{"id":8011,"date":"2025-10-30T17:34:40","date_gmt":"2025-10-30T08:34:40","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=8011"},"modified":"2026-03-30T10:49:57","modified_gmt":"2026-03-30T01:49:57","slug":"bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/","title":{"rendered":"BP+OSD #1 \u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u57fa\u790e"},"content":{"rendered":"\n<script>\nwindow.MathJax = {\n  tex: {\n    inlineMath: [['$', '$'], ['\\\\(', '\\\\)']],\n    packages: {'[+]': ['ams']},\n    tags: 'ams'\n  }\n};\n<\/script>\n\n\n<div class=\"taxonomy-post_tag wp-block-post-terms\"><a 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class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\" >\u6587\u732e\u60c5\u5831<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E6%A6%82%E8%A6%81\" >\u6982\u8981<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E9%87%8F%E5%AD%90%E8%AA%A4%E3%82%8A%E8%A8%82%E6%AD%A3%E7%AC%A6%E5%8F%B7%E3%81%AE%E3%83%A2%E3%83%81%E3%83%99%E3%83%BC%E3%82%B7%E3%83%A7%E3%83%B3\" >\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u30e2\u30c1\u30d9\u30fc\u30b7\u30e7\u30f3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E5%9F%BA%E6%9C%AC%E7%9A%84%E3%81%AA%E3%82%A2%E3%82%A4%E3%83%87%E3%82%A2\" >\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E3%82%A2%E3%82%A4%E3%83%87%E3%82%A2%E3%82%92%E5%AE%9F%E7%8F%BE%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95\" >\u30a2\u30a4\u30c7\u30a2\u3092\u5b9f\u73fe\u3059\u308b\u65b9\u6cd5<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E3%82%A8%E3%83%A9%E3%83%BC%E3%81%AE%E6%9C%89%E7%84%A1%E3%82%92%E5%88%A4%E5%AE%9A%E3%81%99%E3%82%8B%E6%BC%94%E7%AE%97%E5%AD%90%EF%BC%9A%E3%82%B9%E3%82%BF%E3%83%93%E3%83%A9%E3%82%A4%E3%82%B6\" >\u30a8\u30e9\u30fc\u306e\u6709\u7121\u3092\u5224\u5b9a\u3059\u308b\u6f14\u7b97\u5b50\uff1a\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E3%82%B7%E3%83%B3%E3%83%89%E3%83%AD%E3%83%BC%E3%83%A0%E5%80%A4%E3%81%8B%E3%82%89%E3%82%A8%E3%83%A9%E3%83%BC%E3%81%AE%E6%83%85%E5%A0%B1%E3%82%92%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%99\" >\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u306e\u60c5\u5831\u3092\u53d6\u308a\u51fa\u3059<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E3%82%B7%E3%83%B3%E3%83%89%E3%83%AD%E3%83%BC%E3%83%A0%E5%80%A4%E3%81%8B%E3%82%89%E3%82%A8%E3%83%A9%E3%83%BC%E3%82%92%E6%8E%A8%E5%AE%9A%E3%81%99%E3%82%8B%EF%BC%9A%E3%83%87%E3%82%B3%E3%83%BC%E3%83%89\" >\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u3092\u63a8\u5b9a\u3059\u308b\uff1a\u30c7\u30b3\u30fc\u30c9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E9%87%8F%E5%AD%90%E8%AA%A4%E3%82%8A%E8%A8%82%E6%AD%A3%E3%81%AE%E6%89%8B%E9%A0%86%E3%81%BE%E3%81%A8%E3%82%81\" >\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u306e\u624b\u9806\u307e\u3068\u3081<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E3%83%91%E3%83%AA%E3%83%86%E3%82%A3%E3%83%81%E3%82%A7%E3%83%83%E3%82%AF%E8%A1%8C%E5%88%97\" >\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#CSS%E7%AC%A6%E5%8F%B7\" >CSS\u7b26\u53f7<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E3%81%BE%E3%81%A8%E3%82%81\" >\u307e\u3068\u3081<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/10\/30\/bposd-1-%e9%87%8f%e5%ad%90%e8%aa%a4%e3%82%8a%e8%a8%82%e6%ad%a3%e7%ac%a6%e5%8f%b7%e3%81%ae%e5%9f%ba%e7%a4%8e\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u30bf\u30a4\u30c8\u30eb\uff1a<a href=\"https:\/\/quantum-journal.org\/papers\/q-2021-11-22-585\/#\">Degenerate Quantum LDPC Codes With Good Finite Length Performance<\/a><\/li>\n\n\n\n<li>\u8457\u8005\uff1aPavel Panteleev&nbsp;and&nbsp;Gleb Kalachev<\/li>\n\n\n\n<li>\u66f8\u8a8c\u60c5\u5831(DOI)\uff1a<a href=\"https:\/\/doi.org\/10.22331\/q-2021-11-22-585\">https:\/\/doi.org\/10.22331\/q-2021-11-22-585<\/a><\/li>\n\n\n\n<li>\u51fa\u7248\u5e74\uff1a2021\u5e7411\u6708<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u3001\u5f93\u6765\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u306f\u8a08\u7b97\u304c\u56f0\u96e3\u306a\u4e00\u90e8\u306e\u554f\u984c\u3092\u52b9\u7387\u3088\u304f\u89e3\u3051\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u7269\u6027\u306b\u95a2\u3059\u308b\u8a08\u7b97\u3084\u7d20\u56e0\u6570\u5206\u89e3\u3092\u52b9\u7387\u3088\u304f\u884c\u3046\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3057\u304b\u3057\u3001\u3053\u308c\u3089\u306e\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u52b9\u7387\u3088\u304f\u5b9f\u884c\u3067\u304d\u308b\u3068\u671f\u5f85\u3055\u308c\u3066\u3044\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u5927\u91cf\u306e\u91cf\u5b50\u30d3\u30c3\u30c8\u3068\u5927\u91cf\u306e\u91cf\u5b50\u30b2\u30fc\u30c8\u3092\u5fc5\u8981\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u5927\u898f\u6a21\u306a\u91cf\u5b50\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u751f\u3058\u308b\u30ce\u30a4\u30ba\u3092\u7121\u8996\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u91cf\u5b50\u30d3\u30c3\u30c8\u304c\u591a\u3051\u308c\u3070\u591a\u3044\u307b\u3069\u30a8\u30e9\u30fc\u304c\u8d77\u3053\u308b\u78ba\u7387\u306f\u9ad8\u307e\u308a\u3001\u91cf\u5b50\u30b2\u30fc\u30c8\u304c\u591a\u3051\u308c\u3070\u591a\u3044\u307b\u3069\u30a8\u30e9\u30fc\u306f\u84c4\u7a4d\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306a\u91cf\u5b50\u30a8\u30e9\u30fc\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u306b\u3001\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u306e\u7406\u8ad6\u304c\u69cb\u7bc9\u3055\u308c\u3066\u304d\u307e\u3057\u305f\u3002\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7406\u8ad6\u3067\u306f\u3001\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u3068\u547c\u3070\u308c\u308b\u7b26\u53f7\u3092\u7528\u3044\u3066\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u60c5\u5831\u3092\u4fdd\u8b77\u3057\u307e\u3059\u3002\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u3092\u7528\u3044\u3066\u30a8\u30e9\u30fc\u3092\u8a02\u6b63\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u30a8\u30e9\u30fc\u306e\u60c5\u5831\u3092\u9593\u63a5\u7684\u306b\u8aad\u307f\u51fa\u3057\u3001\u305d\u306e\u60c5\u5831\u304b\u3089\u30a8\u30e9\u30fc\u3092\u63a8\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u51e6\u7406\u3092\u30c7\u30b3\u30fc\u30c9\u3068\u547c\u3073\u3001\u30c7\u30b3\u30fc\u30c9\u3092\u884c\u3046\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u30c7\u30b3\u30fc\u30c0\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001qLDPC\u7b26\u53f7\u3068\u547c\u3070\u308c\u308b\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306b\u304a\u3044\u3066\u9ad8\u6027\u80fd\u306a\u30c7\u30b3\u30fc\u30c0\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308bBP+OSD\u30c7\u30b3\u30fc\u30c0\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u307e\u3059\u3002\u5168\u4f53\u306e\u5185\u5bb9\u306f3\u3064\u306e\u8a18\u4e8b\u304b\u3089\u69cb\u6210\u3055\u308c\u3066\u3044\u3066\u3001\u305d\u308c\u305e\u308c\u6b21\u306e\u3088\u3046\u306a\u5185\u5bb9\u3092\u6271\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u57fa\u790e\uff08#1\uff09<\/li>\n\n\n\n<li>BP\u30c7\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\uff08#2\uff09<\/li>\n\n\n\n<li>OSD\u3068BP\u306e\u9023\u643a\uff08#3\uff09<\/li>\n<\/ul>\n\n\n\n<p>\u4eca\u56de\u306e\u8a18\u4e8b\u3067\u306f\u3001\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u57fa\u790e\u306b\u3064\u3044\u3066\u3001BP+OSD\u30c7\u30b3\u30fc\u30c0\u306e\u7406\u89e3\u306b\u5fc5\u8981\u306a\u90e8\u5206\u3092\u91cd\u70b9\u7684\u306b\u89e3\u8aac\u3057\u307e\u3059\u3002\u306f\u3058\u3081\u306b\u3001\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u30e2\u30c1\u30d9\u30fc\u30b7\u30e7\u30f3\u3068\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u3068\u547c\u3070\u308c\u308b\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u30af\u30e9\u30b9\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u306f\u3059\u3079\u3066\u306e\u8a18\u4e8b\u3092\u901a\u3057\u3066\u4e2d\u5fc3\u7684\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3059\u3002\u7d9a\u3044\u3066\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u3092\u6271\u3044\u3084\u3059\u3044\u5f62\u3067\u8868\u73fe\u3059\u308b\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001BP+OSD\u30c7\u30b3\u30fc\u30c0\u3067\u30c7\u30b3\u30fc\u30c9\u3067\u304d\u308bCSS\u7b26\u53f7\u3068\u547c\u3070\u308c\u308b\u7b26\u53f7\u30af\u30e9\u30b9\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E8%AA%A4%E3%82%8A%E8%A8%82%E6%AD%A3%E7%AC%A6%E5%8F%B7%E3%81%AE%E3%83%A2%E3%83%81%E3%83%99%E3%83%BC%E3%82%B7%E3%83%A7%E3%83%B3\"><\/span>\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u30e2\u30c1\u30d9\u30fc\u30b7\u30e7\u30f3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u91cf\u5b50\u30d3\u30c3\u30c8\u306f\u30ce\u30a4\u30ba\u306b\u3055\u3089\u3055\u308c\u3084\u3059\u304f\u3001\u3069\u308c\u3060\u3051\u6b63\u78ba\u306b\u72b6\u614b\u3092\u6e96\u5099\u3057\u3066\u3082\u305d\u306e\u307e\u307e\u653e\u7f6e\u3057\u3066\u3044\u308c\u3070\u3059\u3050\u306b\u72b6\u614b\u304c\u5909\u308f\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u5177\u4f53\u4f8b\u3092\u898b\u308b\u305f\u3081\u306b\u3001\u307e\u305a\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u3092\u8a18\u8ff0\u3059\u308b\u65b9\u6cd5\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u3042\u308b\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b $\\ket \\psi$\u306f\u4e00\u822c\u306b\u3001<\/p>\n\n\n\n<p>$$ <br>\\begin{align}\\ket{\\psi} = \\alpha \\ket0+\\beta\\ket 1\\quad (\\alpha,\\beta\\in \\mathbb C,|\\alpha|^2+|\\beta|^2=1)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067 $\\ket 0,\\ket 1$\u306f\u76f4\u4ea4\u3059\u308b\u30d9\u30af\u30c8\u30eb\u3067\u3001<\/p>\n\n\n\n<p>$$ <br>\\begin{align}\\ket0=\\begin{pmatrix}1\\\\0\\end{pmatrix},\\quad \\ket1=\\begin{pmatrix}0\\\\1\\end{pmatrix}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u8868\u305b\u307e\u3059\u3002\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b $\\ket{\\psi}$\u306b\u5bfe\u3057\u3066\u30ce\u30a4\u30ba\u304c\u52a0\u308f\u308b\u3068\u3001\u4f8b\u3048\u3070<\/p>\n\n\n\n<p>$$ <br>\\begin{align}\\alpha\\ket0+\\beta\\ket1\\to\\beta\\ket0+\\alpha\\ket1\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306e\u3088\u3046\u306b\u3001\u30d9\u30af\u30c8\u30eb\u306e\u4fc2\u6570\u90e8\u5206\u304c\u3072\u3063\u304f\u308a\u8fd4\u3063\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30a8\u30e9\u30fc\u3092\u300c\u30d3\u30c3\u30c8\u53cd\u8ee2\u30a8\u30e9\u30fc\u300d\u3068\u3044\u3044\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30a8\u30e9\u30fc\u306f\u81ea\u7136\u3068\u3001\u3057\u304b\u3082\u983b\u7e41\u306b\u8d77\u3053\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u3067\u3059\u304b\u3089\u3001\u3069\u3046\u306b\u304b\u3057\u3066\u30a8\u30e9\u30fc\u3092\u691c\u51fa\u3057\u3066\u3001\u305d\u308c\u3092\u6253\u3061\u6d88\u3059\u3088\u3046\u306a\u8a02\u6b63\u64cd\u4f5c\u3092\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%9F%BA%E6%9C%AC%E7%9A%84%E3%81%AA%E3%82%A2%E3%82%A4%E3%83%87%E3%82%A2\"><\/span>\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u306f\u3058\u3081\u306b\u3056\u3063\u304f\u308a\u3068\u3057\u305f\u30a2\u30a4\u30c7\u30a2\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u30a8\u30e9\u30fc\u3092\u691c\u51fa\u3057\u3066\u8a02\u6b63\u3059\u308b\u305f\u3081\u306e\u57fa\u672c\u6226\u7565\u306f<strong>\u91cf\u2f26\u30d3\u30c3\u30c8\u3092\u3088\u308a\u2f24\u304d\u306a\u7a7a\u9593\u306b\u57cb\u3081\u8fbc\u3093\u3067\u5197\u2ed1\u6027\u3092\u3082\u305f\u305b\u308b\u3053\u3068<\/strong>\u3067\u3059\u3002\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u57cb\u3081\u8fbc\u307f\u306f\u6b21\u306e\u3088\u3046\u306a\u624b\u9806\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u57cb\u3081\u8fbc\u3080\u72b6\u614b\u3092\u6e96\u5099\u3059\u308b<\/li>\n\n\n\n<li>\u30a8\u30f3\u30b3\u30fc\u30c0\u3092\u7528\u3044\u3066\u305d\u306e\u72b6\u614b\u3092\u5927\u304d\u306a\u7a7a\u9593\u306b\u57cb\u3081\u8fbc\u307f\u3001\u5927\u304d\u306a\u7a7a\u9593\u4e0a\u3067\u91cf\u5b50\u8a08\u7b97\u3092\u5b9f\u884c\u3059\u308b<\/li>\n\n\n\n<li>\u30c7\u30b3\u30fc\u30c0\u3092\u7528\u3044\u3066\u8a08\u7b97\u5f8c\u306e\u72b6\u614b\u3092\u5fa9\u5143\u3059\u308b\u3053\u3068\u3067\u6b63\u3057\u3044\u72b6\u614b\u3092\u5f97\u308b\u3002\u30c7\u30b3\u30fc\u30c0\u306e\u5185\u90e8\u3067\u306f\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3068\u547c\u3070\u308c\u308b\u7269\u7406\u91cf\u306b\u4ed8\u3044\u3066\u6e2c\u5b9a\u3092\u884c\u3044\u3001\u5f97\u3089\u308c\u305f\u6e2c\u5b9a\u5024\u304b\u3089\u30a8\u30e9\u30fc\u306e\u691c\u51fa\u3068\u63a8\u5b9a\u3092\u884c\u3046<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306e\u624b\u9806\u3092\u56f3\u793a\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306a\u30a4\u30e1\u30fc\u30b8\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"546\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1024x546.png\" alt=\"\" class=\"wp-image-8016\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1024x546.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-300x160.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-768x410.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1536x819.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-2048x1092.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f31: \u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u306e\u5168\u4f53\u50cf<\/figcaption><\/figure>\n\n\n\n<p>\u672c\u6765\u3067\u3042\u308c\u3070\u5927\u304d\u306a\u7a7a\u9593\u306b\u57cb\u3081\u8fbc\u3093\u3060\u307e\u307e\u91cf\u5b50\u8a08\u7b97\u3092\u3059\u308b\u65b9\u6cd5\u306a\u3069\u3092\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u3053\u3067\u306f\u7c21\u5358\u306e\u305f\u3081\u306b\u91cf\u5b50\u8a08\u7b97\u306f\u8003\u3048\u305a\u306b\u91cf\u5b50\u72b6\u614b\u3092\u4fdd\u5b58\u3059\u308b\u3053\u3068\u3060\u3051\u3092\u8003\u3048\u307e\u3059<sup data-fn=\"1f00f91a-3bc5-4115-a3fa-e79e81e58117\" class=\"fn\"><a id=\"1f00f91a-3bc5-4115-a3fa-e79e81e58117-link\" href=\"#1f00f91a-3bc5-4115-a3fa-e79e81e58117\">1<\/a><\/sup>\u3002\u3055\u3089\u306b\u7c21\u5358\u306e\u305f\u3081\u306b\u3001\u30ce\u30a4\u30ba\u306f\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u305f\u72b6\u614b\u306b\u3057\u304b\u751f\u3058\u306a\u3044\u3082\u306e\u3068\u3057\u307e\u3059<sup data-fn=\"36f272c7-526e-49c6-9e00-5b4d1ef473c8\" class=\"fn\"><a id=\"36f272c7-526e-49c6-9e00-5b4d1ef473c8-link\" href=\"#36f272c7-526e-49c6-9e00-5b4d1ef473c8\">2<\/a><\/sup>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%A2%E3%82%A4%E3%83%87%E3%82%A2%E3%82%92%E5%AE%9F%E7%8F%BE%E3%81%99%E3%82%8B%E6%96%B9%E6%B3%95\"><\/span>\u30a2\u30a4\u30c7\u30a2\u3092\u5b9f\u73fe\u3059\u308b\u65b9\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u3053\u304b\u3089\u306f\u300c\u5197\u9577\u6027\u3092\u3082\u305f\u305b\u308b\u300d\u3068\u3044\u3046\u30a2\u30a4\u30c7\u30a2\u3092\u5b9f\u73fe\u3059\u308b\u65b9\u6cd5\u3092\u5177\u4f53\u7684\u306b\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u307e\u305a\u306f\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u57cb\u3081\u8fbc\u307f\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\u3002 $k$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u3092\u305d\u308c\u3088\u308a\u5927\u304d\u306a $n$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b\u3067\u8868\u73fe\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001 $k$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b $\\ket{\\psi}$\u306b\u5bfe\u5fdc\u3059\u308b $n$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b $\\ket{\\psi_L}$\u3092<strong>\u8ad6\u7406\u72b6\u614b<\/strong>\u3068\u3088\u3073\u3001\u8ad6\u7406\u72b6\u614b\u304b\u3089\u306a\u308b\u7a7a\u9593\u3092<strong>\u7b26\u53f7\u7a7a\u9593<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4f55\u3089\u304b\u306e\u5bfe\u5fdc\u898f\u5247\u304b\u3089 $\\ket{\\psi} \\in \\mathbb C^{2^k}$\u3068 $\\ket{\\psi_L}\\in \\mathbb C^{2^n}$\u306b\u3064\u3044\u3066<\/p>\n\n\n\n<p>$$<br>\\begin{align}\\mathcal E: \\ket{\\psi} \\mapsto \\ket{\\psi_L}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u5199\u50cf $\\mathcal E$\u304c\u5f97\u3089\u308c\u3001\u305d\u306e\u5199\u50cf\u306e\u50cf\u3068\u3057\u3066\u7b26\u53f7\u7a7a\u9593 $T$\u304c<\/p>\n\n\n\n<p>$$ <br>\\begin{align}T := \\mathrm{Im}(\\mathcal E)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306b\u3088\u3063\u3066\u5b9a\u307e\u308a\u307e\u3059\u3002\u7b26\u53f7\u7a7a\u9593\u306f $n$\u91cf\u5b50\u30d3\u30c3\u30c8\u7a7a\u9593\u306e\u90e8\u5206\u7a7a\u9593\u306b\u306a\u3063\u3066\u3044\u3066\u3001 $k$\u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u60c5\u5831\u3092\u57cb\u3081\u8fbc\u3081\u308b\u5927\u304d\u3055\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%A8%E3%83%A9%E3%83%BC%E3%81%AE%E6%9C%89%E7%84%A1%E3%82%92%E5%88%A4%E5%AE%9A%E3%81%99%E3%82%8B%E6%BC%94%E7%AE%97%E5%AD%90%EF%BC%9A%E3%82%B9%E3%82%BF%E3%83%93%E3%83%A9%E3%82%A4%E3%82%B6\"><\/span>\u30a8\u30e9\u30fc\u306e\u6709\u7121\u3092\u5224\u5b9a\u3059\u308b\u6f14\u7b97\u5b50\uff1a\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u7d9a\u3044\u3066\u3001\u30a8\u30e9\u30fc\u306e\u6709\u7121\u3092\u5224\u5225\u3059\u308b\u305f\u3081\u306b<strong>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6<\/strong>\u3068\u547c\u3070\u308c\u308b\u7269\u7406\u91cf\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3092\u4f7f\u3046\u3053\u3068\u3067\u7b26\u53f7\u3092\u6307\u5b9a\u3067\u304d\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u30a8\u30e9\u30fc\u306e\u60c5\u5831\u3092\u53d6\u308a\u51fa\u3059\u4e8b\u304c\u3067\u304d\u307e\u3059\u3002\u53e4\u5178\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u3092\u3054\u5b58\u77e5\u306e\u65b9\u306f\u3001\u30d1\u30ea\u30c6\u30a3\u306e\u5bfe\u5fdc\u7269\u3060\u3068\u601d\u3046\u3068\u30a4\u30e1\u30fc\u30b8\u3057\u3084\u3059\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3092\u307e\u3068\u3081\u305f\u3082\u306e\u306f\u3001\u7dda\u5f62\u7b26\u53f7\u306e\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u3066\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\uff08\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306b\u3064\u3044\u3066\u306f\u6b21\u306e\u9805\u3067\u8aac\u660e\u3057\u307e\u3059\u3002\uff09<\/p>\n\n\n\n<p>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3092\u5b9a\u7fa9\u3059\u308b\u305f\u3081\u306b\u3001\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u5b9a\u7fa9\u3059\u308b\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306f\u7269\u7406\u3067\u4e00\u822c\u306b\u4f7f\u308f\u308c\u308b\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u5b9a\u7fa9\u3068\u3084\u3084\u7570\u306a\u308b\u306e\u3067\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u5b9a\u7fa9\u306e\u305f\u3081\u306b\u307e\u305a\u306f\u30d1\u30a6\u30ea\u7fa4\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<strong>\u30d1\u30a6\u30ea\u7fa4<\/strong>\u3068\u306f\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}I=\\begin{pmatrix}1&amp;0\\\\0&amp;1\\end{pmatrix},\\;X=\\begin{pmatrix}0&amp;1\\\\1&amp;0\\end{pmatrix},\\;Y=\\begin{pmatrix}0&amp;-i\\\\i&amp;0\\end{pmatrix},\\;Z=\\begin{pmatrix}1&amp;0\\\\0&amp;-1\\end{pmatrix}\\end{align} $$<\/p>\n\n\n\n<p>\u306e4\u3064\u306e\u6f14\u7b97\u5b50\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u3067\u751f\u6210\u3055\u308c\u308b\u7fa4\u306e\u3053\u3068\u3067\u3059\u3002\u3064\u307e\u308a\u3001 $n$\u91cf\u5b50\u30d3\u30c3\u30c8\u7cfb\u3067\u306e\u30d1\u30a6\u30ea\u7fa4 $P_n$\u306f<\/p>\n\n\n\n<p>$$ <br>\\begin{align}\\{I,X,Y,Z\\}^{\\otimes n}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3067\u751f\u6210\u3055\u308c\u308b\u7fa4\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u30d1\u30a6\u30ea\u7fa4\u306b\u3064\u3044\u3066\u3001\u305d\u306e\u8981\u7d20\u3092<strong>\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u306e\u5b9a\u7fa9\u3067\u306f\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}iZ,\\; -iX\\otimes Z\\otimes I\\otimes Y\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306a\u3069\u3082\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306b\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u306b\u30d1\u30a6\u30ea\u7fa4\u306e\u8981\u7d20\u306f\u30c6\u30f3\u30bd\u30eb\u7a4d\u306b\u5206\u89e3\u53ef\u80fd\u306a\u306e\u3067\u3001\u30d1\u30a6\u30ea\u7fa4 $P_n$\u3092<\/p>\n\n\n\n<p>$$<br>\\begin{align}P_n= \\{\\pm 1,\\pm i\\}\\times \\{I,X,Y,Z\\} ^{\\otimes n}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3059\u308b\u4e8b\u3082\u3067\u304d\u307e\u3059\u3002 $n=2$\u306e\u5834\u5408\u3092\u660e\u793a\u7684\u306b\u66f8\u304f\u3068<\/p>\n\n\n\n<p>$$<br>\\begin{multline}\\{\\pm 1,\\pm i\\}\\times\\{I\\otimes I,I\\otimes X,I\\otimes Y,I\\otimes Z,X\\otimes I,X\\otimes X,X\\otimes Y,X\\otimes Z, \\\\Y\\otimes I,Y\\otimes X, Y\\otimes Y,Y\\otimes Z,Z\\otimes I,Z\\otimes X,Z\\otimes Y,Z\\otimes Z\\}\\end{multline} <br>$$<\/p>\n\n\n\n<p>\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u4fc2\u6570\u3068\u3057\u3066 $\\{\\pm1, \\pm i\\}$\u306e\u3044\u305a\u308c\u304b\u304c\u4ed8\u3044\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p>\u30d1\u30a6\u30ea\u7fa4$P_n$\u3092\u7528\u3044\u3066\u3001\u7b26\u53f7\u7a7a\u9593 $T \\subseteq (\\mathbb C^2)^{\\otimes n}$\u306b\u5bfe\u3059\u308b\u96c6\u5408$S(T)$\u3092<\/p>\n\n\n\n<p>$$<br>\\begin{align}S(T) = \\{M \\in P_n \\mid \\forall \\ket{\\psi_L}\\in T,\\; M\\ket{\\psi_L} =\\ket{\\psi_L}\\}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u3053\u306e\u96c6\u5408\u306e\u8981\u7d20\u306e\u3053\u3068\u3092<strong>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u3053\u3067 $S(T)$\u306f\u7fa4\u306b\u306a\u3063\u3066\u3044\u3066\u3001$S(T)$\u3092<strong>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7fa4<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3068\u306f\u7b26\u53f7\u7a7a\u9593\u3092 $+1$\u56fa\u6709\u7a7a\u9593\u3068\u3057\u3066\u6301\u3064\u3088\u3046\u306a\u6f14\u7b97\u5b50\u306e\u3053\u3068\u3067\u3059\u3002\u300c\u7b26\u53f7\u7a7a\u9593\u300d\u3068\u3044\u3046\u7a7a\u9593\u3092\u6307\u5b9a\u3059\u308b\u305f\u3081\u306b\u6f14\u7b97\u5b50\u3092\u6301\u3061\u51fa\u3057\u3066\u3001\u305d\u306e\u6f14\u7b97\u5b50\u306e\u56fa\u6709\u7a7a\u9593\u3068\u3057\u3066\u7a7a\u9593\u3092\u6307\u5b9a\u3057\u3088\u3046\u3068\u3044\u3046\u30a2\u30a4\u30c7\u30a2\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u306f\u56fa\u6709\u5024\u304c $\\pm 1$\u3057\u304b\u306a\u3044\u3068\u3044\u3046\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u3092\u7c21\u5358\u306b\u793a\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6 $M\\in S(T)$\u306f\u30d1\u30a6\u30ea\u7fa4 $P_n$\u306b\u542b\u307e\u308c\u3066\u3044\u308b\u306e\u3067\u3001\u56fa\u6709\u5024\u306f $\\pm i, \\pm 1$\u306e\u3044\u305a\u308c\u304b\u3067\u3059\u3002\u3053\u3053\u3067\u3001 $M$\u304c\u56fa\u6709\u5024 $\\pm i$\u3092\u6301\u3063\u3066\u3044\u305f\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001$M$\u3092 $\\{\\pm 1,\\pm i\\}\\times \\{I,X,Y,Z\\} ^{\\otimes n}$\u306e\u3088\u3046\u306b\u5206\u89e3\u3057\u305f\u3068\u304d\u306e\u4fc2\u6570\u90e8\u5206\u306f $\\pm i$\u306e\u3044\u305a\u308c\u304b\u306b\u306a\u308a\u307e\u3059\u3002\u3088\u3063\u3066\u3001$M^2 = -I$\u3068\u306a\u308a\u3001 $-I\\in S(T)$\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3067\u3059\u304c\u3001 $-I$\u306f<\/p>\n\n\n\n<p>$$<br>\\begin{align}\\forall \\ket{\\psi}, \\; -I\\ket{\\psi}=-\\ket{\\psi}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306a\u306e\u3067\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306e\u5b9a\u7fa9\u3092\u6e80\u305f\u3057\u307e\u305b\u3093\u3002\u77db\u76fe\u304c\u751f\u3058\u305f\u306e\u3067\u3001 $M$\u304c\u56fa\u6709\u5024 $\\pm i$\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u4eee\u5b9a\u306f\u8aa4\u308a\u3060\u3063\u305f\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001 $M$\u306e\u56fa\u6709\u5024\u306f $\\pm 1$\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u3068\u547c\u3070\u308c\u308b\u7279\u5b9a\u306e\u7b26\u53f7\u3067\u306f\u3001\u72b6\u614b\u304c\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306e+1\u56fa\u6709\u72b6\u614b\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u8abf\u3079\u308b\u3053\u3068\u3067\u305d\u306e\u72b6\u614b\u304c\u8ad6\u7406\u72b6\u614b\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\u3067\u304d\u307e\u3059\u3002\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306e\u5b9a\u7fa9\u304b\u3089\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}\\ket{\\psi} \\in T \\Leftrightarrow \\forall M\\in S(T), \\quad M\\ket{\\psi}=\\ket{\\psi}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3064\u306e\u3067\u3001\u3059\u3079\u3066\u306e\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u3064\u3044\u3066 $+1$\u56fa\u6709\u72b6\u614b\u306b\u306a\u3063\u3066\u3044\u308c\u3070\u8ad6\u7406\u72b6\u614b\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306f\u7269\u7406\u91cf\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u5358\u4f4d\u884c\u5217\u4ee5\u5916\u306e\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306f\u4fc2\u6570\u304c+1\u306a\u3089\u56fa\u6709\u5024\u306f $\\pm 1$\u306e2\u3064\u3057\u304b\u306a\u3044\u3068\u3044\u3046\u6027\u8cea\u304c\u3042\u308b\u3053\u3068\u304b\u3089\u56fa\u6709\u5024\u304c\u5b9f\u6570\u5024\u3067\u3001\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306f\u76f4\u4ea4\u3059\u308b\u304b\u3089\u3067\u3059\u3002\u3055\u3089\u306b\u3001\u4e0e\u3048\u3089\u308c\u305f\u72b6\u614b\u306b\u3064\u3044\u3066\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3092\u6e2c\u5b9a\u3059\u308b\u3068\u6e2c\u5b9a\u5024\u306f $\\pm1$\u306e\u3044\u305a\u308c\u304b\u306b\u306a\u308a\u307e\u3059\u3002\u306a\u306e\u3067\u3001\u3059\u3079\u3066\u306e\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u3064\u3044\u3066\u6e2c\u5b9a\u5024\u304c $+1$\u306a\u3089\u8ad6\u7406\u72b6\u614b\u3067\u3042\u308a\u6b63\u3057\u3044\u72b6\u614b\u3001 1\u3064\u3067\u3082\u6e2c\u5b9a\u5024\u304c$-1$\u3067\u3042\u308b\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u304c\u3042\u308c\u3070\u30a8\u30e9\u30fc\u304c\u751f\u3058\u305f\u9593\u9055\u3063\u305f\u72b6\u614b\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6 $M$\u306e\u6e2c\u5b9a\u306f\u91cf\u5b50\u56de\u8def\u3067\u66f8\u304f\u3068\u6b21\u306e\u56f32\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"546\" src=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1-1024x546.png\" alt=\"\" class=\"wp-image-8018\" srcset=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1-1024x546.png 1024w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1-300x160.png 300w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1-768x410.png 768w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1-1536x819.png 1536w, https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/wp-content\/uploads\/2025\/09\/image-1-2048x1092.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56f32:\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u6e2c\u5b9a\u56de\u8def<\/figcaption><\/figure>\n\n\n\n<p>\u6e2c\u5b9a\u7d50\u679c\u306f\u88dc\u52a9\u91cf\u5b50\u30d3\u30c3\u30c8\u306eZ\u6e2c\u5b9a\u3067\u5f97\u3089\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u6e2c\u5b9a\u5f8c\u306e\u72b6\u614b\u306f\u6e2c\u5b9a\u7d50\u679c\u304c $m$\u3067\u3042\u308b\u3068\u304d\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}\\left(\\frac{I+(-1)^mM}2\\right)\\ket{\\psi}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001 $(I+M)\/2$\u3068 $(I-M)\/2$\u306f\u305d\u308c\u305e\u308c $M$\u306e $+1$\u56fa\u6709\u7a7a\u9593\u3068 $-1$\u56fa\u6709\u7a7a\u9593\u3078\u306e\u5c04\u5f71\u6f14\u7b97\u5b50\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6e2c\u5b9a\u306b\u3088\u3063\u3066\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6 $M$\u306e $+1$\u56fa\u6709\u7a7a\u9593\u304b $-1$\u56fa\u6709\u7a7a\u9593\u306e\u3044\u305a\u308c\u304b\u306b\u5c04\u5f71\u3055\u308c\u307e\u3059\u3002\u6e2c\u5b9a\u5f8c\u306e\u72b6\u614b\u304c\u3059\u3079\u3066\u306e\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u3064\u3044\u3066 $+1$\u56fa\u6709\u72b6\u614b\u3067\u3042\u308b\u3068\u304d\u3001\u3053\u306e\u72b6\u614b\u306f\u8ad6\u7406\u72b6\u614b\u3067\u3042\u308b\u3068\u5224\u5b9a\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u3064\u3044\u3066\u306e\u6e2c\u5b9a\u3092\u884c\u3046\u3053\u3068\u3067\u8ad6\u7406\u72b6\u614b\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u3064\u3044\u3066\u306e\u6e2c\u5b9a\u3092\u884c\u3046\u3053\u3068\u3067\u30a8\u30e9\u30fc\u306e\u6709\u7121\u3092\u5224\u5b9a\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306f\u7fa4\u3092\u6210\u3057\u3066\u3044\u308b\u305f\u3081\u3001 $S(T)$\u306e\u8981\u7d20\u306f\u5927\u91cf\u306b\u3042\u308a\u307e\u3059\u3002\u5f93\u3063\u3066\u3001\u305d\u306e\u3059\u3079\u3066\u306b\u3064\u3044\u3066\u6e2c\u5b9a\u3092\u884c\u3046\u3053\u3068\u306f\u73fe\u5b9f\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001 $S(T)$\u3092\u751f\u6210\u3059\u308b\u751f\u6210\u5143\u306b\u3064\u3044\u3066\u306e\u307f\u6e2c\u5b9a\u3092\u884c\u3044\u307e\u3059\u3002\u751f\u6210\u5143\u3068\u306f\u3001\u6f14\u7b97\u5b50\u306e\u96c6\u5408 $\\{M_1,&#8230;,M_r\\}$\u3067 \u7fa4$S(T)$\u3092\u751f\u6210\u3059\u308b\u3082\u306e\u306e\u4e2d\u3067\u8981\u7d20\u6570\u304c\u6700\u5c0f\u306e\u3082\u306e\u3092\u3044\u3044\u307e\u3059\u3002\u7dda\u5f62\u4ee3\u6570\u3067\u8a00\u3046\u3068\u3053\u308d\u306e\u57fa\u5e95\u306e\u3088\u3046\u306a\u5b58\u5728\u3067\u3059\u3002\u5f93\u3063\u3066\u3001\u30a8\u30e9\u30fc\u306e\u6709\u7121\u3092\u5224\u5b9a\u3059\u308b\u305f\u3081\u306b\u306f\u3001 $S(T)$\u5168\u4f53\u3092\u4f7f\u3046\u4ee3\u308f\u308a\u306b\u751f\u6210\u5143 $\\{M_1,&#8230;,M_r\\}$\u306b\u3064\u3044\u3066\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}M_i \\ket{\\psi} = \\ket{\\psi}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308c\u3070\u5341\u5206\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u30a8\u30e9\u30fc\u306e\u6709\u7121\u306e\u5224\u5b9a\u306b\u306f $\\{M_1,&#8230;,M_r\\}$ \u306e\u6e2c\u5b9a\u5024\u3060\u3051\u304c\u5fc5\u8981\u3067\u3059\u3002\u6e2c\u5b9a\u7d50\u679c\u3092\u6271\u3044\u3084\u3059\u3044\u3088\u3046\u306b\u6e2c\u5b9a\u5024 $\\{-1, +1\\}$ \u304b\u3089\u53e4\u5178\u30d3\u30c3\u30c8\u5217 $\\{0, 1\\}$ \u306b\u5909\u63db\u3057\u307e\u3059\u3002 k \u91cf\u5b50\u30d3\u30c3\u30c8\u306e\u72b6\u614b \\ket{\\psi} \u306b\u3064\u3044\u3066\u3001 $\\{M_1,&#8230;,M_r\\}$ \u3092\u6e2c\u5b9a\u3057\u305f\u7d50\u679c\u3092 $(m_1,&#8230;,m_r)$ \u3068\u3057\u3066\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}m_i = (-1)^{s_i}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3067\u5f97\u3089\u308c\u308b\u53e4\u5178\u30d3\u30c3\u30c8\u5217 $s=(s_1,&#8230;,s_r)$\u306e\u3053\u3068\u3092<strong>\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u3053\u307e\u3067\u306e\u8b70\u8ad6\u304b\u3089\u3001\u3059\u3079\u3066\u306e $i$\u306b\u3064\u3044\u3066 $m_i=+1$\u3067\u3042\u308c\u3070\u8ad6\u7406\u72b6\u614b\u306a\u306e\u3067\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304c<\/p>\n\n\n\n<p>$$<br>\\begin{align}s=(0,0,&#8230;,0)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3067\u3042\u308c\u3070\u8ad6\u7406\u72b6\u614b\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3092\u7528\u3044\u3066\u30a8\u30e9\u30fc\u306e\u6709\u7121\u3092\u5224\u5b9a\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u5b9f\u306f\u3001\u3053\u306e\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304c\u69d8\u3005\u306a\u60c5\u5831\u3092\u6301\u3063\u3066\u3044\u3066\u3001\u30c7\u30b3\u30fc\u30c0\u3092\u8003\u3048\u308b\u4e0a\u3067\u4e2d\u5fc3\u7684\u306a\u5f79\u5272\u3092\u62c5\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%B7%E3%83%B3%E3%83%89%E3%83%AD%E3%83%BC%E3%83%A0%E5%80%A4%E3%81%8B%E3%82%89%E3%82%A8%E3%83%A9%E3%83%BC%E3%81%AE%E6%83%85%E5%A0%B1%E3%82%92%E5%8F%96%E3%82%8A%E5%87%BA%E3%81%99\"><\/span>\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u306e\u60c5\u5831\u3092\u53d6\u308a\u51fa\u3059<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u3053\u307e\u3067\u306f\u30a8\u30e9\u30fc\u306e\u6709\u7121\u3060\u3051\u3092\u8003\u3048\u3066\u3044\u307e\u3057\u305f\u304c\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3069\u306e\u3088\u3046\u306a\u30a8\u30e9\u30fc\u304c\u8d77\u3053\u3063\u305f\u304b\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u7c21\u5358\u306e\u305f\u3081\u306b\u3001\u8d77\u3053\u308a\u5f97\u308b\u30a8\u30e9\u30fc\u3092\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u3092\u7528\u3044\u305f\u6b21\u306e\u3088\u3046\u306a\u5f62\u5f0f\u306e\u30a8\u30e9\u30fc\u306b\u9650\u5b9a\u3057\u307e\u3059<\/p>\n\n\n\n<p>$$<br>\\begin{align}\\ket{\\psi_L}\\to P\\ket{\\psi_L}\\quad (P\\in P_n)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067 $\\ket{\\psi_L}$\u306f\u8ad6\u7406\u72b6\u614b\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30a8\u30e9\u30fc\u306e\u3053\u3068\u3092<strong>\u30d1\u30a6\u30ea\u30a8\u30e9\u30fc<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u5b9f\u306f\u3001<strong>\u30d1\u30a6\u30ea\u30a8\u30e9\u30fc\u306b\u5bfe\u3057\u3066\u8a02\u6b63\u3067\u304d\u308c\u3070\u5404\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u72ec\u7acb\u306b\u304b\u304b\u308b\u30a8\u30e9\u30fc\u304c\u3042\u308b\u7a0b\u5ea6\u306e\u7cbe\u5ea6\u3067\u8a02\u6b63\u3067\u304d\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059<\/strong><sup