{"id":505499,"date":"2024-01-07T09:57:39","date_gmt":"2024-01-07T09:57:39","guid":{"rendered":"https:\/\/quantumai.co\/understanding-bqp-in-quantum-computing\/"},"modified":"2025-08-04T20:53:12","modified_gmt":"2025-08-04T20:53:12","slug":"%e7%9e%ad%e8%a7%a3%e9%87%8f%e5%ad%90%e9%81%8b%e7%ae%97%e4%b8%ad%e7%9a%84-bqp","status":"publish","type":"post","link":"https:\/\/quantumaieu.com\/zh\/%e7%9e%ad%e8%a7%a3%e9%87%8f%e5%ad%90%e9%81%8b%e7%ae%97%e4%b8%ad%e7%9a%84-bqp\/","title":{"rendered":"\u77ad\u89e3\u91cf\u5b50\u904b\u7b97\u4e2d\u7684 BQP"},"content":{"rendered":"

\u5728\u6211\u5011\u63a2\u7d22\u4e0d\u65b7\u6f14\u9032\u7684 \u91cf\u5b50\u8a08\u7b97<\/b>\u6211\u5011\u5c07\u6df1\u5165\u63a2\u8a0e BQP<\/b> (Bounded-error \u91cf\u5b50\u591a\u9879\u5f0f\u65f6\u95f4<\/b>).\u9019\u500b\u57fa\u77f3\u6982\u5ff5\u662f \u91cf\u5b50\u8907\u96dc\u6027\u7406\u8ad6<\/b>\uff0c\u5212\u5b9a\u4e86 \u6c7a\u7b56\u554f\u984c<\/b> \u91cf\u5b50\u6a5f\u5668\u80fd\u5920\u6709\u6548\u4e14\u7cbe\u78ba\u5730\u89e3\u6c7a\u7684\u554f\u984c\u3002\u900f\u904e\u805a\u7126\u65bc \u91cf\u5b50\u6f14\u7b97\u6cd5<\/b>\u6211\u5011\u8a66\u5716\u89e3\u78bc BQP<\/b> \u53ca\u5176\u5728\u8ffd\u6c42 \u91cf\u5b50\u81f3\u4e0a<\/b>.<\/p>\n

\u52a0\u5165\u6211\u5011\u7684\u884c\u5217\uff0c\u8e0f\u4e0a\u7a7f\u8d8a\u4ee5\u4e0b\u9818\u57df\u7684\u65c5\u7a0b \u91cf\u5b50\u529b\u5b78<\/b> \u548c\u8a08\u7b97\u5947\u8de1\uff0c\u95e1\u660e\u9019\u4e9b\u5148\u9032\u6f14\u7b97\u6cd5\u5c0d\u672a\u4f86\u79d1\u6280\u7684\u6df1\u9060\u5f71\u97ff\u3002\u77ad\u89e3 BQP<\/b> \u9019\u4e0d\u50c5\u95dc\u4fc2\u5230\u904b\u7b97\u7684\u524d\u6cbf\uff1b\u66f4\u95dc\u4e4e\u6253\u958b\u901a\u5f80\u65b0\u53ef\u80fd\u6027\u7684\u5927\u9580\uff0c\u91cd\u65b0\u5b9a\u7fa9\u6211\u5011\u5728\u6578\u4f4d\u6642\u4ee3\u5982\u4f55\u89e3\u6c7a\u8907\u96dc\u7684\u554f\u984c\u3002<\/p>\n

\u91cf\u5b50\u8907\u96dc\u6027\u7406\u8ad6\u4e2d BQP \u7684\u7cbe\u9ad3<\/h2>\n

\u7576\u6211\u5011\u6df1\u5165\u63a2\u8a0e \u91cf\u5b50\u8a08\u7b97<\/b>\u56e0\u6b64\uff0c\u77ad\u89e3 BQP \u5b9a\u7fa9<\/b>\u3001\u5176\u610f\u7fa9\u53ca\u5176\u5f71\u97ff\u3002BQP \u6216\u6709\u754c\u932f\u8aa4 \u91cf\u5b50\u591a\u9879\u5f0f\u65f6\u95f4<\/b>\uff0c\u662f\u4e00\u985e \u6c7a\u7b56\u554f\u984c<\/b> \u91cf\u5b50\u96fb\u8166\u53ef\u5728 \u591a\u9879\u5f0f\u65f6\u95f4<\/b>\uff0c\u5176\u4e2d \u91cf\u5b50\u529b\u5b78<\/b> \u7684\u57fa\u790e\u3002\u9019\u9580\u8ab2\u4e0d\u50c5\u53cd\u6620\u91cf\u5b50\u8cc7\u8a0a\u8655\u7406\u7684\u6838\u5fc3\u539f\u5247\uff0c\u4e5f\u78ba\u4fdd\u5c0d\u9019\u4e9b\u5148\u9032\u8a08\u7b97\u6a21\u578b\u7684\u904b\u4f5c\u80fd\u529b\u6709\u6df1\u9060\u7684\u5f71\u97ff\u3002<\/p>\n

\u5b9a\u7fa9 BQP\uff08\u6709\u754c\u932f\u8aa4\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593\uff09<\/h3>\n

\u7684 BQP \u5b9a\u7fa9<\/b> \u63d0\u4f9b\u4e86\u4e00\u500b\u7279\u5b9a\u7684\u93e1\u982d\uff0c\u8b93\u6211\u5011\u53ef\u4ee5\u900f\u904e\u9019\u500b\u93e1\u982d\u4f86\u6aa2\u8996 \u91cf\u5b50\u6f14\u7b97\u6cd5<\/b>.\u5f9e\u5f62\u5f0f\u4e0a\u4f86\u770b\uff0c\u5982\u679c\u6709\u91cf\u5b50\u6f14\u7b97\u6cd5\u80fd\u5920\u4ee5\u8d85\u904e\u4e09\u5206\u4e4b\u4e8c\u7684\u6a5f\u7387\u627e\u5230\u6b63\u78ba\u7b54\u6848\uff0c\u5247\u6c7a\u7b56\u554f\u984c\u5c31\u5c6c\u65bc BQP \u985e\u5225\u3002\u9019\u500b\u6982\u7387\u81e8\u754c\u503c\u4ee3\u8868\u6211\u5011\u53ef\u4ee5\u6709\u6548\u5730\u8655\u7406\u932f\u8aa4\uff0c\u9019\u8981\u6b78\u529f\u65bc \u91cf\u5b50\u932f\u8aa4\u6821\u6b63<\/b> \u65b9\u6cd5\u7d2e\u6839\u65bc BQP \u6f14\u7b97\u6cd5\u7684\u7d50\u69cb\u4e2d\u3002<\/p>\n

