{"id":1051,"date":"2026-10-18T22:00:00","date_gmt":"2026-10-18T13:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=1051"},"modified":"2026-10-18T14:47:32","modified_gmt":"2026-10-18T05:47:32","slug":"qs-fourth-order-negative-substeps-20261018","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=1051","title":{"rendered":"\u9ad8\u6b21\u306e\u5206\u5272\u516c\u5f0f\u306b\u8ca0\u306e\u523b\u307f\u304c\u73fe\u308c\u308b\u7406\u7531"},"content":{"rendered":"<p>\u91cf\u5b50\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u8fd1\u4f3c\u3092\u7d30\u304b\u304f\u3057\u3066\u3044\u304f\u3068\u3001\u5206\u5272\u306e\u9014\u4e2d\u306b\u300c\u8ca0\u306e\u523b\u307f\u300d\u304c\u73fe\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u8a08\u7b97\u304c\u904e\u53bb\u3078\u623b\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u305d\u308c\u3068\u3082\u3001\u9593\u9055\u3063\u305f\u4fc2\u6570\u306a\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\u3001\u5bfe\u79f0\u306a\u4e8c\u6b21\u306e\u5206\u5272\u516c\u5f0f\u3092\u7d44\u307f\u5408\u308f\u305b\u3001\u56db\u6b21\u3078\u7cbe\u5ea6\u3092\u4e0a\u3052\u308b\u4e8c\u3064\u306e\u69cb\u6210\u3092\u898b\u307e\u3059\u3002\u8ca0\u306e\u4fc2\u6570\u306f\u3001\u6b8b\u3063\u3066\u3044\u308b\u8aa4\u5dee\u3092\u6253\u3061\u6d88\u3059\u305f\u3081\u306b\u73fe\u308c\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u5f0f\u3068\u3057\u3066\u8aa4\u5dee\u3092\u6d88\u305b\u308b\u3053\u3068\u3068\u3001\u305d\u306e\u5404\u64cd\u4f5c\u3092\u8a08\u7b97\u6a5f\u3084\u5b9f\u6a5f\u3067\u5b9f\u884c\u3067\u304d\u308b\u3053\u3068\u306f\u3001\u5225\u306b\u78ba\u304b\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<sup class=\"source-note\"><a href=\"#ref1\">[1]<\/a><\/sup><\/p>\n<section class=\"influvetor-quick-summary\" aria-label=\"\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f\">\n<p><strong>\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f<\/strong><\/p>\n<ul>\n<li>\u5bfe\u79f0\u306a\u4e8c\u6b21\u516c\u5f0f\u306e\u4e09\u6b21\u306e\u8aa4\u5dee\u3092\u6d88\u3059\u305f\u3081\u3001\u3053\u3053\u3067\u6271\u3046\u56db\u6b21\u306e\u69cb\u6210\u306f\u3001\u6b63\u306e\u523b\u307f\u3068\u8ca0\u306e\u523b\u307f\u3092\u7d44\u307f\u5408\u308f\u305b\u307e\u3059\u3002<\/li>\n<li>3\u30d6\u30ed\u30c3\u30af\u7248\u306f\u9014\u4e2d\u306e\u7d2f\u7a4d\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u76ee\u6a19\u533a\u9593\u306e\u5916\u3078\u51fa\u307e\u3059\u30025\u30d6\u30ed\u30c3\u30af\u7248\u306f\u30d6\u30ed\u30c3\u30af\u5883\u754c\u306e\u7d2f\u7a4d\u5024\u304c\u533a\u9593\u5185\u306b\u53ce\u307e\u308a\u307e\u3059\u304c\u3001\u4e2d\u592e\u306e\u523b\u307f\u306f\u3084\u306f\u308a\u8ca0\u3067\u3059\u3002<\/li>\n<li>\u8ca0\u306e\u523b\u307f\u306f\u3001\u6570\u5f0f\u306e\u767a\u5c55\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u9006\u5411\u304d\u306b\u4f7f\u3046\u3053\u3068\u3067\u3059\u3002\u5b9f\u9a13\u5ba4\u306e\u6642\u9593\u304c\u9006\u884c\u3059\u308b\u610f\u5473\u3067\u306f\u306a\u304f\u3001\u9006\u64cd\u4f5c\u306e\u53ef\u5426\u3001\u5b89\u5b9a\u6027\u3001\u5fc5\u8981\u306a\u6f14\u7b97\u6570\u3092\u78ba\u304b\u3081\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/section>\n<h2>\u56db\u6b21\u3078\u9032\u3080\u524d\u306b\u3001\u4e8c\u6b21\u306e\u30d6\u30ed\u30c3\u30af\u3092\u7528\u610f\u3059\u308b<\/h2>\n<p>\u6642\u9593\u306b\u3088\u3089\u306a\u3044\u4e8c\u3064\u306e\u6f14\u7b97\u5b50A\u3068B\u306b\u5bfe\u3057\u3001\u76ee\u6a19\u3092 <code style=\"overflow-wrap:anywhere;\">exp[h(A+B)]<\/code> \u3068\u3057\u307e\u3059\u3002h\u306f\u4e00\u5ea6\u306b\u9032\u3081\u305f\u3044\u767a\u5c55\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3059\u3002\u9589\u3058\u305f\u91cf\u5b50\u7cfb\u306e\u5b9f\u6642\u9593\u767a\u5c55\u306a\u3089\u3001\u210f\u30921\u3068\u3059\u308b\u5358\u4f4d\u3067 <code>A=\u2212iH_A<\/code>\u3001<code>B=\u2212iH_B<\/code> \u3068\u7f6e\u3051\u307e\u3059\u3002H_A\u3068H_B\u306f\u30a8\u30eb\u30df\u30fc\u30c8\u306a\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3067\u3001\u91cf\u5b50\u7cfb\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3084\u76f8\u4e92\u4f5c\u7528\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<p>A\u3068B\u3092\u5225\u3005\u306b\u6271\u3046\u5bfe\u79f0\u306a\u4e8c\u6b21\u516c\u5f0f\u306f\u3001\u6b21\u306e\u5f62\u3067\u3059\u3002A\u3092\u534a\u5206\u3001B\u3092\u5168\u91cf\u3001\u6700\u5f8c\u306bA\u3092\u534a\u5206\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<p><code style=\"overflow-wrap:anywhere;\">S\u2082(h)=exp(hA\/2) exp(hB) exp(hA\/2)<\/code><\/p>\n<p>\u4e00\u822c\u306bA\u3068B\u306f\u4ea4\u63db\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u3053\u306e\u7a4d\u306f\u76ee\u6a19\u306e\u6307\u6570\u3068\u5b8c\u5168\u306b\u306f\u4e00\u81f4\u3057\u307e\u305b\u3093\u3002\u5341\u5206\u5c0f\u3055\u306ah\u3067\u5c55\u958b\u3067\u304d\u308b\u6761\u4ef6\u3067\u306f\u3001\u6307\u6570\u306e\u4e2d\u306b <code>h\u00b3R\u2083<\/code> \u3068\u3044\u3046\u5148\u982d\u306e\u8aa4\u5dee\u304c\u6b8b\u308a\u307e\u3059\u3002R\u2083\u306fA\u3068B\u306e\u7d44\u5408\u305b\u3067\u6c7a\u307e\u308b\u6f14\u7b97\u5b50\u3067\u3059\u3002\u5bfe\u79f0\u6027\u304b\u3089 <code style=\"overflow-wrap:anywhere;\">S\u2082(h)S\u2082(\u2212h)=I<\/code> \u304c\u6210\u308a\u7acb\u3061\u3001\u6307\u6570\u306e\u5c55\u958b\u306b\u306f\u5076\u6570\u6b21\u306e\u9805\u304c\u73fe\u308c\u307e\u305b\u3093\u3002\u539f\u8cc7\u6599\u306f\u3053\u306e\u6027\u8cea\u3092\u5f0f(37)\u30fb(38)\u3067\u793a\u3057\u3066\u3044\u307e\u3059\u3002<sup class=\"source-note\"><a href=\"#ref1\">[1]<\/a><\/sup><\/p>\n<p>\u4ee5\u4e0b\u306e\u6b21\u6570\u306e\u8aac\u660e\u306f\u3001\u4f8b\u3048\u3070\u6709\u9650\u6b21\u5143\u306e\u6709\u754c\u306a\u884c\u5217\u3092\u3001\u5c0f\u3055\u306ah\u3067\u6271\u3046\u5834\u5408\u3092\u60f3\u5b9a\u3057\u307e\u3059\u3002\u7279\u5225\u306a\u53ef\u63db\u6027\u306a\u3069\u3067R\u2083\u81ea\u4f53\u304c\u6d88\u3048\u308b\u5834\u5408\u307e\u3067\u3001\u5fc5\u305a\u4e09\u6b21\u306e\u8aa4\u5dee\u304c\u51fa\u308b\u3068\u4e3b\u5f35\u3059\u308b\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<h2>\u8ca0\u306e\u4fc2\u6570\u306f\u3001\u4e09\u6b21\u306e\u8aa4\u5dee\u3092\u6253\u3061\u6d88\u3059\u305f\u3081\u306b\u73fe\u308c\u308b<\/h2>\n<p>S\u2082\u306e\u523b\u307f\u3092ch\u3078\u5909\u3048\u308b\u3068\u3001\u76ee\u6a19\u306e\u4e00\u6b21\u306e\u90e8\u5206\u306fc\u500d\u3001\u5148\u982d\u306e\u8aa4\u5dee\u306fc\u00b3\u500d\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067S\u2082\u30923\u500b\u3001\u4fc2\u6570 <code style=\"overflow-wrap:anywhere;\">s\u30011\u22122s\u3001s<\/code> \u3067\u7d44\u307f\u5408\u308f\u305b\u307e\u3059\u3002<\/p>\n<p><code style=\"overflow-wrap:anywhere;\">F\u2083(h)=S\u2082(sh) S\u2082((1\u22122s)h) S\u2082(sh)<\/code><\/p>\n<p>\u4fc2\u6570\u306e\u548c\u306f1\u306a\u306e\u3067\u3001\u9032\u3081\u305f\u3044\u4e00\u6b21\u306e\u90e8\u5206\u306fh\u306e\u307e\u307e\u3067\u3059\u3002\u540c\u3058\u5bfe\u79f0\u30d6\u30ed\u30c3\u30af\u3092\u5de6\u53f3\u5bfe\u79f0\u306b\u4e26\u3079\u308b\u3053\u306e\u69cb\u6210\u3067\u306f\u3001\u4e09\u6b21\u306e\u8aa4\u5dee\u4fc2\u6570\u306f <code style=\"overflow-wrap:anywhere;\">2s\u00b3+(1\u22122s)\u00b3<\/code> \u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u30920\u306b\u3059\u308b\u89e3\u304c\u3001\u6b21\u306e\u5024\u3067\u3059\u3002<\/p>\n<p><code style=\"overflow-wrap:anywhere;\">s=1\/(2\u2212\u221b2) \u2248 1.351207<\/code><\/p>\n<p>\u4e2d\u592e\u306e\u4fc2\u6570 <code>1\u22122s<\/code> \u306f\u7d04\u22121.702414\u3067\u3059\u3002\u6b63\u306e\u4fc2\u6570\u3060\u3051\u306a\u3089\u3001\u305d\u306e\u4e09\u4e57\u306e\u548c\u30920\u306b\u3057\u306a\u304c\u3089\u4fc2\u6570\u306e\u548c\u30921\u306b\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3053\u306e\u69cb\u6210\u3067\u306f\u3001\u8ca0\u306e\u523b\u307f\u304c\u4e09\u6b21\u306e\u8aa4\u5dee\u3092\u53cd\u5bfe\u7b26\u53f7\u3067\u5bc4\u4e0e\u3055\u305b\u307e\u3059\u3002\u5bfe\u79f0\u6027\u3092\u4fdd\u3063\u305f\u307e\u307e\u4e09\u6b21\u306e\u9805\u3092\u6d88\u3059\u305f\u3081\u3001\u6b21\u306b\u6b8b\u308b\u306e\u306f\u901a\u5e38\u3001\u4e94\u6b21\u306e\u5c40\u6240\u8aa4\u5dee\u3067\u3059\u3002<sup class=\"source-note\"><a href=\"#ref1\">[1]<\/a><\/sup><\/p>\n<p>\u3053\u308c\u304c\u300c\u56db\u6b21\u300d\u306e\u610f\u5473\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002\u56fa\u5b9a\u3057\u305f\u5168\u533a\u9593\u3092\u5c0f\u3055\u306ah\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u9032\u3081\u308b\u3068\u3001\u9069\u5207\u306a\u6709\u754c\u6027\u30fb\u5b89\u5b9a\u6027\u306e\u6761\u4ef6\u306e\u4e0b\u3067\u3001\u5168\u4f53\u306e\u8aa4\u5dee\u306fO(h\u2074)\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u6b69\u306eO(h\u2075)\u3068\u3001\u5168\u533a\u9593\u306eO(h\u2074)\u3092\u533a\u5225\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u4e09\u4e57\u3092\u8db3\u3059\u3060\u3051\u306e\u8aac\u660e\u3092\u3001\u305d\u306e\u307e\u307e\u4e94\u6b21\u4ee5\u4e0a\u306e\u8aa4\u5dee\u3078\u4f7f\u3046\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u539f\u8cc7\u6599\u3082\u3001\u3088\u308a\u9ad8\u3044\u6b21\u6570\u306b\u306f\u540c\u3058\u5358\u7d14\u306a\u8db3\u3057\u7b97\u304c\u901a\u7528\u3057\u306