data-fn=\"e264920d-c97d-49f0-a832-b0c71a3845e6\" class=\"fn\"><a id=\"e264920d-c97d-49f0-a832-b0c71a3845e6-link\" href=\"#e264920d-c97d-49f0-a832-b0c71a3845e6\">3<\/a><\/sup>\u3002<\/p>\n\n\n\n<p>\u30a8\u30e9\u30fc\u304c\u8d77\u3053\u308b\u3053\u3068\u3067\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u3044\u307e\u3001\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u9855\u8457\u306a\u6027\u8cea\u3068\u3057\u3066\u3001\u4efb\u610f\u306e\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50 $P,Q$\u306b\u3064\u3044\u3066<\/p>\n\n\n\n<p>$$<br>\\begin{align}PQ=\\begin{cases}QP\\\\-QP\\end{cases}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306e\u3044\u305a\u308c\u304b\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u3092\u304b\u3051\u308b\u9806\u756a\u3092\u5165\u308c\u66ff\u3048\u308b\u3068\u3001\u7b26\u53f7\u304c\u305d\u306e\u307e\u307e\u306e\u5834\u5408\u3068\u5165\u308c\u66ff\u308f\u308b\u5834\u5408\u304c\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u6027\u8cea\u3068\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u304c\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u30010\u304b1\u306e\u5024\u3092\u53d6\u308b $b_i$\u304c\u5b58\u5728\u3057\u3066<\/p>\n\n\n\n<p>$$<br>\\begin{align}P\\ket{\\psi_L}=PM_i\\ket{\\psi_L}=(-1)^{b_i}M_iP\\ket{\\psi_L}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3053\u306e\u5f0f\u306f\u30a8\u30e9\u30fc\u304c\u8d77\u304d\u305f\u72b6\u614b $P\\ket{\\psi_L}$\u306e $M_i$\u306e\u56fa\u6709\u5024\u304c $(-1)^{b_i}$\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u3066\u3001 $M_i$\u306b\u3064\u3044\u3066\u306e\u6e2c\u5b9a\u3092\u884c\u3046\u3068 $b_i$\u304c\u5f97\u3089\u308c\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u304b\u3089\u3001 $\\{M_1,&#8230;,M_r\\}$\u3092\u6e2c\u5b9a\u3059\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024 $s =(s_1,&#8230;,s_r)$\u306f<\/p>\n\n\n\n<p>$$<br>\\begin{align}s=(b_1,b_2,&#8230;,b_r)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 $b_i$\u306f\u30a8\u30e9\u30fc $P$\u306b\u3088\u3063\u3066\u5b9a\u307e\u308b\u5024\u3060\u3063\u305f\u306e\u3067\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306f\u30a8\u30e9\u30fc\u306b\u3064\u3044\u3066\u306e\u60c5\u5831\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%82%B7%E3%83%B3%E3%83%89%E3%83%AD%E3%83%BC%E3%83%A0%E5%80%A4%E3%81%8B%E3%82%89%E3%82%A8%E3%83%A9%E3%83%BC%E3%82%92%E6%8E%A8%E5%AE%9A%E3%81%99%E3%82%8B%EF%BC%9A%E3%83%87%E3%82%B3%E3%83%BC%E3%83%89\"><\/span>\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u3092\u63a8\u5b9a\u3059\u308b\uff1a\u30c7\u30b3\u30fc\u30c9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u91cf\u5b50\u30d3\u30c3\u30c8\u306b\u767a\u751f\u3057\u305f\u30a8\u30e9\u30fc\u306e\u60c5\u5831\u3092\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306b\u3088\u3063\u3066\u8868\u3059\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u3053\u306e\u3053\u3068\u304b\u3089\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3092\u7528\u3044\u3066\u30a8\u30e9\u30fc\u304c\u63a8\u5b9a\u3067\u304d\u305d\u3046\u3060\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u672c\u6765\u3067\u3042\u308c\u3070\u3001\u3082\u3046\u5c11\u3057\u8a73\u7d30\u306a\u8b70\u8ad6\u3092\u884c\u3046\u3053\u3068\u3067\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3068\u30a8\u30e9\u30fc\u306e\u95a2\u4fc2\u3092\u660e\u78ba\u306b\u3059\u308b\u3079\u304d\u3067\u3059\u304c\u3001\u3053\u3053\u3067\u306f\u305d\u308c\u3092\u7701\u7565\u3057\u3066\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u3092\u30d9\u30a4\u30ba\u63a8\u5b9a\u3067\u63a8\u5b9a\u3059\u308b\u4e8b\u3092\u8003\u3048\u307e\u3059\u3002\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024 $s$\u304b\u3089\u30a8\u30e9\u30fc $E$\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u306f\u3001\u7d50\u679c\u304b\u3089\u539f\u56e0\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u4e8b\u5f8c\u78ba\u7387 $\\mathrm{Pr}(E \\mid s)$\u3092\u6c42\u3081\u3066\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}E^* = \\arg \\max_{E\\in P_n} \\mathrm{Pr}(E \\mid s)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u3059\u308b\u3053\u3068\u3067\u63a8\u5b9a\u30a8\u30e9\u30fc $E^*$\u3092\u6c42\u3081\u307e\u3059\uff08\u3053\u306e\u3088\u3046\u306a\u63a8\u5b9a\u6cd5\u306f\u4e8b\u5f8c\u78ba\u7387\u6700\u5927\u5316 (MAP) \u63a8\u5b9a\u3068\u547c\u3070\u308c\u307e\u3059\uff09\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u3092\u63a8\u5b9a\u3059\u308b\u51e6\u7406\u306e\u3053\u3068\u3092<strong>\u30c7\u30b3\u30fc\u30c9<\/strong>\u3068\u547c\u3073\u3001\u305d\u306e\u51e6\u7406\u3092\u5b9f\u884c\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u3053\u3068\u3092<strong>\u30c7\u30b3\u30fc\u30c0<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u306e\u63a8\u5b9a\u306e\u305f\u3081\u306b\u306f\u4e8b\u5f8c\u78ba\u7387\u3092\u6c42\u3081\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3001\u5f97\u3089\u308c\u305f\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3092\u7528\u3044\u3066\u30a8\u30e9\u30fc\u306b\u3064\u3044\u3066\u306e\u4e8b\u524d\u5206\u5e03\u3092\u66f4\u65b0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u305d\u306e\u51e6\u7406\u3092\u52b9\u7387\u826f\u304f\u884c\u3046\u65b9\u6cd5\u306f\u3001\u6b21\u306e\u8a18\u4e8b\u3067\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30c7\u30b3\u30fc\u30c0\u3092\u7528\u3044\u3066\u30a8\u30e9\u30fc\u3092\u63a8\u5b9a\u3057\u305f\u3089\u3001\u305d\u306e\u7d50\u679c\u306b\u57fa\u3065\u3044\u3066\u30a8\u30e9\u30fc\u3092\u6253\u3061\u6d88\u3059\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u304c\u30a8\u30e9\u30fc\u3068\u3057\u3066\u751f\u3058\u308b\u4e8b\u3092\u8003\u3048\u3066\u3044\u308b\u305f\u3081\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}\\forall P\\in P_n, \\quad PP=e^{i\\theta}I\\quad(\\theta=0,\\pi)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u30b0\u30ed\u30fc\u30d0\u30eb\u4f4d\u76f8\u306f\u7121\u8996\u3067\u304d\u308b\u306e\u3067\u3001\u63a8\u5b9a\u30a8\u30e9\u30fc \u3092\u305d\u306e\u307e\u307e\u91cf\u5b50\u30b2\u30fc\u30c8\u3068\u3057\u3066\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u30a8\u30e9\u30fc\u3092\u6253\u3061\u6d88\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u30a8\u30e9\u30fc\u3092\u6253\u3061\u6d88\u3059\u64cd\u4f5c\u306e\u3053\u3068\u3092<strong>\u30ea\u30ab\u30d0\u30ea\u64cd\u4f5c<\/strong>\u3068\u547c\u3073\u3001\u30ea\u30ab\u30d0\u30ea\u64cd\u4f5c\u306e\u305f\u3081\u306b\u6253\u3064\u30b2\u30fc\u30c8\u3092<strong>\u30ea\u30ab\u30d0\u30ea\u30b2\u30fc\u30c8<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E9%87%8F%E5%AD%90%E8%AA%A4%E3%82%8A%E8%A8%82%E6%AD%A3%E3%81%AE%E6%89%8B%E9%A0%86%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u306e\u624b\u9806\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>\u3053\u3053\u307e\u3067\u306e\u624b\u9806\u3092\u307e\u3068\u3081\u308b\u3068\u3001\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u306e\u5168\u4f53\u306e\u64cd\u4f5c\u306f<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3092\u6e2c\u5b9a\u3057\u3066\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3092\u5f97\u308b\uff08\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u6e2c\u5b9a\uff09<\/li>\n\n\n\n<li>\u30c7\u30b3\u30fc\u30c0\u3092\u7528\u3044\u3066\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u3092\u63a8\u5b9a\u3059\u308b<\/li>\n\n\n\n<li>\u30a8\u30e9\u30fc\u3092\u6253\u3061\u6d88\u3059\u3088\u3046\u306a\u64cd\u4f5c\u3092\u3059\u308b\uff08\u30ea\u30ab\u30d0\u30ea\u64cd\u4f5c\uff09<\/li>\n<\/ol>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u306e\u6027\u80fd\u5411\u4e0a\u306e\u305f\u3081\u306b\u306f\u305d\u308c\u305e\u308c\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u3064\u3044\u3066\u6027\u80fd\u3092\u5411\u4e0a\u3055\u305b\u3066\u3044\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b9\u30c6\u30c3\u30d7\u306e\u4e2d\u3067\u3082\u30011\u30683\u306f\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u5b9f\u6a5f\u306e\u6027\u80fd\u5411\u4e0a\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u304c\u30012