BQP \u5167\u6c7a\u7b56\u554f\u984c\u7684\u95dc\u9375\u7279\u6027<\/h3>\n

\u6c7a\u7b56\u554f\u984c<\/b> \u5728 BQP \u7684\u7bc4\u570d\u5167\uff0c\u6709\u5e7e\u500b\u57fa\u672c\u7279\u6027\u3002\u9019\u4e9b\u7279\u6027\u4e0d\u50c5\u5b9a\u7fa9\u4e86\u5b83\u5011\u7684\u8907\u96dc\u6027\uff0c\u4e5f\u70ba\u91cf\u5b50\u81f3\u4e0a\u5960\u5b9a\u4e86\u57fa\u790e\u3002 \u91cf\u5b50\u8a08\u7b97<\/b> \u6beb\u7121\u7591\u554f\u5730\u8d85\u8d8a\u4e86\u53e4\u5178\u904b\u7b97\u3002<\/p>\n

    \n
  • **\u591a\u6578\u6642\u9593\u5167\u7684\u53ef\u5224\u65b7\u6027**\uff1aBQP \u4e2d\u7684\u554f\u984c\u53ef\u4ee5\u6709\u6548\u5730\u5224\u5b9a\uff0c\u5176\u6f14\u7b97\u6cd5\u7684\u904b\u884c\u6642\u9593\u70ba \u591a\u9879\u5f0f\u65f6\u95f4<\/b>.<\/li>\n
  • **\u91cf\u5b50\u9598\u9580\u7684\u4fdd\u771f\u5ea6**\uff1a\u91cf\u5b50\u9598\u9580\u662f\u7528\u4f86\u64cd\u4f5c\u91cf\u5b50\u4f4d\u5143\u7684\uff0c\u5176\u904b\u4f5c\u61c9\u8a72\u8aa4\u5dee\u6700\u5c0f\u3002<\/li>\n
  • **\u932f\u8aa4\u6982\u7387**\uff1a\u96d6\u7136\u5728\u8a08\u7b97\u4e0a\u4ecd\u7121\u6cd5\u9054\u5230\u5b8c\u7f8e\uff0c\u4f46 BQP \u5c0d\u65bc\u554f\u984c\u7684\u4efb\u4f55\u5be6\u4f8b\uff0c\u90fd\u80fd\u7dad\u6301\u4e0d\u8d85\u904e 1\/3 \u7684\u6709\u754c\u932f\u8aa4\u6982\u7387\u3002<\/li>\n
  • **\u91cf\u5b50\u7cfe\u7e8f\u8207\u758a\u52a0**\uff1a\u5229\u7528\u91cf\u5b50\u7cfe\u7e8f\u8207\u758a\u52a0\uff0cBQP \u554f\u984c\u53ef\u5229\u7528\u9019\u4e9b\u91cf\u5b50\u529b\u5b78\u7279\u6027\uff0c\u9054\u5230\u524d\u6240\u672a\u6709\u7684\u554f\u984c\u89e3\u6c7a\u80fd\u529b\u3002<\/li>\n<\/ul>\n

    BQP \u5982\u4f55\u5ef6\u4f38\u7d93\u5178\u8907\u96dc\u6027\u7406\u8ad6<\/h3>\n

    BQP \u7684\u51fa\u73fe\u64f4\u5c55\u4e86\u7d93\u5178\u7684 \u8907\u96dc\u5ea6\u8ad6<\/b>.\u900f\u904e\u5c07\u91cf\u5b50\u529b\u5b78\u539f\u7406\u5c0e\u5165\u8a08\u7b97\u67b6\u69cb\uff0c\u6211\u5011\u76ee\u7779\u4e86\u89e3\u6c7a\u554f\u984c\u7684\u6b66\u5668\u5eab\u5927\u5e45\u64f4\u5145\uff0c\u4f7f\u6211\u5011\u7684\u80fd\u529b\u8d85\u8d8a\u50b3\u7d71\u6f14\u7b97\u6cd5\u3002<\/p>\n\n\n\n\n\n\n
    \u7d93\u5178\u8907\u96dc\u6027\u7406\u8ad6<\/th>\nBQP \u8207\u91cf\u5b50\u529b\u5b78<\/th>\n<\/tr>\n
    \u4f9d\u8cf4\u7d93\u5178\u6f14\u7b97\u6cd5<\/td>\n\u96c7\u7528 \u91cf\u5b50\u6f14\u7b97\u6cd5<\/b><\/td>\n<\/tr>\n
    \u4e0d\u9069\u7528\u65bc\u91cf\u5b50\u73fe\u8c61<\/td>\n\u5229\u7528\u7cfe\u7e8f\u3001\u8d85\u73fe\u5be6<\/td>\n<\/tr>\n
    \u5728\u78ba\u5b9a\u6027\u6846\u67b6\u5167\u904b\u4f5c<\/td>\n\u6982\u7387\u8a08\u7b97\u7684\u7279\u9ede<\/td>\n<\/tr>\n
    \u53d7\u5230\u50b3\u7d71\u8cc7\u8a0a\u8655\u7406\u7684\u9650\u5236<\/td>\n\u91cf\u5b50\u932f\u8aa4\u6821\u6b63<\/b> \u63d0\u4f9b\u8cc7\u8a0a\u5fe0\u5be6\u7684\u65b0\u9014\u5f91<\/td>\n<\/tr>\n<\/table>\n

    \u7576\u6211\u5011\u7e7c\u7e8c\u7a7f\u8d8a \u91cf\u5b50\u8907\u96dc\u6027\u7406\u8ad6<\/b>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6211\u5011\u5728\u6b64\u6240\u53d6\u5f97\u7684\u9032\u5c55\u4e0d\u53ea\u662f\u7406\u8ad6\u4e0a\u7684\u601d\u8003\u3002\u9019\u4e9b\u9032\u5c55\u662f\u5229\u7528\u91cf\u5b50\u904b\u7b97\u7684\u771f\u6b63\u5a01\u529b\u3001\u89e3\u958b\u66fe\u88ab\u8a8d\u70ba\u96e3\u4ee5\u89e3\u6c7a\u7684\u554f\u984c\uff0c\u4ee5\u53ca\u958b\u62d3\u79d1\u6280\u8207\u79d1\u5b78\u65b0\u9818\u57df\u7684\u91cd\u8981\u6b65\u9a5f\u3002<\/p>\n