a\u3044\u3068\u6ce8\u610f\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2>5\u30d6\u30ed\u30c3\u30af\u306b\u3057\u3066\u3082\u3001\u8ca0\u306e\u523b\u307f\u306f\u6b8b\u308b<\/h2>\n<p>\u5225\u306e\u56db\u6b21\u516c\u5f0f\u3067\u306f\u3001\u5de6\u53f3\u306b\u540c\u3058\u30d6\u30ed\u30c3\u30af\u30922\u500b\u305a\u3064\u7f6e\u304d\u307e\u3059\u3002\u539f\u8cc7\u6599\u306es\u2082\u3092\u3001\u3053\u3053\u3067\u306f3\u30d6\u30ed\u30c3\u30af\u7248\u306es\u3068\u533a\u5225\u3057\u3066q\u3068\u66f8\u304d\u307e\u3059\u3002<\/p>\n<p><code style=\"overflow-wrap:anywhere;\">F\u2085(h)=S\u2082(qh)\u00b2 S\u2082((1\u22124q)h) S\u2082(qh)\u00b2<\/code><\/p>\n<p>\u4eca\u5ea6\u306f <code style=\"overflow-wrap:anywhere;\">4q\u00b3+(1\u22124q)\u00b3=0<\/code> \u3068\u3059\u308c\u3070\u3088\u304f\u3001<code style=\"overflow-wrap:anywhere;\">q=1\/(4\u2212\u221b4) \u2248 0.414491<\/code> \u3067\u3059\u3002\u4e2d\u592e\u306e\u4fc2\u6570\u306f\u7d04\u22120.657963\u306b\u306a\u308a\u307e\u3059\u3002\u6b63\u306e\u30d6\u30ed\u30c3\u30af\u3092\u5897\u3084\u3059\u3053\u3068\u3067\u30013\u30d6\u30ed\u30c3\u30af\u7248\u3068\u306f\u9055\u3046\u5927\u304d\u3055\u306e\u6b63\u8ca0\u306e\u523b\u307f\u3067\u3001\u540c\u3058\u4e09\u6b21\u306e\u8aa4\u5dee\u3092\u6d88\u3057\u3066\u3044\u307e\u3059\u3002<sup class=\"source-note\"><a href=\"#ref1\">[1]<\/a><\/sup><\/p>\n<div style=\"overflow-x:auto;max-width:100%;\">\n<table style=\"min-width:620px;\">\n<caption>\u88681\uff1a\u4e8c\u3064\u306e\u56db\u6b21\u69cb\u6210\u3002\u4fc2\u6570\u306f\u672c\u7a3f\u3067\u5f0f(42)\u30fb(45)\u304b\u3089\u8a08\u7b97\u3057\u3001\u5c0f\u6570\u7b2c6\u4f4d\u307e\u3067\u8868\u793a\u3002<\/caption>\n<thead>\n<tr>\n<th>\u69cb\u6210<\/th>\n<th>\u5de6\u53f3\u306e\u4fc2\u6570<\/th>\n<th>\u4e2d\u592e\u306e\u4fc2\u6570<\/th>\n<th>A\u30fbB\u306e\u6307\u6570\u56e0\u5b50\u6570<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>3\u30d6\u30ed\u30c3\u30af F\u2083<\/td>\n<td>s \u2248 1.351207<\/td>\n<td>1\u22122s \u2248 \u22121.702414<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>5\u30d6\u30ed\u30c3\u30af F\u2085<\/td>\n<td>q \u2248 0.414491\uff08\u5de6\u53f3\u54042\u500b\uff09<\/td>\n<td>1\u22124q \u2248 \u22120.657963<\/td>\n<td>11<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u8868\u306e\u5c0f\u6570\u306f\u8868\u793a\u7528\u306e\u4e38\u3081\u5024\u3067\u3059\u3002\u8a08\u7b97\u3067\u306f\u6839\u53f7\u3092\u542b\u3080\u5f0f\u304b\u3089\u5341\u5206\u306a\u7cbe\u5ea6\u3067\u4fc2\u6570\u3092\u6c42\u3081\u3001\u4fc2\u6570\u548c\u3068\u4e09\u6b21\u306e\u76f8\u6bba\u6761\u4ef6\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u4e38\u3081\u8aa4\u5dee\u304c\u6b8b\u308c\u3070\u3001\u7406\u60f3\u7684\u306a\u56db\u6b21\u306e\u632f\u308b\u821e\u3044\u304b\u3089\u5916\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u6307\u6570\u56e0\u5b50\u6570\u306f\u3001\u96a3\u308a\u5408\u3046\u540c\u3058A\u306e\u6307\u6570\u3092\u307e\u3068\u3081\u305f\u5834\u5408\u3067\u3059\u3002n\u500b\u306eS\u2082\u3092\u305d\u306e\u307e\u307e\u5c55\u958b\u3059\u308c\u30703n\u500b\u3