\u306f\u30c7\u30b3\u30fc\u30c0\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u6539\u5584\u3059\u308b\u3053\u3068\u3067\u6027\u80fd\u5411\u4e0a\u304c\u671f\u5f85\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u3001\u30c7\u30b3\u30fc\u30c0\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u53e4\u5178\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u5b9f\u884c\u3055\u308c\u308b\u53e4\u5178\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306a\u306e\u3067\u3053\u308c\u307e\u3067\u3082\u591a\u304f\u306e\u7814\u7a76\u304c\u306a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%83%91%E3%83%AA%E3%83%86%E3%82%A3%E3%83%81%E3%82%A7%E3%83%83%E3%82%AF%E8%A1%8C%E5%88%97\"><\/span>\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u6700\u5f8c\u306b\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3068\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306e\u95a2\u4fc2\u3092\u8a18\u8ff0\u3057\u3084\u3059\u304f\u3059\u308b\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3068\u3044\u3046\u3082\u306e\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002<strong>\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217<\/strong>\u3068\u306f\u884c\u5217\u306e\u5404\u884c\u304c\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u884c\u5217\u3067\u3001\u3059\u3079\u3066\u306e\u6210\u5206\u304c0\u304b1\u3067\u3042\u308b\u884c\u5217\u306e\u3053\u3068\u3067\u3059\u3002\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306f\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u304b\u3089\u4f5c\u308c\u308b\u306e\u3067\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u306e\u60c5\u5831\u3092\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306b\u57cb\u3081\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306f\u7fa4\u306e\u8981\u7d20\u3067\u3042\u308a\u6f14\u7b97\u5b50\u306a\u306e\u3067\u6271\u3044\u306b\u304f\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u304c\u3001\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306f\u6210\u5206\u304c0\u304b1\u306e\u884c\u5217\u306a\u306e\u3067\u6271\u3044\u3084\u3059\u304f\u3068\u3066\u3082\u4fbf\u5229\u3067\u3059\u3002\u7279\u306b\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e2d\u3067\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3092\u4f7f\u3046\u3068\u304d\u306b\u4fbf\u5229\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3092\u5b9a\u7fa9\u3059\u308b\u305f\u3081\u306b\u300c\u30d0\u30a4\u30ca\u30ea-\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u8868\u73fe\u300d\u3068\u547c\u3070\u308c\u308b\u6982\u5ff5\u3092\u5c0e\u5165\u3057\u3001\u3055\u3089\u306b\u300c\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u5f62\u5f0f\u300d\u3068\u547c\u3070\u308c\u308b\u6f14\u7b97\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3068\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306e\u95a2\u4fc2\u3092\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306b\u5bfe\u5fdc\u3059\u308b\u30d3\u30c3\u30c8\u5217\u3092\u8003\u3048\u308b\u305f\u3081\u306b<strong>\u30d0\u30a4\u30ca\u30ea-\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u8868\u73fe<\/strong>\u3068\u3044\u3046\u6982\u5ff5\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u30d1\u30a6\u30ea\u884c\u5217\u306f\u4e00\u822c\u306b<\/p>\n\n\n\n<p>$$<br>\\begin{align}P = i^lX^aZ^b\\quad (a,b \\in \\mathbb Z_2, \\;l\\in\\mathbb Z_4)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u5206\u89e3\u3059\u308b\u4e8b\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001 $\\mathbb Z_n =\\mathbb Z\/n\\mathbb Z$\u3067\u3059\u3002\u3088\u3063\u3066\u3001\u4f4d\u76f8\u3092\u8868\u3059 $i^l$\u3092\u7121\u8996\u3059\u308c\u3070<\/p>\n\n\n\n<p>$$<br>\\begin{align}P \\mapsto (a|b)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u5bfe\u5fdc\u3092\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u62ec\u5f27\u306e\u4e2d\u306b\u3042\u308b\u7e26\u68d2\u306f\u3001\u3053\u306e\u7d44\u304c $\\mathbb Z_2\\times \\mathbb Z_2$\u306e\u5143\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3092\u30c6\u30f3\u30bd\u30eb\u7a4d\u306e\u5834\u5408\u306b\u3082\u62e1\u5f35\u3057\u3066\u3001 $P_i \\mapsto (a_i|b_i)$\u3068\u7f6e\u304f\u3068\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}P_1\\otimes P_2\\otimes \\cdots \\otimes P_n\\mapsto (a_1a_2\\cdots a_n|b_1b_2\\cdots b_n)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u5bfe\u5fdc\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}X\\otimes Z\\otimes I\\otimes Y\\mapsto (1001|0101)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u5bfe\u5fdc\u3092<strong>\u30d0\u30a4\u30ca\u30ea-\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u8868\u73fe<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u9577\u3044\u306e\u3067\u3053\u3053\u304b\u3089\u306fBS\u8868\u73fe\u3068\u547c\u3076\u3053\u3068\u306b\u3057\u307e\u3059\uff08\u3053\u306e\u547c\u3073\u65b9\u306f\u4e00\u822c\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff09<sup data-fn=\"ea725cdd-58a8-4220-bab1-6e7c68e59166\" class=\"fn\"><a id=\"ea725cdd-58a8-4220-bab1-6e7c68e59166-link\" href=\"#ea725cdd-58a8-4220-bab1-6e7c68e59166\">4<\/a><\/sup>\u3002<\/p>\n\n\n\n<p>BS\u8868\u73fe\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u304b\u3089\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3078\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5177\u4f53\u4f8b\u3067\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u6b21\u306e5\u3064\u306e\u6f14\u7b97\u5b50\u304c\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u751f\u6210\u5143\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>\\begin{split}<br>M_1&amp;=ZXXZI \\\\<br>M_2&amp;=IZXXZ\\\\<br>M_3&amp;=ZIZXX\\\\<br>M_4&amp;=XZIZX<br>\\end{split}<br>\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3053\u306e\u3068\u304d\u3001\u305d\u308c\u305e\u308c\u306b\u5bfe\u5fdc\u3059\u308bBS\u8868\u73fe\u306f<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>\\begin{split}<br>M_1&amp;\\to (01100|10010)\\\\<br>M_2&amp;\\to(00110|01001)\\\\<br>M_3&amp;\\to(00011|10100)\\\\<br>M_4&amp;\\to(10001|01010)<br>\\end{split}<br>\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u5217\u6210\u5206\u306b\u6301\u3064\u3088\u3046\u306a\u884c\u5217 $H$\u3092<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>H:=\\left(<br>\\begin{array}{c|c} <br>01100 &amp; 10010\\\\ <br>00110&amp;01001\\\\ <br>00011&amp;10100\\\\<br>10001&amp;01010 <br>\\end{array}<br>\\right)<br>\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u5b9a\u3081\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u5f97\u3089\u308c\u308b\u884c\u5217 $H$\u3092<strong>\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u304b\u3089\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u751f\u6210\u5143\u3092\u5fa9\u5143\u3067\u304d\u308b\u3053\u3068\u304b\u3089\u3001\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u304c\u4e0e\u3048\u3089\u308c\u308c\u3070\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u3092\u6307\u5b9a\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306f\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u306b\u3064\u3044\u3066\u306e\u60c5\u5831\u3092\u30d3\u30c3\u30c8\u5217\u3067\u8868\u73fe\u3057\u305f\u3082\u306e\u3068\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3055\u3089\u306b\u3001\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306b\u306f\u30a8\u30e9\u30fc\u3068\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306e\u95a2\u4fc2\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u3044\u3046\u91cd\u8981\u306a\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u306e\u6e96\u5099\u3068\u3057\u3066\u3001BS\u8868\u73fe\u306b\u304a\u3051\u308b\u6f14\u7b97\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u30022\u3064\u306e\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50 $P,Q \\in P_n$\u306b\u5bfe\u5fdc\u3059\u308bBS\u8868\u73fe<\/p>\n\n\n\n<p>$$ <br>\\begin{align}<br>P &amp;\\to v_P =(x_P|z_P)\\in \\mathbb Z_2^n\\times \\mathbb Z_2^n \\\\ <br>Q &amp;\\to v_Q = (x_Q|z_Q)\\in \\mathbb Z_2^n\\times \\mathbb Z_2^n <br>\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3092\u8003\u3048\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u5f97\u3089\u308c\u308b2\u3064\u306e\u30d9\u30af\u30c8\u30eb $v_P,v_Q$\u306b\u3064\u3044\u3066<\/p>\n\n\n\n<p>$$ <br>\\begin{align}v_P \\odot v_Q = x_P z_Q^{\\top} \\oplus