    \u63a2\u7d22\u91cf\u5b50\u96fb\u8def\u6a21\u578b\u548c BQP<\/h2>\n

    \u5728\u63ed\u793a\u91cf\u5b50\u904b\u7b97\u8907\u96dc\u6027\u7684\u65c5\u7a0b\u4e2d\uff0c\u6211\u5011\u5fc5\u9808\u6df1\u5165\u4e86\u89e3 \u91cf\u5b50\u96fb\u8def\u6a21\u578b<\/b>\u662f BQP\uff08\u6709\u908a\u969b\u932f\u8aa4\uff09\u64cd\u4f5c\u6846\u67b6\u7684\u57fa\u77f3\u6982\u5ff5\u3002 \u91cf\u5b50\u591a\u9879\u5f0f\u65f6\u95f4<\/b>).\u9019\u4e9b\u91cf\u5b50\u9598\u9580\u7db2\u8def\u662f\u88fd\u9020\u548c\u904b\u884c\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u9aa8\u5e79\uff0c\u5f15\u9818\u6211\u5011\u66f4\u63a5\u8fd1\u5922\u5bd0\u4ee5\u6c42\u7684\u91cc\u7a0b\u7891--\u91cf\u5b50\u6f14\u7b97\u6cd5\u3002 \u91cf\u5b50\u81f3\u4e0a<\/b>.<\/p>\n

    \"\u5747\u4e00\u91cf\u5b50\u96fb\u8def\"<\/picture><\/p>\n

    \u91cf\u5b50\u96fb\u8def\u5728 BQP \u6f14\u7b97\u6cd5\u4e2d\u7684\u89d2\u8272<\/h3>\n

    \u91cf\u5b50\u96fb\u8def\u662f\u8a08\u7b97\u9818\u57df\u7684\u7cbe\u9ad3\u3002 \u91cf\u5b50\u529b\u5b78<\/b>.\u4e0d\u540c\u65bc\u4ee5\u4e8c\u9032\u4f4d\u5e8f\u5217\u904b\u4f5c\u7684\u53e4\u5178\u96fb\u8def\uff0c\u91cf\u5b50\u96fb\u8def\u64c1\u6709\u91cf\u5b50\u4f4d\u5143\u7684\u529b\u91cf\u3002\u9019\u4e9b\u91cf\u5b50\u4f4d\u5143\u900f\u904e\u4e00\u9023\u4e32\u91cf\u5b50\u9598\u9580\u9032\u884c\u8f49\u63db\uff0c\u7cbe\u5fc3\u7de8\u6392\u4ee5\u57f7\u884c \u91cf\u5b50\u6f14\u7b97\u6cd5<\/em>.<\/p>\n

    \u6b63\u662f\u9019\u4e9b\u6f14\u7b97\u6cd5\u4ea4\u97ff\u66f2\u8b93\u6211\u5011\u53ef\u4ee5\u57f7\u884c\u50b3\u7d71\u96fb\u8166\u7121\u6cd5\u5be6\u73fe\u7684\u8a08\u7b97\u3002\u7576\u6211\u5011\u8ac7\u5230 \u91cf\u5b50\u81f3\u4e0a<\/em>\u6211\u5011\u6240\u6307\u7684\u6b63\u662f\u9019\u7a2e\u60c5\u6cc1-\u91cf\u5b50\u96fb\u8166\u6240\u89e3\u6c7a\u7684\u554f\u984c\uff0c\u751a\u81f3\u8d85\u8d8a\u4e86\u6700\u5148\u9032\u7684\u53e4\u5178\u8d85\u7d1a\u96fb\u8166\u3002<\/p>\n

    \u77ad\u89e3\u91cf\u5b50\u96fb\u8def\u7684\u7d71\u4e00\u7cfb\u5217<\/h3>\n

    \u8981\u638c\u63e1\u91cf\u5b50\u904b\u7b97\u7684\u5168\u90e8\u6f5b\u529b\uff0c\u5c31\u5fc5\u9808\u77ad\u89e3 \u5747\u4e00\u91cf\u5b50\u96fb\u8def<\/em>.\u9019\u88e1\u7684\u7d71\u4e00\u6027\u662f\u4e00\u500b\u85dd\u8853\u7528\u8a9e\uff0c\u8868\u793a\u55ae\u4e00\u6f14\u7b97\u6cd5\u53ef\u7522\u751f\u4efb\u4f55\u6307\u5b9a\u5927\u5c0f\u7684\u91cf\u5b50\u96fb\u8def\u4f48\u5c40\uff0c\u78ba\u4fdd\u53ef\u64f4\u5145\u6027\u53ca\u65b9\u6cd5\u4e0a\u7684\u7cbe\u78ba\u6027\u3002<\/p>\n

    \u9019\u7a2e\u5747\u52fb\u6027\u975e\u5e38\u91cd\u8981\uff1b\u6c92\u6709\u5b83\uff0c\u64f4\u5927\u91cf\u5b50\u6f14\u7b97\u6cd5\u4ee5\u89e3\u6c7a\u66f4\u91cd\u8981\u3001\u66f4\u8907\u96dc\u554f\u984c\u7684\u6548\u7387\u548c\u53ef\u9760\u6027\u53ef\u80fd\u6703\u53d7\u5230\u5f71\u97ff\uff0c\u4e26\u53ef\u80fd\u59a8\u7919\u9081\u5411\u91cf\u5b50\u5316\u7684\u9032\u7a0b\u3002 \u91cf\u5b50\u81f3\u4e0a<\/b>.<\/p>\n

