\u30c8\u306e$Z$\u306e\u671f\u5f85\u5024\u306b\u304a\u3044\u3066\u826f\u597d\u306b\u8fd1\u4f3c\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u6ce8\u76ee\u3059\u3079\u304d\u306f\u3001\u3088\u308a\u8907\u96d1\u306a $10$ \u30b9\u30d4\u30f3\u7cfb\u306e $3$ \u3064\u306e\u89b3\u6e2c\u91cf\u304c\u3001$6$ \u91cf\u5b50\u30d3\u30c3\u30c8\u56de\u8def\u306e $3$ \u3064\u306e\u89b3\u6e2c\u91cf\u306b\u3088\u3063\u3066\u540c\u6642\u306b\u518d\u73fe\u3055\u308c\u3066\u3044\u308b\u70b9\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u3053\u3053\u3067\u884c\u3063\u3066\u3044\u308b\u306e\u306f\u901a\u5e38\u306e\u610f\u5473\u3067\u306e\u91cf\u5b50\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5bfe\u8c61\u7cfb\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3092\u91cf\u5b50\u56de\u8def\u4e0a\u306b\u518d\u73fe\u3057\u3066\u3044\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u6642\u9593 $t$ 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-->\n<p>\u307e\u305f\u3001\u51fa\u529b\u3092$x$\u306b\u95a2\u3057\u3066\u5fae\u5206\u3059\u308b\u3053\u3068\u3067\u3001\u30b7\u30b9\u30c6\u30e0\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u90e8\u5206\u7684\u306a\u60c5\u5831\u3092\u62bd\u51fa\u3059\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u52fe\u914d\u3092\u8a08\u7b97\u3059\u308b\u306e\u3068\u540c\u3058\u65b9\u6cd5\u3067\u5bb9\u6613\u306b\u5b9f\u884c\u3067\u304d\u308b\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E8%AB%96\"><\/span>\u7d50\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u672c\u8ad6\u6587\u3067\u306f\u65b0\u305f\u306a\u91cf\u5b50\u6a5f\u68b0\u5b66\u7fd2\u306e\u67a0\u7d44\u307f\u3068\u3057\u3066\u3001\u5165\u529b\u30c7\u30fc\u30bf\u3092\u91cf\u5b50\u56de\u8def\u306b\u4e0e\u3048\u3001\u51fa\u529b\u304c\u6559\u5e2b\u4fe1\u53f7\u306b\u4e00\u81f4\u3059\u308b\u3088\u3046\u306b\u56de\u8def\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u8abf\u6574\u3059\u308b\u91cf\u5b50\u56de\u8def\u5b66\u7fd2\u3092\u63d0\u6848\u3057\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u7d50\u679c\u306b\u3088\u308a\u3001\u95a2\u6570\u306e\u8868\u73fe\u3001\u5206\u985e\u3001\u6bd4\u8f03\u7684\u5927\u304d\u306a\u91cf\u5b50\u30b7\u30b9\u30c6\u30e0\u306e\u9069\u5408\u304c\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u672c\u8ad6\u6587\u306e\u89e3\u8aac\u8a18\u4e8b\u3092\u66f8\u304f\u306b\u3042\u305f\u3063\u3066\u3001\u7dda\u5f62\u4ee3\u6570\u306e\u77e5\u8b58\u304c\u3042\u308c\u3070\u7406\u89e3\u3067\u304d\u308b\u69cb\u6210\u3092\u610f\u8b58\u3057\u3066\u4f5c\u6210\u3057\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u91cf\u5b50\u56de\u8def\u5b66\u7fd2\u306e\u30a2\u30a4\u30c7\u30a2\u81ea\u4f53\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6301\u3063\u305f\u30e