x_Q z_P^{\\top} \\in \\mathbb Z_2\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u6f14\u7b97\u306e\u3053\u3068\u3092<strong>\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u5f62\u5f0f<\/strong>\u3068\u547c\u3073\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u53f3\u8fba\u306b\u3042\u308b\u548c\u306f $\\mathbb Z_2$\u306b\u304a\u3051\u308b\u548c\u3067\u3042\u308a\u3001\u6392\u4ed6\u7684\u8ad6\u7406\u548c(XOR)\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u5f62\u5f0f\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u30a8\u30e9\u30fc\u3068\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306e\u95a2\u4fc2\u3092\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u30d1\u30a6\u30ea\u30a8\u30e9\u30fc $E \\in P_n$\u306b\u5bfe\u3057\u3066BS\u8868\u73fe\u306b\u3088\u308b\u5bfe\u5fdc<\/p>\n\n\n\n<p>$$ <br>\\begin{align}E \\to v_E\\in \\mathbb Z_2^n\\times \\mathbb Z_2^n\\end{align} <br>$$<\/p>\n\n\n\n<p>\u306b\u3088\u3063\u3066\u30d0\u30a4\u30ca\u30ea\u30d9\u30af\u30c8\u30eb $v_E$\u3092\u5b9a\u3081\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306e\u751f\u6210\u5143\u3092<\/p>\n\n\n\n<p>$$ <br>\\begin{align}M_i\\to v_{M_i} \\in \\mathbb Z_2^n \\times \\mathbb Z_2^n\\quad(1\\le i\\le r)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u5bfe\u5fdc\u3055\u305b\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u30a8\u30e9\u30fc $E$\u306e $M_i$\u306b\u95a2\u3059\u308b\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024 $s_i$\u306f<\/p>\n\n\n\n<p>$$<br>\\begin{align}M_iE=(-1)^{s_i}EM_i\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3067\u5b9a\u307e\u308a\u3001\u3053\u306e $s_i$\u3068\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u5f62\u5f0f\u306e\u9593\u306b\u306f<\/p>\n\n\n\n<p>$$<br>\\begin{align}s_i = v_{M_i} \\odot v_E\\end{align} <br>$$<\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u8a3c\u660e\u306f\u3084\u3084\u624b\u9806\u304c\u591a\u3044\u3067\u3059\u304c\u3001\u5b9a\u7fa9\u3092\u9806\u306b\u8ffd\u3063\u3066\u3044\u304f\u3053\u3068\u3067\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u5f62\u5f0f\u3068\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306e\u95a2\u4fc2\u304c\u660e\u3089\u304b\u306b\u306a\u3063\u305f\u306e\u3067\u3001\u3064\u3044\u306b\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3068\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u306e\u95a2\u4fc2\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306f\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u306e\u751f\u6210\u5143\u3092 $M_i$\u3001\u305d\u306eBS\u8868\u73fe\u3092 $v_{M_i}$\u3068\u3059\u308b\u3068<\/p>\n\n\n\n<p>$$<br>\\begin{align}H=\\begin{pmatrix}v_{M_1}\\\\ \\vdots \\\\ v_{M_r}\\end{pmatrix}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3088\u3046\u306a\u884c\u5217\u306e\u3053\u3068\u3067\u3057\u305f\u3002\u5148\u7a0b\u306e\u8a71\u304b\u3089\u3001\u30a8\u30e9\u30fc $E$\u306e $M_i$\u306b\u95a2\u3059\u308b\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024 $s_i$\u306f $s_i = v_{M_i} \\odot v_E$\u3092\u307f\u305f\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u3053\u3068\u304b\u3089\u3001\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u5f62\u5f0f\u3092\u7a4d\u3068\u898b\u7acb\u3066\u3066\u884c\u5217 $H$\u3068\u30d9\u30af\u30c8\u30eb $v_E$\u306e\u7a4d\u3092\u53d6\u308b\u3053\u3068\u3067<\/p>\n\n\n\n<p>$$<br>\\begin{align}Hv_E=\\begin{pmatrix}v_{M_1} \\odot v_E \\\\ \\vdots \\\\ v_{M_r} \\odot v_E\\end{pmatrix} =\\begin{pmatrix} s_1 \\\\ \\vdots \\\\ s_r \\end{pmatrix}\\end{align} <br>$$<\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u307e\u3068\u3081\u308b\u3068\u3001\u30b7\u30f3\u30d7\u30ec\u30af\u30c6\u30a3\u30c3\u30af\u5f62\u5f0f\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067\u3001\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217 $H$\u306f\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u751f\u6210\u5143\u306e\u60c5\u5831\u3092\u6301\u3064\u3060\u3051\u3067\u306a\u304f\u3001\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u3092\u76f4\u63a5\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"CSS%E7%AC%A6%E5%8F%B7\"><\/span>CSS\u7b26\u53f7<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u304c\u5358\u7d14\u306b\u306a\u308b\u7279\u5225\u306a\u7b26\u53f7\u3067Calderbank-Shor-Steane (CSS) \u7b26\u53f7\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002CSS\u7b26\u53f7\u306f\u3001\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3092$X$\u30a8\u30e9\u30fc\u3092\u76e3\u8996\u3059\u308b\u3082\u306e\u3068 $Z$\u30a8\u30e9\u30fc\u3092\u76e3\u8996\u3059\u308b\u3082\u306e\u306b\u5206\u96e2\u3067\u304d\u308b\u3088\u3046\u306a\u7b26\u53f7\u3067\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u304c<\/p>\n\n\n\n<p>$$<br>\\begin{align}H=\\left(\\begin{array}{c|c}H_X&amp;O\\\\O&amp;H_Z\\end{array}\\right)\\end{align} <br>$$<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u5f62\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u7b26\u53f7\u3092\u7528\u3044\u308b\u3068\u3001 $Z$\u30a8\u30e9\u30fc\u306b\u3064\u3044\u3066$H_X$\u3001 $X$\u306b\u3064\u3044\u3066$H_Z$\u3068\u3044\u3046\u3088\u3046\u306b\u30a8\u30e9\u30fc\u306e\u7a2e\u985e\u3054\u3068\u306b\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3092\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u3001\u3055\u3089\u306b$H_X,H_Z$\u306f\u53e4\u5178\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3068\u540c\u3058\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30a8\u30e9\u30fc\u306e\u7a2e\u985e\u304c $X$\u30a8\u30e9\u30fc\u3068 $Z$\u30a8\u30e9\u30fc\u306e2\u7a2e\u985e\u3067\u3001\u3057\u304b\u3082\u305d\u308c\u3089\u3092\u72ec\u7acb\u306b\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u53e4\u5178\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306b\u3064\u3044\u3066\u306e\u77e5\u898b\u3092\u6d3b\u304b\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6b21\u306e\u9805\u304b\u3089\u898b\u3066\u3044\u304f\u30c7\u30b3\u30fc\u30c0\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3082\u53e4\u5178\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306b\u5bfe\u3057\u3066\u4f7f\u308f\u308c\u3066\u3044\u308b\u3082\u306e\u3092\u6d41\u7528\u3057\u305f\u3082\u306e\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u6700\u5f8c\u307e\u3067\u8aad\u3093\u3067\u3044\u305f\u3060\u304d\u3042\u308a\u304c\u3068\u3046\u3054\u3056\u3044\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u57fa\u790e\u7684\u306a\u77e5\u8b58\u3092\u99c6\u3051\u8db3\u3067\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u7279\u306b\u91cd\u8981\u306a\u306e\u304c\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u3068\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u3067\u3059\u3002\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u306f\u53e4\u5178\u306e\u7dda\u5f62\u7b26\u53f7\u306b\u5bfe\u5fdc\u3059\u308b\u3088\u3046\u306a\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u3067\u3001\u6271\u3044\u3084\u3059\u304f\u30a8\u30e9\u30fc\u306e\u60c5\u5831\u3092\u7c21\u5358\u306b\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u306f\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u3092\u8868\u73fe\u3059\u308b\u65b9\u6cd5\u306e\u3072\u3068\u3064\u3067\u3001\u30b9\u30bf\u30d3\u30e9\u30a4\u30b6\u7b26\u53f7\u306e\u60c5\u5831\u3092\u30b3\u30f3\u30d1\u30af\u30c8\u306b\u6271\u3044\u3084\u3059\u3044\u5f62\u3067\u8868\u73fe\u3059\u308b\u4e8b\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306b\u3064\u3044\u3066\u3088\u308a\u6df1\u304f\u77e5\u308a\u305f\u3044\u65b9\u306b\u306f\u3001\u6559\u79d1\u66f8\u3068\u3057\u3066\u6587\u732e[1]\u3092\u304a\u3059\u3059\u3081\u3057\u307e\u3059\u3002\u3053\u306e\u8a18\u4e8b\u306e\u5927\u90e8\u5206\u306e\u5185\u5bb9\u306f\u6587\u732e[1]\u3092\u53c2\u8003\u306b\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u56de\u306f\u3001\u3053\u306e\u8a18\u4e8b\u3067\u5177\u4f53\u7684\u306b\u8aac\u660e\u3067\u304d\u306a\u304b\u3063\u305f\u30c7\u30b3\u30fc\u30c9\u306e\u624b\u9806\u3001\u3064\u307e\u308a\u30b7\u30f3\u30c9\u30ed\u30fc\u30e0\u5024\u304b\u3089\u30a8\u30e9\u30fc\u3092\u63a8\u5b9a\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u6b21\u56de\u306e\u8a18\u4e8b\u3067\u3082\u30d1\u30ea\u30c6\u30a3\u30c1\u30a7\u30c3\u30af\u884c\u5217\u304c\u3068\u3066\u3082\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n<ol