    \u8b93\u6211\u5011\u4f86\u770b\u770b\u9019\u4e9b\u91cf\u5b50\u96fb\u8def\u7684\u4e00\u4e9b\u57fa\u672c\u53c3\u6578\uff1a<\/p>\n\n\n\n\n\n\n
    \u5916\u89c0<\/th>\n\u91cd\u8981\u6027<\/th>\n\u5c0d\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u5f71\u97ff<\/th>\n<\/tr>\n
    Qubit \u6578\u91cf<\/td>\n\u8868\u793a\u8a08\u7b97\u898f\u6a21\u548c\u554f\u984c\u8907\u96dc\u6027<\/td>\n\u78ba\u5b9a\u89e3\u6c7a\u7279\u5b9a\u91cf\u5b50\u554f\u984c\u7684\u53ef\u884c\u6027<\/td>\n<\/tr>\n
    \u9598\u9580\u4fdd\u771f\u5ea6<\/td>\n\u53cd\u6620\u91cf\u5b50\u64cd\u4f5c\u5167\u7684\u7cbe\u78ba\u5ea6\u8207\u932f\u8aa4\u7387<\/td>\n\u5c0d\u65bc\u7dad\u6301\u6f14\u7b97\u6cd5\u7684\u5b8c\u6574\u6027\u548c\u53d6\u5f97\u7cbe\u78ba\u7684\u7d50\u679c\u81f3\u95dc\u91cd\u8981<\/td>\n<\/tr>\n
    \u96fb\u8def\u6df1\u5ea6<\/td>\n\u6e2c\u91cf\u53ef\u57f7\u884c\u7684\u9023\u7e8c\u4f5c\u696d\u6578\u91cf<\/td>\n\u5f71\u97ff\u91cf\u5b50\u8a08\u7b97\u7a0b\u5e8f\u7684\u901f\u5ea6\u8207\u6548\u7387<\/td>\n<\/tr>\n
    \u5747\u4e00\u6027<\/td>\n\u78ba\u4fdd\u4efb\u4f55\u554f\u984c\u5927\u5c0f\u7684\u96fb\u8def\u7d50\u69cb\u4e00\u81f4\u6027<\/td>\n\u4fc3\u9032\u53ef\u64f4\u5145\u8207\u53ef\u8907\u88fd\u7684\u91cf\u5b50\u904b\u7b97\u7a0b\u5e8f<\/td>\n<\/tr>\n<\/table>\n

    \u7e3d\u800c\u8a00\u4e4b\uff0c\u91cf\u5b50\u904b\u7b97\u7684\u9818\u57df\u975e\u5e38\u907c\u95ca\uff0c\u800c\u4e14\u5145\u6eff\u6f5b\u529b\u3002 \u91cf\u5b50\u96fb\u8def\u6a21\u578b<\/b> \u7684\u91cd\u8981\u57fa\u790e\u8a2d\u65bd\u3002\u900f\u904e\u78ba\u4fdd\u5efa\u9020 \u5747\u4e00\u91cf\u5b50\u96fb\u8def<\/em>\u6211\u5011\u5c07\u7e7c\u7e8c\u70ba\u8a72\u9818\u57df\u7684\u7a81\u7834\u6027\u9032\u5c55\u92ea\u8def\uff0c\u63a8\u52d5\u6211\u5011\u9081\u5411\u4ee5\u4e0b\u8a98\u4eba\u7684\u9802\u5cf0 \u91cf\u5b50\u81f3\u4e0a<\/em>.<\/p>\n

    BQP (\u6709\u9650\u932f\u8aa4\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593) \u89e3\u91cb<\/h2>\n

    \u5728\u91cf\u5b50\u904b\u7b97\u4e0d\u65b7\u6f14\u9032\u7684\u74b0\u5883\u4e2d\u3001 \u6709\u754c\u932f\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593<\/em> (BQP<\/strong>)\u662f\u4e00\u500b\u8209\u8db3\u8f15\u91cd\u7684\u8907\u96dc\u6027\u985e\u5225\u3002BQP \u9ad4\u73fe\u4e86\u91cf\u5b50\u96fb\u8166\u6e96\u78ba\u3001\u6709\u6548\u7387\u5730\u89e3\u6c7a\u6c7a\u7b56\u554f\u984c\u7684\u80fd\u529b\u3002\u6211\u5011\u6df1\u5165\u63a2\u8a0e\u4f55\u8b02 BQP<\/strong>\u5176\u5c0d \u91cf\u5b50\u591a\u9879\u5f0f\u65f6\u95f4<\/strong>\uff0c\u4e26\u63a8\u9032 \u91cf\u5b50\u932f\u8aa4\u6821\u6b63<\/strong> \u6280\u8853\u7684\u95dc\u9375 \u91cf\u5b50\u6f14\u7b97\u6cd5<\/strong>.\u6211\u5011\u7684\u8a0e\u8ad6\u8003\u616e\u5230\u4e86\u8a08\u7b97\u901f\u5ea6\u8207\u932f\u8aa4\u7de9\u89e3\u7684\u8907\u96dc\u7d50\u5408\uff0c\u800c BQP \u6b63\u662f\u91cf\u5b50\u8a08\u7b97\u6f5b\u529b\u7684\u6a19\u8a8c\u3002<\/p>\n

    \u5176\u6838\u5fc3\u662f\uff0cBQP \u5b9a\u7fa9\u4e86\u91cf\u5b50\u8a08\u7b97\u5668\u53ef\u5728\u4e0b\u5217\u7bc4\u570d\u5167\u8655\u7406\u554f\u984c\u7684\u9580\u6abb \u591a\u9879\u5f0f\u65f6\u95f4<\/b> \u540c\u6642\u7dad\u6301\u6709\u754c\u7dda\u7684\u932f\u8aa4\u6982\u7387\u3002\u9019\u610f\u5473\u8457\uff0c\u5c0d\u65bc\u901a\u904e BQP \u6f14\u7b97\u6cd5\u7684\u4efb\u4f55\u5be6\u4f8b\uff0c\u5f97\u51fa\u932f\u8aa4\u7d50\u8ad6\u7684\u53ef\u80fd\u6027\u4e0d\u6703\u8d85\u904e 1\/3\u3002\u6700\u91cd\u8981\u7684\u662f\uff0c\u900f\u904e\u57f7\u884c\u6f14\u7b97\u6cd5\u7684\u591a\u6b21\u904b\u884c\uff0c\u4e26\u61c9\u7528\u591a\u6578\u7968\u539f\u5247\uff0c\u53ef\u4ee5\u5927\u5e45\u6e1b\u5c11\u932f\u8aa4\u3002\u9019\u500b\u4ee5 Chernoff \u754c\u7dda\u70ba\u57fa\u790e\u7684\u904e\u7a0b\uff0c\u8b49\u660e\u4e86 BP \u6f14\u7b97\u6cd5\u7684\u5f48\u6027\u548c\u9069\u61c9\u6027\u3002 \u91cf\u5b50\u932f\u8aa4\u6821\u6b63<\/strong> \u4fdd\u969c\u91cf\u5b50\u8a08\u7b97\u5b8c\u6574\u6027\u8207\u7cbe\u78ba\u6027\u7684\u65b9\u6cd5\u3002<\/p>\n