2\u30c7\u30eb\u3092\u7528\u610f\u3057\u3066\u51fa\u529b\u304c\u6559\u5e2b\u4fe1\u53f7\u306b\u8fd1\u3065\u304f\u3088\u3046\u306b\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b\u3068\u3044\u3046\u3001\u53e4\u5178\u7684\u306a\u6a5f\u68b0\u5b66\u7fd2\u3068\u540c\u3058\u69cb\u56f3\u3067\u3042\u308a\u3001\u67a0\u7d44\u307f\u3060\u3051\u3092\u8ffd\u3046\u306e\u3067\u3042\u308c\u3070\u96e3\u3057\u3044\u3068\u3053\u308d\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u306a\u305c\u305d\u308c\u3067\u975e\u7dda\u5f62\u306a\u95a2\u6570\u304c\u8868\u73fe\u3067\u304d\u308b\u306e\u304b\u3001\u306a\u305c\u52fe\u914d\u304c\u671f\u5f85\u5024\u306e\u6e2c\u5b9a\u3060\u3051\u3067\u53b3\u5bc6\u306b\u6c42\u307e\u308b\u306e\u304b\u3092\u7d0d\u5f97\u3059\u308b\u306b\u306f\u3001\u91cf\u5b50\u72b6\u614b\u3092\u5bc6\u5ea6\u6f14\u7b97\u5b50\u3068\u30d1\u30a6\u30ea\u57fa\u5e95\u3067\u8868\u3059\u898b\u65b9\u304c\u5fc5\u8981\u3060\u3063\u305f\u305f\u3081\u3001\u80cc\u666f\u3067\u306f\u305d\u306e\u70b9\u306b\u3064\u3044\u3066\u91cd\u70b9\u7684\u306b\u6271\u3044\u307e\u3057\u305f\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u6574\u7406\u3057\u3066\u3044\u3066\u7279\u306b\u9762\u767d\u3044\u3068\u611f\u3058\u305f\u306e\u306f\u3001\u5165\u529b\u30c7\u30fc\u30bf$x_i$\u306e$2$\u6b21\u4ee5\u4e0a\u306e\u9805\u304c\u3001\u7b26\u53f7\u5316\u306e\u6bb5\u968e\u3067\u3059\u3067\u306b\u72b6\u614b\u306e\u4fc2\u6570\u3068\u3057\u3066\u73fe\u308c\u3066\u3044\u308b\u3068\u3044\u3046\u70b9\u3067\u3059\u3002\u9ad8\u6b21\u306e\u9805\u306f\u56de\u8def\u304c\u4f5c\u308a\u51fa\u3059\u306e\u3067\u306f\u306a\u304f\u6700\u521d\u304b\u3089\u72b6\u614b\u306e\u4e2d\u306b\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u306e\u9805\u306e\u6e2c\u5b9a\u3078\u306e\u5bc4\u4e0e\u3092\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u30b2\u30fc\u30c8\u3067\u64cd\u4f5c\u3059\u308b\u3068\u3044\u3046\u69cb\u9020\u304c\u3068\u3066\u3082\u8208\u5473\u6df1\u304b\u3063\u305f\u3067\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4e00\u65b9\u3067\u3001\u672c\u8ad6\u6587\u306e\u6570\u5024\u5b9f\u9a13\u306f\u6700\u5927\u3067$N=6$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u53e4\u5178\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u3042\u308a\u3001\u5b9f\u6a5f\u3067\u540c\u3058\u6027\u80fd\u304c\u5f97\u3089\u308c\u308b\u304b\u306f\u5225\u306e\u554f\u984c\u3067\u3059\u3002\u307e\u305f\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u6570\u3092\u5897\u3084\u3059\u3068\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u52fe\u914d\u304c\u307b\u3068\u3093\u3069$0$\u306b\u306a\u308a\u6700\u9069\u5316\u304c\u9032\u307e\u306a\u304f\u306a\u308b\u73fe\u8c61(\u30d0\u30ec\u30f3\u30d7\u30e9\u30c8\u30fc\u3001barren