{"id":2234,"date":"2026-11-06T08:00:00","date_gmt":"2026-11-05T23:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=2234"},"modified":"2026-11-05T08:40:27","modified_gmt":"2026-11-04T23:40:27","slug":"qs-approximate-circuit-hardness-20261105","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=2234","title":{"rendered":"\u91cf\u5b50\u56de\u8def\u306f\u3069\u3053\u307e\u3067\u77ed\u304f\u3067\u304d\u308b\u304b\u3001\u8fd1\u4f3c\u6700\u9069\u5316\u306e\u8a08\u7b97\u91cf"},"content":{"rendered":"<p>\u91cf\u5b50\u56de\u8def\u306e\u540c\u3058\u8a08\u7b97\u3092\u3001\u3082\u3063\u3068\u5c11\u306a\u3044\u64cd\u4f5c\u3067\u5b9f\u884c\u3057\u305f\u3044\u3002\u5c11\u3057\u306e\u8aa4\u5dee\u3092\u8a31\u305b\u3070\u3001\u5019\u88dc\u306f\u5897\u3048\u3001\u77ed\u3044\u56de\u8def\u3092\u898b\u3064\u3051\u3084\u3059\u304f\u306a\u308b\u3088\u3046\u306b\u601d\u3048\u307e\u3059\u3002\u305d\u308c\u3067\u3082\u3001<strong>\u3069\u3093\u306a\u5165\u529b\u56de\u8def\u306b\u5bfe\u3057\u3066\u3082\u3001\u8a31\u5bb9\u7bc4\u56f2\u5185\u306e\u6700\u826f\u306e\u77ed\u7e2e\u3092\u5224\u5b9a\u3059\u308b<\/strong>\u3053\u3068\u306b\u306f\u3001\u5f37\u3044\u8a08\u7b97\u4e0a\u306e\u96e3\u3057\u3055\u304c\u6b8b\u308a\u307e\u3059\u3002<\/p>\n<p>2026\u5e7411\u67083\u65e5\u306b\u516c\u958b\u3055\u308c\u305f\u3001\u30aa\u30fc\u30d5\u30b9\u5927\u5b66\u306eAdam 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style=\"min-width:620px;width:100%;border-collapse:collapse\">\n<thead>\n<tr>\n<th>\u8ad6\u6587\u306e\u8ddd\u96e2<\/th>\n<th>\u6349\u3048\u308b\u9055\u3044<\/th>\n<th>\u5168\u4f53\u306e\u4f4d\u76f8<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Sine\u8ddd\u96e2<\/td>\n<td>\u4e8c\u3064\u306e\u5909\u63db\u306e\u30c8\u30ec\u30fc\u30b9\u306e\u91cd\u306a\u308a\u306b\u57fa\u3065\u304f\u3001\u5168\u4f53\u3092\u5e73\u5747\u3059\u308b\u6027\u683c\u306e\u6307\u6a19<\/td>\n<td>\u5168\u4f53\u306e\u4f4d\u76f8\u3060\u3051\u306e\u9055\u3044\u306f\u6570\u3048\u306a\u3044<\/td>\n<\/tr>\n<tr>\n<td>Spectral\u8ddd\u96e2<\/td>\n<td>\u5165\u529b\u72b6\u614b\u306b\u3064\u3044\u3066\u6700\u3082\u5927\u304d\u304f\u306a\u308b\u3001\u72b6\u614b\u30d9\u30af\u30c8\u30eb\u306e\u9055\u3044<\/td>\n<td>\u5168\u4f53\u306e\u4f4d\u76f8\u306e\u9055\u3044\u3082\u6570\u3048\u308b<\/td>\n<\/tr>\n<tr>\n<td>Operator\u8ddd\u96e2<\/td>\n<td>\u5168\u4f53\u306e\u4f4d\u76f8\u3092\u305d\u308d\u3048\u305f\u3046\u3048\u3067\u3001\u6700\u3082\u5927\u304d\u304f\u306a\u308b\u9055