067\u3059\u304c\u3001\u30d6\u30ed\u30c3\u30af\u9593\u306eA\u3069\u3046\u3057\u3092n\u22121\u304b\u6240\u3067\u7d71\u5408\u3067\u304d\u308b\u305f\u3081\u30012n+1\u500b\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e7\u306811\u306f\u6570\u5f0f\u4e0a\u306e\u6307\u6570\u56e0\u5b50\u306e\u6570\u3067\u3001\u88c5\u7f6e\u306e\u30b2\u30fc\u30c8\u6570\u3084\u5b9f\u884c\u6642\u9593\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5404\u6307\u6570\u306e\u5b9f\u88c5\u3084\u7d71\u5408\u306e\u53ef\u5426\u306b\u3088\u3063\u3066\u3001\u5b9f\u969b\u306e\u8ca0\u62c5\u306f\u5909\u308f\u308a\u307e\u3059\u3002<\/p>\n<h2>\u300c\u8ca0\u306e\u523b\u307f\u300d\u3068\u300c\u9014\u4e2d\u3067\u533a\u9593\u306e\u5916\u3078\u51fa\u308b\u300d\u306f\u5225\u306e\u6761\u4ef6<\/h2>\n<p>\u523b\u307f\u3092\u8db3\u3057\u5408\u308f\u305b\u305f\u5024\u3092\u3001\u76ee\u6a19h\u3067\u5272\u3063\u3066\u898b\u307e\u3059\u3002\u958b\u59cb\u30920\u3001\u7d42\u4e86\u30921\u3068\u3059\u308b\u3068\u30013\u30d6\u30ed\u30c3\u30af\u7248\u306e\u30d6\u30ed\u30c3\u30af\u5883\u754c\u306f\u6b21\u306e\u9806\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><code style=\"overflow-wrap:anywhere;\">0 \u2192 1.351207 \u2192 \u22120.351207 \u2192 1<\/code><\/p>\n<p>\u6700\u521d\u306b\u76ee\u6a191\u3092\u8d8a\u3048\u3001\u4e2d\u592e\u306e\u8ca0\u306e\u523b\u307f\u3067\u958b\u59cb0\u3088\u308a\u5c0f\u3055\u304f\u306a\u308a\u3001\u6700\u5f8c\u306b1\u3078\u5230\u9054\u3057\u307e\u3059\u3002\u4e00\u65b9\u30015\u30d6\u30ed\u30c3\u30af\u7248\u306f\u6b21\u306e\u7d4c\u8def\u3067\u3059\u3002<\/p>\n<p><code style=\"overflow-wrap:anywhere;\">0 \u2192 0.414491 \u2192 0.828982 \u2192 0.171018 \u2192 0.585509 \u2192 1<\/code><\/p>\n<p>\u3053\u3061\u3089\u306f\u30d6\u30ed\u30c3\u30af\u5883\u754c\u306e\u7d2f\u7a4d\u5024\u304c0\u304b\u30891\u306e\u9593\u306b\u53ce\u307e\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u30010.828982\u304b\u30890.171018\u3078\u4e0b\u304c\u308b\u4e2d\u592e\u306e\u6bb5\u306f\u3001\u78ba\u304b\u306b\u8ca0\u3067\u3059\u3002\u300c\u76ee\u6a19\u533a\u9593\u306e\u5916\u3078\u51fa\u306a\u3044\u300d\u3068\u300c\u3059\u3079\u3066\u306e\u6bb5\u304c\u6b63\u300d\u306f\u3001\u540c\u3058\u610f\u5473\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-fourth-order-negative-substeps-20261018-figure-5333b4b2223b.png\" alt=\"3\u30d6\u30ed\u30c3\u30af\u7248\u306f\u7d2f\u7a4d\u30d1\u30e9\u30e1\u30fc\u30bf\u304c1\u3092\u8d8a\u3048\u3001\u6b21\u306b0\u3088\u308a\u4e0b\u3078\u623b\u3063\u3066\u304b\u30891\u3078\u7740\u304f\u30025\u30d6\u30ed\u30c3\u30af\u7248\u306f0\u304b\u30891\u306e\u7bc4\u56f2\u5185\u3060\u304c\u4e2d\u592e\u3067\u5024\u304c\u4e0b\u304c\u308b\u3002\u6a2a\u8ef8\u306f\u30d6\u30ed\u30c3\u30af\u51e6\u7406\u9806\u3067\u5b9f\u9a13\u5ba4\u306e\u6642\u9593\u3067\u306f\u306a\u3044\u72ec\u81ea\u8a08\u7b97\u56f3\u3002\" width=\"1200\" height=\"1160\" style=\"max-width:100%;height:auto;\"><figcaption>\u56f31\uff1a\u5404S\u2082\u30d6\u30ed\u30c3\u30af\u7d42\u4e86\u6642\u306e\u7d2f\u7a4d\u5206\u5272\u30d1\u30e9\u30e1\u30fc\u30bf\u3092h\u3067\u898f\u683