plateau)\u306a\u3069\u3001\u3053\u306e\u67a0\u7d44\u307f\u306b\u306f\u8fd1\u5e74\u6307\u6458\u3055\u308c\u3066\u3044\u308b\u8ab2\u984c\u3082\u3042\u308a\u307e\u3059\u3002\u672c\u8ad6\u6587\u306f\u305d\u3046\u3057\u305f\u8b70\u8ad6\u306e\u51fa\u767a\u70b9\u306b\u3042\u305f\u308b\u63d0\u6848\u3067\u3042\u308a\u3001\u73fe\u5728\u306e\u91cf\u5b50\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u3067\u6a5f\u68b0\u5b66\u7fd2\u3092\u884c\u3046\u969b\u306e\u8a2d\u8a08\u306e\u8003\u3048\u65b9\u3092\u77e5\u308b\u3046\u3048\u3067\u3001\u3044\u307e\u8aad\u3093\u3067\u3082\u5f97\u308b\u3082\u306e\u306e\u591a\u3044\u8ad6\u6587\u3060\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph \/-->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Appendix\"><\/span>Appendix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%86%E3%83%B3%E3%82%BD%E3%83%AB%E7%A9%8D\"><\/span>\u30c6\u30f3\u30bd\u30eb\u7a4d<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><!-- \/wp:heading -->\n\n<!-- wp:paragraph --><\/p>\n<p>\u30c6\u30f3\u30bd\u30eb\u7a4d\u3068\u306f\u3001$2$ \u3064\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u57fa\u5e95\u306e\u3042\u3089\u3086\u308b\u7d44\u307f\u5408\u308f\u305b\u3092\u65b0\u3057\u3044\u57fa\u5e95\u3068\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u5927\u304d\u306a\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092\u4f5c\u308b\u69cb\u6210\u306e\u3053\u3068\u3067\u3059\u3002$m$ \u6b21\u5143\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593 $V$ \u306e\u57fa\u5e95\u3092 $\\{\\bm{e}_i\\}$\u3001$n$ \u6b21\u5143\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593 $W$ \u306e\u57fa\u5e95\u3092 $\\{\\bm{f}_j\\}$ \u3068\u3059\u308b\u3068\u3001\u305d\u306e\u7d44\u307f\u5408\u308f\u305b $\\bm{e}_i\\otimes\\bm{f}_j$ \u306f $mn$ \u901a\u308a\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u3092\u57fa\u5e95\u3068\u3059\u308b $mn$ \u6b21\u5143\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092 $V$ \u3068 $W$ \u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u7a7a\u9593\u3068\u547c\u3073\u3001$V\\otimes W$ \u3068\u66f8\u304d\u307e\u3059\u3002<\/p>\n<p>\u5408\u6210\u7cfb\u306e\u72b6\u614b\u7a7a\u9593\u304c\u3053\u306e\u69cb\u6210\u3067\u4e0e\u3048\u3089\u308c\u308b\u306e\u306f\u3001\u672c\u6587\u306e\u591a\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u306e\u7bc0\u3067\u8ff0\u3079\u305f\u3068\u304a\u308a\u3001\u5404\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u53d6\u308a\u3046\u308b\u72b6\u614b\u306e\u3042\u3089\u3086\u308b\u7d44\u307f\u5408\u308f\u305b\u304c\u72ec\u7acb\u306a\u72b6\u614b\u3068\u3057\u3066\u8a31\u3055\u308c\u308b\u304b\u3089\u3067\u3059\u3002$1$ \u91cf\u5b50\u30d3\u30c3\u30c8\u76ee\u304c $\\ket{0},\\ket{1}$ \u306e $2$ \u901a\u308a\u3001$2$ \u91cf\u5b50\u30d3\u30c3\u30c8\u76ee\u3082 $2$ \u901a\u308a\u3067\u3042\u308c\u3070\u3001$2$ \u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u3067\u306f $4$ \u901a\u308a\u304c\u72ec\u7acb\u306a\u57fa\u5e95\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u30d9\u30af\u30c8\u30eb\u540c\u58eb\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d $\\bm{v}\\otimes\\bm{w}$ \u306f\u3001\u6210\u5206\u304c $\\left(\\bm{v}\\otimes\\bm{w}\\right)_{ij}=v_iw_j$ \u3068\u306a\u308b\u3082\u306e\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u884c\u5217\u3068\u3057\u3066\u66f8\u3051\u3070<\/p>\n<p>$$\\bm{v}\\otimes\\bm{w}\\ \\longleftrightarrow\\ \\begin{pmatrix}v_0w_0&amp;v_0w_1\\\\v_1w_0&amp;v_1w_1\\end{pmatrix}=\\begin{pmatrix}v_0\\\\v_1\\end{pmatrix}\\begin{pmatrix}w_0&amp;w_1\\end{pmatrix}\\tag{76}$$<\/p>\n<p>\u3068\u306a\u308a\u3001\u5217\u30d9\u30af\u30c8\u30eb\u3068\u884c\u30d9\u30af\u30c8\u30eb\u306e\u7a4d\u306e\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u3002\u305f\u3060\u3057 $V\\otimes W$ \u306e\u5143\u304c\u3059\u3079\u3066 $\\bm{v}\\otimes\\bm{w}$ \u306e\u5f62\u306b\u66f8\u3051\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30c6\u30f3\u30bd\u30eb\u7a4d\u306f\u57fa\u5e95\u3092\u62e1\u5f35\u3057\u305f\u3060\u3051\u306a\u306e\u3067\u305d\u306e\u4fc2\u6570\u306f\u5236\u7d04\u3092\u53d7\u3051\u305a\u3001$V\\otimes W$ \u306e\u5143\u306f\u4e00\u822c\u7684\u306b\u5f0f(77)\u306e\u5f62\u3067\u66f8\u3051\u307e\u3059\u3002<br \/>$$\\bm{u}\\ \\longleftrightarrow\\ \\begin{pmatrix}u_{00}&amp;u_{01}\\\\u_{10}&amp;u_{11}\\end{pmatrix}\\tag{77}$$<\/p>\n<p>\u5f0f(76)\u306e\u5f62\u3067\u66f8\u3051\u308b\u5143\u304c\u672c\u6587\u3067\u3044\u3046\u300c\u5404\u30d3\u30c3\u30c8\u304c\u72ec\u7acb\u306a\u72b6\u614b\u300d\u3001\u66f8\u3051\u306a\u3044\u5143\u304c\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\u3001\u30c6\u30f3\u30bd\u30eb\u7a4d\u306e\u5f62\u3067\u304b\u3051\u308b\u884c\u5217\u306f\u30e9\u30f3\u30af\u304c\u6700\u5927\u3067\u3082 $1$ \u3067\u3059\u304c\u3001\u5f0f(77)\u306e\u4e00\u822c\u306e\u5143\u306f\u30e9\u30f3\u30af $2$ \u4ee5\u4e0a\u306b\u3082\u306a\u308a\u5f97\u307e\u3059\u3002<br \/>\u30e9\u30f3\u30af $2$ \u4ee5\u4e0a\u306e\u3068\u304d\u3001\u305d\u306e\u7cfb\u306f\u30a8\u30f3\u30bf\u30f3\u30b0\u30eb\u72b6\u614b\u3067\u3042\u308b\u3068\u3044\u3048\u307e\u3059\u3002<\/p>\n<p>$2\\times2$ \u306e\u5834\u5408\u3001\u30e9\u30f3\u30af\u304c$2$\u3067\u6b63\u5247\u884c\u5217\u3068\u306a\u308b\u305f\u3081\u3053\u306e\u5224\u5b9a\u306f\u884c\u5217\u5f0f\u304c $0$ \u304b\u3069\u3046\u304b\u3067\u884c\u3048\u307e\u3059\u3002\u5b9f\u969b\u306b\u5f0f(76)\u3067\u306f$0$\u306b\u306a\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u6f14\u7b97\u5b50\u306b\u3064\u3044\u3066\u3082\u540c\u3058\u3067\u3059\u3002$V$ \u306b\u4f5c\u7528\u3059\u308b\u884c\u5217 $A$ \u3068 $W$ \u306b\u4f5c\u7528\u3059\u308b\u884c\u5217 $B$ \u304b\u3089\u3001$V\\otimes W$ \u306b\u4f5c\u7528\u3059\u308b\u884c\u5217 $A\\otimes B$ \u304c<\/p>\n<p>$$\\left(A\\otimes B\\right)_{ij,kl}=a_{ik}b_{jl}\\tag{78}$$<\/p>\n<p>\u306b\u3088\u3063\u3066\u5b9a\u307e\u308a\u307e\u3059\u3002\u884c\u5217\u306e\u6210\u5206\u304c $2$ \u6dfb\u5b57\u3060\u3063\u305f\u306e\u3067\u3001$A\\otimes B$\u306e\u6210\u5206\u306f $4$ \u6dfb\u5b57\u306e\u914d\u5217\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3068\u3053\u308d\u304c\u672c\u6587\u3067\u306f\u3001\u72b6\u614b\u3092 $2^N$ \u6b21\u5143\u306e\u5217\u30d9\u30af\u30c8\u30eb\u3001\u30b2\u30fc\u30c8\u3092 $2^N\\times2^N$ \u884c\u5217\u3068\u3057\u3066\u3001\u72b6\u614b\u306e\u30c6\u30f3\u30bd\u30eb\u306e\u6dfb\u5b57\u3092 $1$ \u3064\u306b\u307e\u3068\u3081\u305f\u5f62\u3067\u66f8\u3044\u3066\u3044\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u7406\u7531\u306f\u3001$1$ \u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u3068\u304d\u3068\u540c\u3058\u3088\u3046\u306b\u884c\u5217\u306e\u7a4d\u3001\u56fa\u6709\u5024\u3001\u30e6\u30cb\u30bf\u30ea\u6027\u306a\u3069\u306e\u7dda\u5f62\u4ee3\u6570\u306b\u304a\u3051\u308b\u6027\u8cea\u304c\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u3088\u3046\u306b\u3059\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<p>$$\\begin{pmatrix}u_{00}&amp;u_{01}\\\\u_{10}&amp;u_{11}\\end{pmatrix}\\ \\longrightarrow\\ \\begin{pmatrix}u_{00}\\\\u_{01}\\\\u_{10}\\\\u_{11}\\end{pmatrix}\\tag{79}$$<\/p>\n<p>\u91cf\u5b50\u8ad6\u304c\u72b6\u614b\u7a7a\u9593\u306b\u8981\u6c42\u3059\u308b\u306e\u306f\u30d2\u30eb\u30d9\u30eb\u30c8\u7a7a\u9593\u3067\u3042\u308b\u3053\u3068\u3060\u3051\u306a\u306e\u3067\u3001\u3053\u308c\u306f\u91cf\u5b50\u8ad6\u306b\u304a\u3044\u3066\u4e00\u822c\u7684\u306b\u7528\u3044\u3089\u308c\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/p>\n<p>\u672c\u6587\u3067\u306f $C_{00},C_{01},C_{10},C_{11}$ \u306e\u3088\u3046\u306b$2$\u9032\u6570\u3067\u898b\u3066\u6607\u9806\u306b\u4e26\u3079\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0a\u3092\u8e0f\u307e\u3048\u3066\u5f0f(76)\u306e\u64cd\u4f5c\u3092\u8003\u3048\u308b\u3068\u5f0f(80)\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$\\begin{pmatrix}v_0\\\\v_1\\end{pmatrix}\\otimes\\begin{pmatrix}w_0\\\\w_1\\end{pmatrix}=\\begin{pmatrix}v_0\\begin{pmatrix}w_0\\\\w_1\\end{pmatrix}\\\\v_1\\begin{pmatrix}w_0\\\\w_1\\end{pmatrix}\\end{pmatrix}=\\begin{pmatrix}v_0w_0\\\\v_0w_1\\\\v_1w_0\\\\v_1w_1\\end{pmatrix}\\tag{80}$$<\/p>\n<p>$\\ket{0}=\\begin{pmatrix}1\\\\0\\end{pmatrix}$\u3001$\\ket{1}=\\begin{pmatrix}0\\\\1\\end{pmatrix}$ \u3092\u4ee3\u5165\u3059\u308b\u3068<\/p>\n<p>$$\\ket{0}\\otimes\\ket{0}=\\begin{pmatrix}1\\\\0\\\\0\\\\0\\end{pmatrix},\\hspace{5pt}\\ket{0}\\otimes\\ket{1}=\\begin{pmatrix}0\\\\1\\\\0\\\\0\\end{pmatrix},\\hspace{5pt}\\ket{1}\\otimes\\ket{0}=\\begin{pmatrix}0\\\\0\\\\1\\\\0\\end{pmatrix},\\hspace{5pt}\\ket{1}\\otimes\\ket{1}=\\begin{pmatrix}0\\\\0\\\\0\\\\1\\end{pmatrix}\\tag{81}$$<\/p>\n<p>\u3068\u306a\u308a\u3001\u4e92\u3044\u306b\u76f4\u4ea4\u3059\u308b $4$ \u3064\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u672c\u6587\u3067\u306f\u3053\u308c\u3089\u3092 $\\ket{00},\\ket{01},\\ket{10},\\ket{11}$ \u3068\u7565\u8a18\u3057\u3066\u304a\u308a\u3001\u5de6\u5074\u304c $1$ \u91cf\u5b50\u30d3\u30c3\u30c8\u76ee\u3001\u53f3\u5074\u304c $2$ \u91cf\u5b50\u30d3\u30c3\u30c8\u76ee\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002$N$ \u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u3067\u306f\u3053\u308c\u3092 $N$ \u500b\u7e70\u308a\u8fd4\u3059\u3053\u3068\u306b\u306a\u308a\u3001\u672c\u6587\u306e $\\bigotimes_{j=1}^{N}$ \u306f\u305d\u306e\u7e70\u308a\u8fd4\u3057\u3092\u8868\u3059\u8a18\u53f7\u3067\u3059\u3002<\/p>\n<p>\u6f14\u7b97\u5b50\u306b\u3064\u3044\u3066\u3082\u540c\u3058\u7d04\u675f\u306e\u3082\u3068\u3067 $4$ \u6dfb\u5b57\u304c $2$ \u6dfb\u5b57\u306b\u307e\u3068\u307e\u308a\u3001\u5f0f(78)\u306f\u4e00\u65b9\u306e\u884c\u5217\u306e\u5404\u6210\u5206\u306b\u3082\u3046\u4e00\u65b9\u306e\u884c\u5217\u3092\u639b\u3051\u305f\u30d6\u30ed\u30c3\u30af\u884c\u5217\u3068\u3057\u3066\u66f8\u3051\u307e\u3059\u3002<\/p>\n<p>$$A\\otimes B=\\begin{pmatrix}a_{00}&amp;a_{01}\\\\a_{10}&amp;a_{11}\\end{pmatrix}\\otimes B=\\begin{pmatrix}a_{00}B&amp;a_{01}B\\\\a_{10}B&amp;a_{11}B\\end{pmatrix}\\tag{82}$$<\/p>\n<p>\u305f\u3068\u3048\u3070 $1$ \u91cf\u5b50\u30d3\u30c3\u30c8\u76ee\u306b\u306e\u307f $X$ \u30b2\u30fc\u30c8\u3092\u4f5c\u7528\u3055\u305b\u308b\u64cd\u4f5c\u306f $X\\otimes I$ \u3068\u66f8\u3051\u3001<\/p>\n<p>$$X\\otimes I=\\begin{pmatrix}0\\cdot I&amp;1\\cdot I\\\\1\\cdot I&amp;0\\cdot I\\end{pmatrix}=\\begin{pmatrix}0&amp;0&amp;1&amp;0\\\\0&amp;0&amp;0&amp;1\\\\1&amp;0&amp;0&amp;0\\\\0&amp;1&amp;0&amp;0\\end{pmatrix}\\tag{83}$$<\/p>\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u672c\u6587\u3067 $CNOT$ \u3092\u5165\u308c\u5b50\u306e\u30d6\u30ed\u30c3\u30af\u884c\u5217\u3068\u3057\u3066\u66f8\u3044\u3066\u3044\u308b\u306e\u3082\u3001\u3053\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u306e\u69cb\u9020\u3092\u53cd\u6620\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u30c6\u30f3\u30bd\u30eb\u7a4d\u306f\u9806\u5e8f\u3092\u5165\u308c\u66ff\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002$A\\otimes B$ \u3068 $B\\otimes A$ \u306f\u4e00\u822c\u306b\u7570\u306a\u308b\u884c\u5217\u3067\u3001\u3053\u308c\u306f\u300c\u3069\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u3069\u306e\u30b2\u30fc\u30c8\u3092\u4f5c\u7528\u3055\u305b\u308b\u304b\u300d\u304c\u9055\u3046\u305f\u3081\u3067\u3059\u3002\u672c\u6587\u3067 $X\\otimes I\\otimes I\\otimes\\cdots$ \u3092 $X_1$ \u3068\u7565\u8a18\u3057\u3066\u3044\u308b\u306e\u306f\u3001\u3053\u306e\u4f4d\u7f6e\u306e\u60c5\u5831\u3092\u6dfb\u5b57\u3067\u8868\u3057\u305f\u3082\u306e\u3067\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Uthetae-itheta_H%E3%81%AE%E5%B0%8E%E5%87%BA\"><\/span>$U(\\theta)=e^{-i\\theta H}$\u306e\u5c0e\u51fa<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u307e\u305a\u30e6\u30cb\u30bf\u30ea\u6027\u306e\u6761\u4ef6\u304b\u3089<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$U(\\theta)U(\\theta)^\u2020=I\\tag{84}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4e21\u8fba\u3092$\\theta$\u3067\u5fae\u5206\u3057\u3066<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{dU(\\theta)}{d\\theta}U(\\theta)^\u2020+U(\\theta)\\frac{dU(\\theta)^\u2020}{d\\theta}=0\\tag{85}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{dU(\\theta)}{d\\theta}U(\\theta)^\u2020=-U(\\theta)\\frac{dU(\\theta)^\u2020}{d\\theta}\\tag{86}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u53f3\u8fba\u306e\u5171\u5f79\u8ee2\u7f6e\u3092\u62ec\u308a\u51fa\u3057\u3066(\u8ee2\u7f6e\u306a\u306e\u3067\u884c\u5217\u306e\u7a4d\u306e\u9806\u5e8f\u304c\u9006\u306b\u306a\u308a\u307e\u3059)<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{dU(\\theta)}{d\\theta}U(\\theta)^\u2020=-(\\frac{dU(\\theta)}{d\\theta}U(\\theta)^\u2020)^\u2020\\tag{87}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u308c\u306f$\\frac{dU(\\theta)}{d\\theta}U(\\theta)^\u2020$\u304c\u53cd\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217(\u5171\u5f79\u8ee2\u7f6e\u3092\u3068\u308b\u3068\u81ea\u5206\u81ea\u8eab\u306b$-1$\u3092\u639b\u3051\u305f\u5024\u306b\u306a\u308b\u884c\u5217)\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u53cd\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306b$i$\u3092\u304b\u3051\u308b\u3053\u3068\u3067\u8868\u73fe\u3067\u304d\u308b\u305f\u3081(\u5171\u5f79\u3092\u3068\u3063\u3066\u7b26\u53f7\u304c\u53cd\u8ee2\u3059\u308b\u3088\u3046\u306b)\u3001$\\theta$\u306b\u4f9d\u5b58\u3057\u306a\u3044\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217$H$\u3092\u4f7f\u3063\u3066<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{dU(\\theta)}{d\\theta}U(\\theta)^\u2020=-iH\\tag{88}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3068\u8868\u305b\u307e\u3059\u3002\u3053\u3053\u3067\u30de\u30a4\u30ca\u30b9\u3092\u304b\u3051\u3066\u3044\u308b\u306e\u306f\u6700\u7d42\u7684\u306a\u5f62\u3092\u4e0a\u8a18\u306e\u5f0f\u306b\u5408\