\u3044<\/td>\n<td>\u5168\u4f53\u306e\u4f4d\u76f8\u3060\u3051\u306e\u9055\u3044\u306f\u6570\u3048\u306a\u3044<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u305f\u3068\u3048\u3070I\u3068\u2212I\u306f\u3001\u72b6\u614b\u5168\u4f53\u306b\u540c\u3058\u4f4d\u76f8\u304c\u4ed8\u304f\u70b9\u3060\u3051\u304c\u9055\u3044\u307e\u3059\u3002\u8ad6\u6587\u306eSpectral\u8ddd\u96e2\u3067\u306f2\u3067\u3059\u304c\u3001\u5168\u4f53\u306e\u4f4d\u76f8\u3092\u8abf\u6574\u3059\u308bOperator\u8ddd\u96e2\u3067\u306f0\u3067\u3059\u3002Sine\u8ddd\u96e2\u3067\u30820\u306b\u306a\u308a\u307e\u3059\u3002\u540c\u3058\u6570\u5024\u306e\u03b5\u3092\u7f6e\u3044\u3066\u3082\u3001\u540c\u3058\u8aa4\u5dee\u6761\u4ef6\u3092\u8ab2\u3057\u305f\u3053\u3068\u306b\u306f\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u4e3b\u5b9a\u7406\u306f\u3001Clifford\uff0bT\u3092\u53b3\u5bc6\u306b\u5b9f\u88c5\u3067\u304d\u308b\u30b2\u30fc\u30c8\u96c6\u5408\u3068\u3001\u5fc5\u8981\u306a\u7cbe\u5ea6\u307e\u3067\u52b9\u7387\u3088\u304f\u8a08\u7b97\u3067\u304d\u308b\u03b5\u3092\u5bfe\u8c61\u306b\u3057\u307e\u3059\u3002\u6052\u7b49\u5909\u63db\u3078\u306e\u8fd1\u4f3c\u3084\u7dcf\u30b2\u30fc\u30c8\u6570\u30fb\u7dcf\u6df1\u3055\u306e\u6700\u9069\u5316\u3067\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u8ddd\u96e2\u306e\u81ea\u660e\u3067\u306a\u3044\u8a31\u5bb9\u7bc4\u56f2\u5168\u4f53\u3067PP\u56f0\u96e3\u6027\u304c\u793a\u3055\u308c\u307e\u3059\u3002\u4e00\u65b9\u3001\u975eClifford\u30b2\u30fc\u30c8\u306a\u3069\u7279\u5b9a\u306e\u8cc7\u6e90\u3060\u3051\u3092\u524a\u308b\u5834\u5408\u306b\u306f\u3001\u8a3c\u660e\u304c\u5c4a\u304f\u03b5\u306e\u7bc4\u56f2\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u8cc7\u6e90\u3001\u3059\u3079\u3066\u306e\u8a31\u5bb9\u8aa4\u5dee\u3067\u540c\u3058\u7d50\u8ad6\u304c\u51fa\u305f\u3001\u3068\u5e83\u3052\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<h2>\u5883\u754c\u306b\u8fd1\u3044\u5165\u529b\u3092\u9664\u304f\u304b\u3069\u3046\u304b\u3082\u6761\u4ef6\u306b\u306a\u308b<\/h2>\n<p>\u5f93\u6765\u306e\u8fd1\u4f3c\u6052\u7b49\u6027\u306e\u7814\u7a76\u306b\u306f\u3001\u5165\u529b\u56de\u8def\u304c\u300c\u5341\u5206\u8fd1\u3044\u300d\u304b\u300c\u5341\u5206\u9060\u3044\u300d\u304b\u306e\u3069\u3061\u3089\u304b\u3067\u3001\u4e2d\u9593\u306e\u66d6\u6627\u306a\u9818\u57df\u306b\u306f\u5165\u3089\u306a\u3044\u3068\u3044\u3046\u7d04\u675f\u3092\u7f6e\u304f\u8a2d\u5b9a\u304c\u3042\u308a\u307e\u3059\u3002\u8fd1\u3044\u5074