c\u5316\u3057\u305f\u72ec\u81ea\u56f3\u3002\u6a2a\u8ef8\u306f\u30d6\u30ed\u30c3\u30af\u51e6\u7406\u306e\u9806\u756a\u3067\u3001\u5b9f\u6642\u9593\u3084\u6f14\u7b97\u30b3\u30b9\u30c8\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5404S\u2082\u5185\u90e8\u306eA\u30fbB\u306e\u4e2d\u9593\u72b6\u614b\u3092\u63cf\u3044\u305f\u56f3\u3067\u3082\u3042\u308a\u307e\u305b\u3093\u3002<\/figcaption><\/figure>\n<p>\u539f\u8cc7\u6599\u306f3\u30d6\u30ed\u30c3\u30af\u7248\u304c\u958b\u59cb\u4ee5\u524d\u3078\u53ca\u3076\u3053\u3068\u3092\u3001\u30c7\u30eb\u30bf\u72b6\u306e\u5206\u5e03\u304b\u3089\u306e\u62e1\u6563\u3092\u4f8b\u306b\u6ce8\u610f\u3057\u30015\u30d6\u30ed\u30c3\u30af\u7248\u3068\u306e\u9055\u3044\u3092\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u3053\u306e\u8aac\u660e\u3060\u3051\u304b\u3089\u300c5\u30d6\u30ed\u30c3\u30af\u7248\u306a\u3089\u3001\u3042\u3089\u3086\u308b\u62e1\u6563\u8a08\u7b97\u3092\u5b89\u5b9a\u306b\u5b9f\u884c\u3067\u304d\u308b\u300d\u3068\u306f\u8a00\u3048\u307e\u305b\u3093\u3002\u8ca0\u306e\u6bb5\u305d\u306e\u3082\u306e\u306f\u6b8b\u308b\u305f\u3081\u3001\u9006\u5411\u304d\u306e\u4f5c\u7528\u304c\u5b9a\u7fa9\u3067\u304d\u308b\u304b\u3001\u8aa4\u5dee\u3092\u5897\u5e45\u3057\u306a\u3044\u304b\u306f\u5bfe\u8c61\u3054\u3068\u306b\u78ba\u304b\u3081\u307e\u3059\u3002<sup class=\"source-note\"><a href=\"#ref1\">[1]<\/a><\/sup><\/p>\n<h2>\u9006\u5411\u304d\u306e\u6f14\u7b97\u306f\u3001\u5b9f\u9a13\u5ba4\u306e\u6642\u8a08\u3092\u623b\u3059\u3053\u3068\u3067\u306f\u306a\u3044<\/h2>\n<p>\u91cf\u5b50\u7cfb\u3067H\u304c\u30a8\u30eb\u30df\u30fc\u30c8\u306a\u3089\u3001<code style=\"overflow-wrap:anywhere;\">exp(\u2212i(\u2212a)H)=exp(+iaH)<\/code> \u306f <code>exp(\u2212iaH)<\/code> \u306e\u9006\u6f14\u7b97\u3067\u3059\u3002\u8a08\u7b97\u4e0a\u306f\u8ca0\u306e\u767a\u5c55\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u6307\u5b9a\u3067\u304d\u307e\u3059\u304c\u3001\u305d\u308c\u3092\u5b9f\u6a5f\u3067\u884c\u3046\u306b\u306f\u3001\u4f8b\u3048\u3070\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u7b26\u53f7\u3092\u5909\u3048\u308b\u3001\u307e\u305f\u306f\u540c\u3058\u9006\u30e6\u30cb\u30bf\u30ea\u3092\u5225\u306e\u56de\u8def\u3067\u69cb\u6210\u3059\u308b\u624b\u6bb5\u304c\u8981\u308a\u307e\u3059\u3002\u5b9f\u9a13\u5ba4\u306e\u6642\u8a08\u305d\u306e\u3082\u306e\u304c\u9006\u5411\u304d\u306b\u9032\u3080\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u5e38\u306b\u50cd\u3044\u3066\u3044\u308b\u76f8\u4e92\u4f5c\u7528\u307e\u3067\u81ea\u7531\u306b\u53cd\u8ee2\u3067\u304d\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3057\u3001\u5404\u6307\u6570\u3092\u5225\u306e\u30b2\u30fc\u30c8\u5217\u3067\u5b9f\u88c5\u3059\u308c\u3070\u3001\u305d\u306e\u5408\u6210\u8aa4\u5dee\u3082\u52a0\u308f\u308a\u307e\u3059\u3002\u6570\u5b66\u4e0a\u306e\u56e0\u5b50\u306b\u9006\u6f14\u7b97\u304c\u3042\u308b\u3053\u3068\u306f\u3001\u5bfe\u8c61\u88c5\u7f6e\u304c\u305d\u308c\u3092\u6b63\u78ba\u304b\u3064\u5b89\u4fa1\u306b\u5b9f\u884c\u3067\u304d\u308b\u3068\u3044\u3046\u8a3c\u660e\u306b\u306f\