    \u6211\u5011\u7d93\u5e38\u5f37\u8abf\uff0c\u91cf\u5b50\u8a08\u7b97\u7684\u771f\u6b63\u512a\u52e2\u5728\u65bc\u5176\u5c0d\u5feb\u901f\u8655\u7406\u548c\u7cbe\u7d30\u8a08\u7b97\u7684\u96d9\u91cd\u627f\u8afe\u3002 \u6e1b\u5c11\u932f\u8aa4<\/b>\uff0c\u5171\u540c\u5c07\u6211\u5011\u5e36\u5165\u8a08\u7b97\u80fd\u529b\u7684\u4e0b\u4e00\u500b\u6642\u4ee3\u3002<\/p><\/blockquote>\n

    \u4e0b\u8868\u5c55\u793a\u91cf\u5b50\u6f14\u7b97\u6cd5\u5982\u4f55\u5229\u7528 BQP \u7684\u539f\u7406\u4f86\u5f37\u5316\u8a08\u7b97\uff1a<\/p>\n\n\n\n\n\n\n
    \u539f\u5247<\/th>\n\u5c0d\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u5f71\u97ff<\/th>\n\u6548\u76ca<\/th>\n<\/tr>\n
    \u591a\u6578\u6642\u9593<\/td>\n\u53ef\u5feb\u901f\u8a08\u7b97\u8907\u96dc\u7684\u554f\u984c<\/td>\n\u5927\u898f\u6a21\u554f\u984c\u7684\u9ad8\u6548\u8655\u7406<\/td>\n<\/tr>\n
    \u6709\u754c\u932f\u8aa4\u6982\u7387<\/td>\n\u9650\u5236\u8a08\u7b97\u4e0d\u6e96\u78ba\u7684\u6a5f\u6703<\/td>\n\u7d50\u679c\u7684\u53ef\u9760\u6027<\/td>\n<\/tr>\n
    \u591a\u6578\u7968 (\u6e1b\u5c11\u932f\u8aa4<\/b>)<\/td>\n\u6700\u5c0f\u5316\u8fed\u4ee3\u6f14\u7b97\u6cd5\u904b\u884c\u6642\u7684\u8aa4\u5dee<\/td>\n\u63d0\u9ad8\u7d50\u679c\u7cbe\u78ba\u5ea6<\/td>\n<\/tr>\n
    Chernoff Bound \u61c9\u7528\u7a0b\u5f0f<\/td>\n\u7a69\u5b9a\u91cf\u5b50\u7cfb\u7d71\u7684\u932f\u8aa4\u7387<\/td>\n\u5373\u4f7f\u5b58\u5728\u91cf\u5b50\u96dc\u8a0a\u4e5f\u80fd\u4fdd\u6301\u4e00\u81f4\u6027<\/td>\n<\/tr>\n<\/table>\n

    \u6211\u5011\u5fc5\u9808\u8a8d\u6e05 BQP \u4e0d\u50c5\u53cd\u6620\u91cf\u5b50\u7cfb\u7d71\u7684\u56fa\u6709\u5c6c\u6027\uff0c\u540c\u6642\u4e5f\u5f15\u5c0e\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u6301\u7e8c\u6f14\u9032\u3002\u900f\u904e\u5b8c\u5584 \u91cf\u5b50\u932f\u8aa4\u6821\u6b63<\/b> \u5728\u6b64\u904e\u7a0b\u4e2d\uff0c\u6211\u5011\u4fdd\u8b77\u4e86\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593\u7684\u7cbe\u9ad3\uff0c\u78ba\u4fdd\u96a8\u8457\u91cf\u5b50\u6280\u8853\u7684\u64f4\u5c55\uff0cBQP \u4ecd\u6703\u662f\u6211\u5011\u91cf\u5b50\u904b\u7b97\u96c4\u5fc3\u7684\u57fa\u77f3\u3002<\/p>\n

    \u91cf\u5b50\u6f14\u7b97\u6cd5\u8207 BQP \u7684\u95dc\u4fc2<\/h2>\n

    \u6211\u5011\u7684\u91cf\u5b50\u9818\u57df\u4e4b\u65c5\u986f\u793a\uff0c\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u80fd\u529b\u8207 BQP (Bounded-error Quantum Polynomial time) \u6240\u5b9a\u7fa9\u7684\u8a08\u7b97\u908a\u754c\u5bc6\u4e0d\u53ef\u5206\u3002\u9019\u4e9b\u4ee5\u91cf\u5b50\u529b\u5b78\u539f\u7406\u70ba\u57fa\u790e\u7684\u6f14\u7b97\u6cd5\uff0c\u662f\u70ba\u4e86\u5728\u91cf\u5b50\u5716\u9748\u6a5f\u5668 (Quantum Turing machines) \u4e2d\u904b\u4f5c\u800c\u91cf\u8eab\u6253\u9020\uff0c\u800c\u91cf\u5b50\u5716\u9748\u6a5f\u5668\u6b63\u662f\u91cf\u5b50\u904b\u7b97\u7684\u7d50\u69cb\u3002\u8b93\u6211\u5011\u6df1\u5165\u77ad\u89e3\u9019\u7a2e\u8907\u96dc\u7684\u95dc\u4fc2\uff0c\u4e26\u63a2\u8a0e\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u8fed\u4ee3\u6027\u5982\u4f55\u6709\u52a9\u65bc \u6e1b\u5c11\u932f\u8aa4<\/b>\u6700\u7d42\u52a0\u5f37\u4e86\u4ed6\u5011\u8207 BQP \u7684\u4e00\u81f4\u6027\u3002<\/p>\n

    \u5f9e\u91cf\u5b50\u5716\u9748\u6a5f\u5230 BQP \u6f14\u7b97\u6cd5<\/h3>\n

    \u5b83\u5728 \u91cf\u5b50\u5716\u9748\u6a5f<\/b> \u91cf\u5b50\u6f14\u7b97\u6cd5\u627e\u5230\u4e86\u81ea\u5df1\u7684\u65b9\u5411\u3002\u5118\u7ba1\u9019\u4e9b\u7406\u8ad6\u69cb\u9020\u975e\u5e38\u62bd\u8c61\uff0c\u4f46\u537b\u662f\u73fe\u5be6\u4e16\u754c\u91cf\u5b50\u904b\u7b97\u7684\u91cd\u8981\u57fa\u790e\u3002\u85c9\u7531\u5c07\u8cc7\u6599\u7de8\u78bc\u6210\u91cf\u5b50\u4f4d\u5143\uff0c\u4e26\u900f\u904e\u91cf\u5b50\u908f\u8f2f\u9598\u9580\u4f86\u64cd\u63a7\u9019\u4e9b\u91cf\u5b50\u4f4d\u5143\uff0c\u6f14\u7b97\u6cd5\u6f14\u8b8a\u6210\u8207 BQP \u76f8\u5bb9\u7684\u89e3\u6c7a\u65b9\u6848\uff0c\u4ee5\u89e3\u6c7a\u8d85\u51fa\u7d93\u5178\u8a08\u7b97\u7bc4\u570d\u7684\u554f\u984c\u3002<\/p>\n