\u3068\u9060\u3044\u5074\u306e\u9593\u306b\u3001\u5165\u529b\u30b5\u30a4\u30ba\u306b\u5bfe\u3057\u3066\u4e00\u5b9a\u4ee5\u4e0a\u306e\u9699\u9593\u3092\u6301\u305f\u305b\u308b\u3053\u3068\u3067\u3001\u5224\u5b9a\u3059\u308b\u8ab2\u984c\u3092\u5b9a\u3081\u307e\u3059\u3002<\/p>\n<p>\u4eca\u56de\u306e\u4e3b\u7d50\u679c\u306f\u3001\u305d\u306e\u3088\u3046\u306a\u9699\u9593\u3092\u4fdd\u8a3c\u3057\u306a\u3044\u5165\u529b\u3092\u6271\u3044\u307e\u3059\u3002\u03b5\u306e\u3059\u3050\u8fd1\u304f\u306b\u3042\u308b\u56de\u8def\u3082\u9664\u5916\u305b\u305a\u3001\u3069\u3061\u3089\u5074\u304b\u3092\u5224\u5b9a\u3059\u308b\u8ab2\u984c\u3067\u3059\u3002\u8fd1\u4f3c\u3092\u8a8d\u3081\u308b\u3053\u3068\u3068\u3001\u5224\u5b9a\u306e\u5883\u754c\u306b\u4f59\u88d5\u3092\u8a2d\u3051\u308b\u3053\u3068\u306f\u5225\u3067\u3042\u308a\u3001\u3053\u306e\u6761\u4ef6\u306e\u9055\u3044\u3092\u843d\u3068\u3059\u3068\u3001\u904e\u53bb\u306e\u7d50\u679c\u3068\u306e\u6bd4\u8f03\u3092\u8aa4\u308a\u307e\u3059\u3002<\/p>\n<p>\u5b9f\u7528\u7684\u306a\u30b3\u30f3\u30d1\u30a4\u30e9\u3092\u8a55\u4fa1\u3059\u308b\u969b\u306b\u306f\u3001\u307e\u305a\u3069\u306e\u8ddd\u96e2\u3067\u8aa4\u5dee\u3092\u78ba\u304b\u3081\u3001\u3069\u306e\u8cc7\u6e90\u3092\u6e1b\u3089\u3059\u306e\u304b\u3092\u660e\u793a\u3057\u307e\u3059\u3002\u305d\u306e\u3046\u3048\u3067\u3001\u6539\u5584\u3057\u305f\u56de\u8def\u304c\u5f97\u3089\u308c\u305f\u3053\u3068\u3068\u3001\u6700\u826f\u3060\u3068\u4fdd\u8a3c\u3067\u304d\u305f\u3053\u3068\u3092\u5206\u3051\u307e\u3059\u3002\u7279\u5b9a\u306e\u69cb\u9020\u306b\u7d5e\u308b\u3001\u5c40\u6240\u7684\u306a\u7f6e\u63db\u3092\u4f7f\u3046\u3001\u6642\u9593\u3092\u6c7a\u3081\u3066\u826f\u3044\u5019\u88dc\u3092\u63a2\u3059\u3001\u3068\u3044\u3063\u305f\u65b9\u6cd5\u306e\u4fa1\u5024\u306f\u3001\u3053\u306e\u6700\u60aa\u6642\u306e\u96e3\u3057\u3055\u306b\u3088\u3063\u3066\u5931\u308f\u308c\u307e\u305b\u3093\u3002<\/p>\n<p>\u3053\u306e\u8ad6\u6587\u304c\u793a\u3059\u306e\u306f\u3001\u8fd1\u4f3c\u3092\u8a31\u305b\u3070\u6700\u9069\u5316\u306e\u6839\u672c\u7684\u306a\u96e3\u3057\u3055\u3082\u6d88\u3048\u308b\u3001\u3068\u306f\u9650\u3089\u306a\u3044\u3068\u3044\u3046\u5883\u754c\u3067\u3059\u3002\u56de\u8def\u3092\u77ed\u304f\u3059\u308b\u6210\u679c\u3092\u8aad\u3080\u3068\u304d\u3082\u3001\u77ed\u7e2e\u7387\u3068\u3042\u308f\u305b\u3066\u3001\u8a31\u3057\u305f\u8aa4\u5dee\u3001\u5bfe\u8c61\u3068\u3057\u305f\u5165\u529b\u3001\u4fdd\u8a3c\u3057\u305f\u7bc4\u56f2\u3092\u898b\u308b\u3053\u3068\u304c\u5927\u5207\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h2>\u51fa\u5178<\/h2>\n<ul>\n<li>Adam