class=\"wp-block-footnotes\"><li id=\"1f00f91a-3bc5-4115-a3fa-e79e81e58117\">\u3053\u306e\u3088\u3046\u306b\u91cf\u5b50\u72b6\u614b\u3092\u4fdd\u5b58\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u306b\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u3092\u884c\u3046\u3053\u3068\u3092\u91cf\u5b50\u30e1\u30e2\u30ea (quantum memory)\u3068\u547c\u3076\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u7b26\u53f7\u5316\u3057\u305f\u72b6\u614b\u3067\u91cf\u5b50\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u3092\u8aa4\u308a\u8010\u6027\u91cf\u5b50\u8a08\u7b97 (fault tolerant quantum computation\uff09\u3068\u547c\u3073\u3001\u4e00\u822c\u306b\u91cf\u5b50\u30e1\u30e2\u30ea\u3088\u308a\u3082\u3055\u3089\u306b\u96e3\u3057\u3044\u6280\u8853\u3067\u3059\u3002\u8aa4\u308a\u8010\u6027\u91cf\u5b50\u8a08\u7b97\u3092\u884c\u3046\u65b9\u6cd5\u306f\u591a\u304f\u63d0\u6848\u3055\u308c\u3066\u304a\u308a\u3001\u8aad\u307f\u3084\u3059\u3044\u8ad6\u6587\u3068\u3057\u3066[2]\u3084\u304c\u3042\u308a\u307e\u3059\u3002 <a href=\"#1f00f91a-3bc5-4115-a3fa-e79e81e58117-link\" aria-label=\"\u811a\u6ce8\u53c2\u71671\u306b\u30b8\u30e3\u30f3\u30d7\">\u21a9\ufe0e<\/a><\/li><li id=\"36f272c7-526e-49c6-9e00-5b4d1ef473c8\">\u73fe\u5b9f\u3067\u306f\u30a8\u30f3\u30b3\u30fc\u30c9\u30fb\u30c7\u30b3\u30fc\u30c9\u306e\u904e\u7a0b\u3067\u3082\u30ce\u30a4\u30ba\u304c\u767a\u751f\u3057\u3066\u30a8\u30e9\u30fc\u304c\u751f\u3058\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30a8\u30e9\u30fc\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u306b\u3001\u3055\u307e\u3056\u307e\u306a\u624b\u6cd5\u5b58\u5728\u3057\u307e\u3059\u304c\u3001\u30c6\u30af\u30cb\u30ab\u30eb\u3067\u4eca\u56de\u306e\u8a71\u306b\u306f\u3042\u307e\u308a\u95a2\u4fc2\u306a\u3044\u306e\u3067\u7701\u7565\u3057\u307e\u3059\u3002\u8208\u5473\u306e\u3042\u308b\u65b9\u306f\u4f8b\u3048\u3070\u6587\u732e[1]\u306e12\u7ae013\u7ae0\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 <a href=\"#36f272c7-526e-49c6-9e00-5b4d1ef473c8-link\" aria-label=\"\u811a\u6ce8\u53c2\u71672\u306b\u30b8\u30e3\u30f3\u30d7\">\u21a9\ufe0e<\/a><\/li><li id=\"e264920d-c97d-49f0-a832-b0c71a3845e6\">\u8a73\u3057\u304f\u306f\u6587\u732e[1]\u306eTheorem 2.4\u3068Corollary 2.5\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3055\u3089\u306b\u4e00\u822c\u306b\u3001\u30a8\u30e9\u30fc\u304cCPTP\u5199\u50cf\u3067\u3042\u308b\u5834\u5408\u306b\u8208\u5473\u304c\u3042\u308b\u4eba\u306f\u6587\u732e[1]\u306eTheorem 2.6\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 <a href=\"#e264920d-c97d-49f0-a832-b0c71a3845e6-link\" aria-label=\"\u811a\u6ce8\u53c2\u71673\u306b\u30b8\u30e3\u30f3\u30d7\">\u21a9\ufe0e<\/a><\/li><li id=\"ea725cdd-58a8-4220-bab1-6e7c68e59166\">\u4f4d\u76f8\u306f\u7121\u8996\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002BS\u8868\u73fe\u306f\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u4f4d\u76f8\u6210\u5206\u3092\u7121\u8996\u3057\u305f\u5546\u7fa4 $P_n\/\\{I,-I,iI,-iI\\}$\u304b\u3089 $\\mathbb Z_2^n\\times \\mathbb Z_2^n$\u3078\u306e\u540c\u578b\u3067\u3059 <a href=\"#ea725cdd-58a8-4220-bab1-6e7c68e59166-link\" aria-label=\"\u811a\u6ce8\u53c2\u71674\u306b\u30b8\u30e3\u30f3\u30d7\">\u21a9\ufe0e<\/a><\/li><\/ol>\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>[1] Daniel Gottesman. <em>Surviving as a Quantum Computer in a Classical World<\/em>(2024) <a href=\"https:\/\/www.cs.umd.edu\/class\/spring2024\/cmsc858G\/QECCbook-2024-ch1-15.pdf\">PDF<\/a><\/p>\n\n\n\n<p>[2] Panos Aliferis,&nbsp;Daniel Gottesman,&nbsp;John Preskill. &#8220;Quantum accuracy threshold for concatenated distance-3 codes&#8221;, Quantum Info. Comput. 6, 2(2006), <a href=\"https:\/\/arxiv.org\/abs\/quant-ph\/0504218\">arXiv:quant-ph\/0504218<\/a> <a href=\"https:\/\/dl.acm.org\/doi\/10.5555\/2011665.2011666\">DOI<\/a><\/p>\n\n\n\n<p>[3] Austin G. Fowler,&nbsp;Craig Gidney. &#8220;Low overhead quantum computation using lattice surgery&#8221;(2018), <a href=\"https:\/\/arxiv.org\/abs\/1808.06709\">arXiv:1808.06709<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\"><\/span>\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div class=\"sabox-plus-item\"><div class=\"saboxplugin-wrap\" itemtype=\"http:\/\/schema.org\/Person\" itemscope itemprop=\"author\"><div class=\"saboxplugin-tab\"><div class=\"saboxplugin-gravatar\"><img alt='Shun Hasegawa' src='https:\/\/secure.gravatar.com\/avatar\/86624558a04468337363ffec6f104bc50416c2dd36dd047dbd1fa04c75d58ed2?s=100&#038;d=mm&#038;r=g' srcset='https:\/\/secure.gravatar.com\/avatar\/86624558a04468337363ffec6f104bc50416c2dd36dd047dbd1fa04c75d58ed2?s=200&#038;d=mm&#038;r=g 2x' class='avatar avatar-100 photo' height='100' width='100' itemprop=\"image\"\/><\/div><div class=\"saboxplugin-authorname\"><a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/author\/shun-hasegawa\/\" class=\"vcard author\" rel=\"author\"><span class=\"fn\">Shun Hasegawa<\/span><\/a><\/div><div class=\"saboxplugin-desc\"><div itemprop=\"description\"><p>\u6771\u4eac\u79d1\u5b66\u5927\u5b66 \u60c5\u5831\u7406\u5de5\u5b66\u9662 \u6570\u7406\u30fb\u8a08\u7b97\u79d1\u5b66\u7cfb \u5b66\u58eb\u8ab2\u7a0b<\/p>\n<\/div><\/div><div class=\"clearfix\"><\/div><\/div><\/div><\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u5fa9\u53f7\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u77e5\u3089\u308c\u308bBP+OSD\u306e\u89e3\u8aac\u8a18\u4e8b\u3067\u3059\u3002#1\u306f\u524d\u63d0\u77e5\u8b58\u3068\u306a\u308b\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u7b26\u53f7\u306e\u57fa\u790e\u306e\u89e3\u8aac\u3067\u3059\u3002<\/p>\n","protected":false},"author":25,"featured_media":8522,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"[{\"content\":\"\u3053\u306e\u3088\u3046\u306b\u91cf\u5b50\u72b6\u614b\u3092\u4fdd\u5b58\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u306b\u91cf\u5b50\u8aa4\u308a\u8a02\u6b63\u3092\u884c\u3046\u3053\u3068\u3092\u91cf\u5b50\u30e1\u30e2\u30ea (quantum memory)\u3068\u547c\u3076\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u7b26\u53f7\u5316\u3057\u305f\u72b6\u614b\u3067\u91cf\u5b50\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u3092\u8aa4\u308a\u8010\u6027\u91cf\u5b50\u8a08\u7b97 (fault tolerant quantum computation\uff09\u3068\u547c\u3073\u3001\u4e00\u822c\u306b\u91cf\u5b50\u30e1\u30e2\u30ea\u3088\u308a\u3082\u3055\u3089\u306b\u96e3\u3057\u3044\u6280\u8853\u3067\u3059\u3002\u8aa4\u308a\u8010\u6027\u91cf\u5b50\u8a08\u7b97\u3092\u884c\u3046\u65b9\u6cd5\u306f\u591a\u304f\u63d0\u6848\u3055\u308c\u3066\u304a\u308a\u3001\u8aad\u307f\u3084\u3059\u3044\u8ad6\u6587\u3068\u3057\u3066[2]\u3084\u304c\u3042\u308a\u307e\u3059\u3002\",\"id\":\"1f00f91a-3bc5-4115-a3fa-e79e81e58117\"},{\"content\":\"\u73fe\u5b9f\u3067\u306f\u30a8\u30f3\u30b3\u30fc\u30c9\u30fb\u30c7\u30b3\u30fc\u30c9\u306e\u904e\u7a0b\u3067\u3082\u30ce\u30a4\u30ba\u304c\u767a\u751f\u3057\u3066\u30a8\u30e9\u30fc\u304c\u751f\u3058\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30a8\u30e9\u30fc\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u306b\u3001\u3055\u307e\u3056\u307e\u306a\u624b\u6cd5\u5b58\u5728\u3057\u307e\u3059\u304c\u3001\u30c6\u30af\u30cb\u30ab\u30eb\u3067\u4eca\u56de\u306e\u8a71\u306b\u306f\u3042\u307e\u308a\u95a2\u4fc2\u306a\u3044\u306e\u3067\u7701\u7565\u3057\u307e\u3059\u3002\u8208\u5473\u306e\u3042\u308b\u65b9\u306f\u4f8b\u3048\u3070\u6587\u732e[1]\u306e12\u7ae013\u7ae0\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002\",\"id\":\"36f272c7-526e-49c6-9e00-5b4d1ef473c8\"},{\"content\":\"\u8a73\u3057\u304f\u306f\u6587\u732e[1]\u306eTheorem 2.4\u3068Corollary 2.5\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3055\u3089\u306b\u4e00\u822c\u306b\u3001\u30a8\u30e9\u30fc\u304cCPTP\u5199\u50cf\u3067\u3042\u308b\u5834\u5408\u306b\u8208\u5473\u304c\u3042\u308b\u4eba\u306f\u6587\u732e[1]\u306eTheorem 2.6\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\",\"id\":\"e264920d-c97d-49f0-a832-b0c71a3845e6\"},{\"content\":\"\u4f4d\u76f8\u306f\u7121\u8996\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002BS\u8868\u73fe\u306f\u30d1\u30a6\u30ea\u6f14\u7b97\u5b50\u306e\u4f4d\u76f8\u6210\u5206\u3092\u7121\u8996\u3057\u305f\u5546\u7fa4 $P_n\/\\\\{I,-I,iI,-iI\\\\}$\u304b\u3089 $\\\\mathbb Z_2^n\\\\times \\\\mathbb 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