    BQP \u6f14\u7b97\u6cd5\u4e2d\u7684\u8fed\u4ee3\u8207\u932f\u8aa4\u6e1b\u5c11<\/h3>\n

    \u91cf\u5b50\u6f14\u7b97\u6cd5\u80fd\u529b\u7684\u6838\u5fc3\u5728\u65bc\u5f37\u5927\u7684 \u8fed\u4ee3<\/b>.\u900f\u904e\u53cd\u8986\u5faa\u74b0\u7684\u6f14\u7b97\u6cd5\u57f7\u884c\uff0c\u91cf\u5b50\u7cfb\u7d71\u53ef\u4ee5\u9010\u6b65\u7cbe\u9032\u7b54\u6848\uff0c\u4e0d\u65b7\u63a5\u8fd1\u7406\u60f3\u7684\u89e3\u6c7a\u65b9\u6848\u3002\u6bcf\u6b21\u8fed\u4ee3\u90fd\u80fd\u964d\u4f4e\u51fa\u932f\u7684\u53ef\u80fd\u6027\uff0c\u9019\u5c0d\u65bc\u8ffd\u6c42\u5be6\u969b\u4e0a\u53ef\u5ffd\u7565\u7684\u932f\u8aa4\u6982\u7387\u662f\u975e\u5e38\u91cd\u8981\u7684\uff0c\u800c\u9019\u6b63\u662f\u6211\u5011\u8003\u616e\u91cf\u5b50\u904b\u7b97\u7cbe\u78ba\u5ea6\u8981\u6c42\u6642\u7684\u57fa\u77f3\u76ee\u6a19\u3002<\/p>\n\n\n\n\n\n\n
    \u91cf\u5b50\u6982\u5ff5<\/th>\n\u5728\u6e1b\u5c11\u932f\u8aa4\u4e2d\u7684\u4f5c\u7528<\/th>\n\u5c0d BQP \u95dc\u4fc2\u7684\u5f71\u97ff<\/th>\n<\/tr>\n
    \u91cf\u5b50\u908f\u8f2f\u9598\u9580<\/td>\n\u57f7\u884c\u7cbe\u78ba\u7684\u64cd\u4f5c\uff0c\u5c07\u521d\u59cb\u932f\u8aa4\u7387\u964d\u5230\u6700\u4f4e<\/td>\n\u4fc3\u9032 BQP \u53c3\u6578\u5167\u7684\u8907\u96dc\u8a08\u7b97<\/td>\n<\/tr>\n
    \u91cf\u5b50\u758a\u52a0<\/td>\n\u540c\u6642\u63a2\u7d22\u591a\u7a2e\u72c0\u614b\uff0c\u512a\u5316\u8a08\u7b97\u8def\u5f91<\/td>\n\u589e\u9032 BQP \u53ef\u89e3\u6c7a\u554f\u984c\u7684\u5ee3\u5ea6<\/td>\n<\/tr>\n
    \u7e8f\u64fe<\/td>\n\u53ef\u9032\u884c\u76f8\u95dc\u8a08\u7b97\uff0c\u9032\u4e00\u6b65\u7cbe\u7149\u8f38\u51fa<\/td>\n\u52a0\u5f37 BQP \u5167\u90e8\u89e3\u6c7a\u554f\u984c\u7684\u6548\u7387<\/td>\n<\/tr>\n
    \u932f\u8aa4\u4fee\u6b63\u78bc<\/td>\n\u8fed\u4ee3\u5f8c\u4fee\u6b63\u932f\u8aa4\uff0c\u78ba\u4fdd\u7d50\u679c\u4e00\u81f4<\/td>\n\u78ba\u4fdd BQP \u6f14\u7b97\u6cd5\u7d50\u679c\u7684\u4e00\u81f4\u6027\u8207\u53ef\u9760\u6027<\/td>\n<\/tr>\n<\/table>\n

    \u7576\u6211\u5011\u601d\u8003\u9019\u4e9b\u91cf\u5b50\u5de5\u5177\u7684\u610f\u7fa9\u6642\uff0c\u6211\u5011\u5c0d\u65bc\u91cf\u5b50\u4e16\u754c\u662f\u5982\u4f55\u904b\u4f5c\u7684\u7406\u89e3\u4e5f\u52a0\u6df1\u4e86\u3002 BQP \u95dc\u4fc2<\/b> \u900f\u904e \u8fed\u4ee3<\/b> \u4ee5\u53ca\u8907\u96dc\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u61c9\u7528\u3002\u9019\u4e9b\u91cf\u5b50\u7279\u8cea\u4e0d\u53ea\u662f\u5b78\u8853\u7814\u7a76\u7684\u5c64\u9762\uff0c\u800c\u662f\u9a45\u4f7f\u6211\u5011\u9081\u5411\u5be6\u7528\u91cf\u5b50\u512a\u52e2\u7684\u6a5f\u5236\u3002<\/p>\n

    BQP \u8207\u5176\u4ed6\u6982\u7387\u985e\u5225\u7684\u5340\u5225<\/h2>\n

    \u5728\u63a2\u7d22 \u8907\u96dc\u5ea6\u7b49\u7d1a<\/b> \u5728\u91cf\u5b50\u8a08\u7b97\u4e2d\uff0c\u8a8d\u8b58\u5230\u5982\u4f55 \u6709\u754c\u932f\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593 (BQP)<\/strong> \u6709\u5225\u65bc\u50b3\u7d71\u7684 \u6982\u7387\u985e\u5225<\/b> \u5982 BPP<\/strong>, RP<\/strong>\u4ee5\u53ca ZPP<\/strong>.\u9019\u4e9b\u5340\u5225\u4e0d\u53ea\u662f\u6280\u8853\u4e0a\u7684\u554f\u984c\uff1b\u5b83\u5011\u4ee3\u8868\u4e86\u91cf\u5b50\u529b\u5b78\u8207\u8a08\u7b97\u79d1\u5b78\u7684\u6f5b\u5728\u98db\u8e8d\u3002 \u91cf\u5b50\u8cc7\u8a0a\u8ad6<\/b>.<\/p>\n