Husted Kjelstr\u00f8m, Jaco van de Pol, Andreas Pavlogiannis, <a href=\"https:\/\/arxiv.org\/abs\/2611.04381v1\">On the Hardness of Approximate Quantum Circuit Membership and Optimization<\/a>, arXiv:2611.04381v1\uff082026\u5e7411\u67083\u65e5\u516c\u958b\uff09\u3002\u554f\u984c\u8a2d\u5b9a\u30fb\u4e3b\u5b9a\u7406\u30fb\u8a31\u5bb9\u7bc4\u56f2\u306f\u7b2c1\u7bc0\u3068Table 1\u3001\u8ddd\u96e2\u3068PP\u306e\u5b9a\u7fa9\u306f\u7b2c2\u7bc0\u3001\u53ef\u9006\u56de\u8def\u306b\u3088\u308bSine\u8ddd\u96e2\u306e\u69cb\u6210\u306f\u7b2c3.2.1\u7bc0\u3001\u6700\u9069\u5316\u3078\u306e\u5e30\u7d50\u306fCorollary 1\u3001\u672a\u89e3\u6c7a\u7bc4\u56f2\u306f\u7b2c5\u7bc0\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u91cf\u5b50\u56de\u8def\u306e\u540c\u3058\u8a08\u7b97\u3092\u3001\u3082\u3063\u3068\u5c11\u306a\u3044\u64cd\u4f5c\u3067\u5b9f\u884c\u3057\u305f\u3044\u3002\u5c11\u3057\u306e\u8aa4\u5dee\u3092\u8a31\u305b\u3070\u3001\u5019\u88dc\u306f\u5897\u3048\u3001\u77ed\u3044\u56de\u8def\u3092\u898b\u3064\u3051\u3084\u3059\u304f\u306a\u308b\u3088\u3046\u306b\u601d\u3048\u307e\u3059\u3002\u305d\u308c\u3067\u3082\u3001\u3069\u3093\u306a\u5165\u529b\u56de\u8def\u306b\u5bfe\u3057\u3066\u3082\u3001\u8a31\u5bb9\u7bc4\u56f2\u5185\u306e\u6700\u826f\u306e\u77ed\u7e2e\u3092\u5224\u5b9a\u3059\u308b\u3053\u3068\u306b\u306f\u3001\u5f37\u3044\u8a08\u7b97\u4e0a\u306e\u96e3\u3057 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":2232,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":false,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[30],"tags":[437],"class_list":["post-2234","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-computing","tag-quantum-circuit-complexity"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/11\/qs-approximate-circuit-hardness-20261105-50a98a97f926.png","_links":{"self":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/2234","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2234"}],"version-history":[{"count":1,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/2234\/revisions"}],"predecessor-version":[{"id":2235,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/2234\/revisions\/2235"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/media\/2232"}],"wp:attachment":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}