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u9589\u3058\u305f\u7cfb\u306e\u30e6\u30cb\u30bf\u30ea\u767a\u5c55\u3068\u3001\u4e0d\u53ef\u9006\u306a\u6e1b\u8870\u3084\u62e1\u6563\u3092\u540c\u3058\u6761\u4ef6\u3067\u6271\u3046\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u524d\u5411\u304d\u306b\u60c5\u5831\u3092\u5931\u3046\u767a\u5c55\u3067\u306f\u3001\u8ca0\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u64cd\u4f5c\u304c\u8a31\u3055\u308c\u306a\u3044\u5834\u5408\u3084\u3001\u6570\u5024\u8aa4\u5dee\u306b\u654f\u611f\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u672c\u7a3f\u306e\u4e8c\u3064\u306e\u69cb\u6210\u306e\u6b21\u6570\u3060\u3051\u3092\u6839\u62e0\u306b\u3001\u958b\u3044\u305f\u7cfb\u306e\u8a08\u7b97\u3078\u9069\u7528\u3059\u308b\u3053\u3068\u306f\u907f\u3051\u307e\u3059\u3002<\/p>\n<h2>\u516c\u5f0f\u3092\u9078\u3076\u3068\u304d\u306f\u3001\u6b21\u6570\u306e\u307b\u304b\u306b\u4f55\u3092\u898b\u308b\u304b<\/h2>\n<p>3\u30d6\u30ed\u30c3\u30af\u7248\u30685\u30d6\u30ed\u30c3\u30af\u7248\u306f\u3001\u3069\u3061\u3089\u3082\u56db\u6b21\u3067\u3059\u3002\u3060\u304b\u3089\u3068\u3044\u3063\u3066\u3001\u540c\u3058h\u3067\u8aa4\u5dee\u304c\u540c\u3058\u306b\u306a\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6b8b\u308b\u4e94\u6b21\u4ee5\u4e0a\u306e\u8aa4\u5dee\u306e\u4fc2\u6570\u3001\u5bfe\u8c61\u306eA\u3068B\u3001\u89b3\u6e2c\u91cf\u3001\u8a31\u5bb9\u7cbe\u5ea6\u306b\u3088\u3063\u3066\u7d50\u679c\u306f\u5909\u308f\u308a\u307e\u3059\u3002\u56e0\u5b50\u306e\u6570\u304c\u5c11\u306a\u30443\u30d6\u30ed\u30c3\u30af\u7248\u306b\u3082\u3001\u4e2d\u9593\u306e\u7d2f\u7a4d\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u533a\u9593\u5916\u3078\u51fa\u308b\u3068\u3044\u3046\u6761\u4ef6\u304c\u3042\u308a\u307e\u3059\u30025\u30d6\u30ed\u30c3\u30af\u7248\u306f\u305d\u306e\u30d6\u30ed\u30c3\u30af\u5883\u754c\u306e\u554f\u984c\u3092\u907f\u3051\u307e\u3059\u304c\u3001\u8ca0\u306e\u6bb5\u3068\u8ffd\u52a0\u306e\u6307\u6570\u56e0\u5b50\u3092\u4f34\u3044\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a\u3001A\u30fbB\u304c\u6642\u9593\u306b\u3088\u3089\u306a\u3044\u3068\u3044\u3046\u524d\u63d0\u3001\u5404\u6b63\u8ca0\u306e\u6307\u6570\u6f14\u7b97\u306e\u5b9a\u7fa9\u3068\u5b9f\u88c5\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u305d\u306e\u3046\u3048\u3067\u3001\u5fc5\u8981\u306a\u7cbe\u5ea6\u306b\u5bfe\u3059\u308b\u523b\u307f\u5e45\u3068\u6f14\u7b97\u306e\u8ca0\u62c5\u3092\u6bd4\u3079\u307e\u3059\u3002\u5b9f\u6642\u9593\u306e\u5236\u5fa1\u304c\u9014\u4e2d\u3067\u5909\u308f\u308b\u554f\u984c\u3067\u306f\u3001\u6642\u9593\u9806\u5e8f\u306b\u5bfe\u5fdc\u3057\u305f\u5225\u306e\u6271\u3044\u3082\u5fc5\u8981\u3067\u3059\u3002\u539f\u8cc7\u6599\u3082\u7b2c4\u7bc0\u3067\u3001\u6642\u9593\u4f9d\u5b58\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u3078\u306e\u69cb\u6210\u306b\u306f\u4fee\u6b63\u304c\u8981\u308b\u3068\u533a\u5225\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u4e8c\u6b21\u304b\u3089\u56db\u6b21\u3078\u4e0a\u3052\u308b\u8a08\u7b97\u306f\u3001\u8aa4\u5dee\u3092\u3