    BQP \u8207 BPP\u3001RP\u3001ZPP \u53ca\u5176\u4ed6\u985e\u578b\u7684\u5c0d\u6bd4<\/h3>\n

    \u5728\u6211\u5011\u7684\u5206\u6790\u4e2d\uff0c\u6211\u5011\u63ed\u958b\u4e86 \u91cf\u5b50\u8cc7\u8a0a\u8ad6<\/em> \u7684\u4e3b\u8981\u5340\u5225\u5728\u65bc BQP<\/strong> \u5f9e\u5176\u4ed6 \u8907\u96dc\u5ea6\u7b49\u7d1a<\/b>.\u96d6\u7136 BPP<\/strong> \u901a\u5e38\u88ab\u8996\u70ba BQP \u7684\u7d93\u5178\u5c0d\u61c9\u7269\uff0c\u5141\u8a31\u5728\u591a\u6578\u6b21\u6642\u9593\u5167\u89e3\u6c7a\u7684\u6c7a\u7b56\u554f\u984c\u4e2d\u51fa\u73fe\u932f\u8aa4\uff0c\u4f46\u5b83\u662f\u4ee5\u7d93\u5178\u6982\u7387\u70ba\u754c\u7dda\uff0c\u800c\u7d93\u5178\u6982\u7387\u7121\u6cd5\u6355\u6349\u91cf\u5b50\u6982\u7387\u7684\u5168\u90e8\u7bc4\u570d\u3002<\/p>\n

    \u540c\u6a23\u5730\u3001 RP<\/strong> (Randomized Polynomial time) \u53ea\u9650\u65bc\u5728\u8072\u7a31\u6b63\u78ba\u6642\u6b63\u78ba\u7684\u6f14\u7b97\u6cd5\uff0c\u4f46\u53ef\u80fd\u6703\u504f\u5411\u65bc\u8b39\u614e\uff0c\u800c ZPP<\/strong> (Zero-error Probabilistic Polynomial time\uff0c\u96f6\u932f\u8aa4\u6982\u7387\u591a\u9879\u5f0f\u6642\u9593) \u85c9\u7531\u5141\u8a31\u975e\u7d42\u6b62\u7684\u53ef\u80fd\u6027\u4f86\u9054\u6210\u96f6\u932f\u8aa4\u3002\u7136\u800c\uff0c\u6c92\u6709\u4efb\u4f55\u4e00\u7a2e\u65b9\u6cd5\u80fd\u50cf BQP \u822c\u6574\u5408\u91cf\u5b50\u73fe\u8c61\uff0c\u4f7f\u5176\u7368\u4e00\u7121\u4e8c\u5730\u9069\u7528\u65bc\u91cf\u5b50\u8a08\u7b97\u7a0b\u5e8f\u3002<\/p>\n

    \u91cf\u5b50\u8cc7\u8a0a\u7406\u8ad6\u4e2d BQP \u7684\u7368\u7279\u4e4b\u8655<\/h3>\n

    \u5728 \u91cf\u5b50\u8cc7\u8a0a\u8ad6<\/strong>BQP \u5efa\u7acb\u5728\u91cf\u5b50\u4f4d\u5143 (qubits) \u7684\u57fa\u790e\u4e0a\uff0c\u91cf\u5b50\u4f4d\u5143\u53ef\u4ee5\u4ee5\u758a\u52a0\u7684\u65b9\u5f0f\u5b58\u5728\uff0c\u80fd\u5920\u540c\u6642\u9032\u884c\u7d93\u5178\u4f4d\u5143\u7121\u6cd5\u57f7\u884c\u7684\u8a08\u7b97\u3002\u5149\u662f\u9019\u500b\u7279\u6027\u5c31\u80fd\u8b93\u91cf\u5b50\u6f14\u7b97\u6cd5\u4ee5\u6a19\u6e96\u6982\u7387\u65b9\u6cd5\u7121\u6cd5\u9054\u5230\u7684\u9ad8\u6b63\u78ba\u6027\u6982\u7387\u4f86\u8655\u7406\u8907\u96dc\u7684\u6c7a\u7b56\u554f\u984c\u3002<\/p>\n

    \u9019\u4e9b\u7279\u6027\u7684\u5f71\u97ff\u662f\u6df1\u9060\u7684\uff0c\u56e0\u70ba\u5b83\u5011\u4f7f\u8cea\u56e0\u5f0f\u5206\u89e3\u7b49\u9818\u57df\u5f97\u4ee5\u9032\u6b65\uff0c\u800c\u8cea\u56e0\u5f0f\u5206\u89e3\u76f4\u63a5\u5f71\u97ff\u5bc6\u78bc\u5b78\u3002\u56e0\u6b64 BQP<\/strong> \u91cf\u5b50\u904b\u7b97\u7684\u524d\u666f\uff0c\u9060\u9060\u8d85\u8d8a\u4e86\u50b3\u7d71\u904b\u7b97\u7684\u7bc4\u570d\u3002 \u6982\u7387\u985e\u5225<\/strong>\uff0c\u6a19\u8a8c\u8457\u7406\u8ad6\u8207\u61c9\u7528\u8a08\u7b97\u79d1\u5b78\u7684\u65b0\u7d00\u5143\u3002<\/p>\n

    \u91cf\u5b50\u904b\u7b97\u4e2d\u7684\u627f\u8afe-BQP \u8207\u5b8c\u6574\u554f\u984c<\/h2>\n

    \n\u63a2\u7d22 \u91cf\u5b50\u8a08\u7b97<\/em>\u6211\u5011\u88ab\u4ee5\u4e0b\u7684\u95dc\u9375\u6982\u5ff5\u6240\u5438\u5f15 \u627f\u8afe-BQP<\/em>.\u5b83\u5c6c\u65bc \u8907\u96dc\u5ea6\u8ad6<\/strong>\uff0c\u63d0\u4f9b\u4e86\u4e00\u500b\u8ff7\u4eba\u7684\u5b50\u96c6\uff0c\u5176\u4e2d\u6bcf\u500b\u554f\u984c\uff0c\u7a31\u70ba \u5b8c\u6574\u554f\u984c<\/em>\uff0c\u662f\u9019\u985e\u554f\u984c\u7684\u6838\u5fc3-\u5b83\u5011\u5141\u8a31\u540c\u985e\u554f\u984c\u4e2d\u7684\u5176\u4ed6\u554f\u984c\u6709\u6548\u5730\u9084\u539f\u70ba\u5b83\u5011\u3002\u70ba\u4e86\u6df1\u5165\u63a2\u8a0e\u9019\u500b\u9818\u57df\uff0c\u6211\u5011\u6aa2\u8996\u4e86\u5728 \u627f\u8afe-BQP<\/b> \u9019\u5f37\u8abf\u4e86\u5b83\u5728\u63a8\u9032\u6211\u5011\u7684\u8a08\u7b97\u524d\u6cbf\u7684\u6f5b\u529b\u3002\n<\/p>\n