u308f\u305b\u308b\u305f\u3081\u3067\u3059\u304c\u3001\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u306f\u5b9f\u6570\u3092\u304b\u3051\u3066\u3082\u30a8\u30eb\u30df\u30fc\u30c8\u6027\u3092\u7dad\u6301\u3059\u308b\u305f\u3081\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u4e21\u8fba\u306b$U(\\theta)$\u3092\u53f3\u304b\u3089\u304b\u3051\u308b\u3068\u3001$U(\\theta)^\u2020U(\\theta)=I$\u3088\u308a<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$\\frac{dU(\\theta)}{d\\theta}=-iHU(\\theta)\\tag{89}$$<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>\u3053\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u521d\u671f\u6761\u4ef6$U(0)=I$\u306e\u5143\u3067\u89e3\u304f\u3068<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>$$U(\\theta)=e^{-i\\theta H}\\tag{90}$$<\/p>\n<!-- \/wp:paragraph -->\n<p>&nbsp;<\/p>\n<!-- wp:paragraph -->\n<p>\u304c\u5c0e\u51fa\u3055\u308c\u307e\u3059\u3002<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading \/-->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E4%BD%9C%E6%88%90%E8%80%85\"><\/span>\u672c\u8a18\u4e8b\u306e\u4f5c\u6210\u8005<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p>\u6fa4\u7530\u76f4\u6a39<\/p>\n<!-- \/wp:paragraph -->\n<p>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6301\u3063\u305f\u91cf\u5b50\u56de\u8def\u305d\u306e\u3082\u306e\u3092\u5b66\u7fd2\u30e2\u30c7\u30eb\u3068\u3057\u3066\u6271\u3046\u67a0\u7d44\u307f\u3001\u91cf\u5b50\u56de\u8def\u5b66\u7fd2\u306e\u63d0\u6848\u8ad6\u6587\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002\u306a\u305c\u6d45\u3044\u56de\u8def\u3067\u975e\u7dda\u5f62\u306a\u95a2\u6570\u304c\u8868\u73fe\u3067\u304d\u308b\u306e\u304b\u3001\u306a\u305c\u52fe\u914d\u304c\u671f\u5f85\u5024\u306e\u6e2c\u5b9a\u3060\u3051\u3067\u53b3\u5bc6\u306b\u6c42\u307e\u308b\u306e\u304b\u3092\u3001\u7dda\u5f62\u4ee3\u6570\u306e\u77e5\u8b58\u3060\u3051\u3067\u8ffd\u3048\u308b\u3088\u3046\u306b\u3001\u5bc6\u5ea6\u6f14\u7b97\u5b50\u3068\u30d1\u30a6\u30ea\u57fa\u5e95\u306e\u8996\u70b9\u304b\u3089\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"author":32,"featured_media":9132,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[104,330,329,149,126,331],"class_list":["post-8676","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-review","tag-104","tag-330","tag-329","tag-149","tag-126","tag-331"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u91cf\u5b50\u56de\u8def\u5b66\u7fd2 - 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\/2026\/09\/18\/\u91cf\u5b50\u56de\u8def\u5b66\u7fd2\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u91cf\u5b50\u56de\u8def\u5b66\u7fd2 - T-QARD Harbor\" \/>\n<meta property=\"og:description\" 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