088\u308a\u5de7\u307f\u306b\u6d88\u3059\u8a2d\u8a08\u3067\u3059\u3002\u305d\u306e\u8a2d\u8a08\u3067\u73fe\u308c\u308b\u8ca0\u306e\u4fc2\u6570\u3092\u3001\u5358\u306a\u308b\u7570\u5e38\u5024\u3068\u3057\u3066\u6368\u3066\u308b\u3053\u3068\u3082\u3001\u5b9f\u88c5\u6761\u4ef6\u3092\u78ba\u304b\u3081\u305a\u306b\u305d\u306e\u307e\u307e\u4f7f\u3046\u3053\u3068\u3082\u3067\u304d\u307e\u305b\u3093\u3002\u4fc2\u6570\u306e\u5f79\u5272\u3001\u9014\u4e2d\u306e\u7d2f\u7a4d\u5024\u3001\u9006\u64cd\u4f5c\u306e\u53ef\u5426\u3092\u5206\u3051\u3066\u8aad\u3080\u3053\u3068\u3067\u3001\u81ea\u5206\u306e\u554f\u984c\u306b\u4f7f\u3048\u308b\u516c\u5f0f\u304b\u3092\u5224\u65ad\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<h2>\u51fa\u5178<\/h2>\n<ol>\n<li id=\"ref1\">Naomichi Hatano and Masuo Suzuki, <a href=\"https:\/\/arxiv.org\/abs\/math-ph\/0506007v1\">Finding Exponential Product Formulas of Higher Orders<\/a>, arXiv:math-ph\/0506007v1\uff082005\u5e746\u67082\u65e5\uff09\u3002\u7b2c3\u7bc0\u3001PDF 7\u30da\u30fc\u30b8\u306e\u5f0f(37)\u2013(45)\u3068\u8aac\u660e\u30018\u30da\u30fc\u30b8\u306e\u56f33\u30fb\u7b2c4\u7bc0\u5192\u982d\u3002\u4fc2\u6570\u3068\u7d2f\u7a4d\u5024\u3001\u88681\u30fb\u56f31\u306f\u3001\u56fa\u5b9a\u7248\u306e\u5f0f\u304b\u3089\u672c\u7a3f\u3067\u72ec\u81ea\u8a08\u7b97\u30fb\u4f5c\u56f3\u3057\u307e\u3057\u305f\u3002\u539f\u8cc7\u6599\u306e\u56f3\u306e\u8ee2\u8f09\u3084\u88c5\u7f6e\u6027\u80fd\u306e\u5b9f\u8a3c\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u91cf\u5b50\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306e\u8fd1\u4f3c\u3092\u7d30\u304b\u304f\u3057\u3066\u3044\u304f\u3068\u3001\u5206\u5272\u306e\u9014\u4e2d\u306b\u300c\u8ca0\u306e\u523b\u307f\u300d\u304c\u73fe\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u8a08\u7b97\u304c\u904e\u53bb\u3078\u623b\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u305d\u308c\u3068\u3082\u3001\u9593\u9055\u3063\u305f\u4fc2\u6570\u306a\u306e\u3067\u3057\u3087\u3046\u304b\u3002 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[&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1049,"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":[184],"class_list":["post-1051","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-computing","tag-quantum-computers"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-fourth-order-negative-substeps-20261018-featured-57b3194fcb67.png","_links":{"self":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1051","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=1051"}],"version-history":[{"count":1,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1051\/revisions"}],"predecessor-version":[{"id":1052,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1051\/revisions\/1052"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/media\/1049"}],"wp:attachment":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1051"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1051"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1051"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}