    \"\u91cf\u5b50\u904b\u7b97\u7684\u5b8c\u6574\u554f\u984c\"<\/picture><\/p>\n

    \n\u7279\u5225\u662f \u5b8c\u6574\u554f\u984c<\/em> \u50cf approx-qcircuit-prob<\/em> \u5167\u7684\u6df1\u523b\u4f8b\u5b50 \u627f\u8afe-BQP<\/b>\u9019\u4e9b\u932f\u7d9c\u8907\u96dc\u7684\u554f\u984c\u70ba\u4ee5\u4e0b\u9818\u57df\u7684\u7406\u8ad6\u548c\u5be6\u8e10\u767c\u5c55\u5960\u5b9a\u4e86\u5805\u5be6\u7684\u57fa\u790e \u91cf\u5b50\u8a08\u7b97<\/strong>.\u5b83\u5011\u7684\u53ef\u6015\u6027\u6e90\u65bc\u9019\u6a23\u4e00\u500b\u4e8b\u5be6\uff0c\u5373\u5982\u679c\u6211\u5011\u80fd\u5920\u8a2d\u8a08\u51fa\u91cf\u5b50\u6f14\u7b97\u6cd5\u4f86\u89e3\u6c7a\u9019\u4e9b \u5b8c\u6574\u554f\u984c<\/b>\u56e0\u6b64\uff0c\u6211\u5011\u89e3\u958b\u4e86\u5728\u591a\u6578\u6b21\u6642\u9593\u5167\u89e3\u6c7a\u4e00\u7cfb\u5217\u5176\u4ed6\u8907\u96dc\u554f\u984c\u7684\u9014\u5f91\u3002\n<\/p>\n\n\n\n\n\n
    \u627f\u8afe-BQP \u7279\u6027<\/th>\n\u5c0d\u91cf\u5b50\u904b\u7b97\u7684\u5f71\u97ff<\/th>\n<\/tr>\n
    \u6e1b\u5c11\u554f\u984c<\/td>\n\u65b9\u4fbf\u8655\u7406\u8907\u96dc\u7684\u8cc7\u6599\u96c6<\/td>\n<\/tr>\n
    \u8a08\u7b97\u6311\u6230\u7684\u6df1\u5ea6<\/td>\n\u63a8\u52d5\u91cf\u5b50\u6f14\u7b97\u6cd5\u8a2d\u8a08\u7684\u5275\u65b0<\/td>\n<\/tr>\n
    \u63a8\u9032 \u8907\u96dc\u6027\u7406\u8ad6<\/b><\/td>\n\u67b6\u8d77\u7406\u8ad6\u8207\u5be6\u969b\u8a08\u7b97\u4e4b\u9593\u7684\u6a4b\u6881<\/td>\n<\/tr>\n<\/table>\n

    \n\u4f5c\u70ba \u91cf\u5b50\u8a08\u7b97<\/strong>\u6211\u5011\u6b63\u5728\u898b\u8b49\u4e00\u500b\u4ee4\u4eba\u632f\u596e\u7684\u6642\u4ee3\uff0c\u5728\u9019\u500b\u6642\u4ee3\u88e1\uff0c\u6211\u5011\u7684\u6982\u5ff5\u5982 \u627f\u8afe-BQP<\/b> \u50ac\u5316\u6211\u5011\u5c0d \u5b8c\u6574\u554f\u984c<\/strong> \u53ca\u5176\u5f71\u97ff\u3002\u9019\u4e9b\u767c\u73fe\u4e26\u975e\u7d14\u7cb9\u7684\u5b78\u8853\u7df4\u7fd2\uff1b\u5b83\u5011\u662f\u91cf\u5b50\u767c\u5c55\u7684\u57fa\u77f3\uff0c\u6709\u671b\u5b8c\u5168\u91cd\u65b0\u5b9a\u7fa9\u6211\u5011\u7684\u8a08\u7b97\u9818\u57df\u3002\n<\/p>\n

    \u63a2\u7a76\u95dc\u806f\uff1aBQP \u8207\u7d93\u5178\u8907\u96dc\u6027\u985e\u5225<\/h2>\n

    \u7576\u6211\u5011\u6df1\u5165\u7814\u7a76\u91cf\u5b50\u904b\u7b97\u7684\u8907\u96dc\u6027\u6642\uff0c\u6211\u5011\u6703\u9047\u5230 BQP\uff0c\u9019\u500b\u8907\u96dc\u6027\u985e\u5225\u662f\u6211\u5011\u4e86\u89e3\u9019\u500b\u5c16\u7aef\u9818\u57df\u7684\u57fa\u77f3\u3002BQP \u6216\u6709\u754c\u932f\u8aa4\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593\uff0c\u5c0d\u65bc\u6211\u5011\u5982\u4f55\u6982\u5ff5\u5316\u9069\u5408\u91cf\u5b50\u904b\u7b97\u7684\u554f\u984c\uff0c\u4ee5\u53ca\u9019\u4e9b\u554f\u984c\u8207\u7d93\u5178\u904b\u7b97\u4e4b\u9593\u7684\u95dc\u4fc2\uff0c\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\u3002 \u8907\u96dc\u5ea6\u7b49\u7d1a<\/b>.<\/p>\n

    BQP \u7d0d\u5165 P \u548c BPP \u985e\u5225<\/h3>\n

    \u5728\u7a7f\u8d8a\u8907\u96dc\u6027\u985e\u5225\u7684\u904e\u7a0b\u4e2d\uff0c\u6211\u5011\u767c\u73fe BQP \u5c0d\u65bc\u985e\u5225 P \u7684\u7406\u89e3\u975e\u5e38\u6709\u8da3\uff0c\u985e\u5225 P \u662f\u4f7f\u7528\u78ba\u5b9a\u6027\u5716\u9748\u6a5f\u5668\u5728\u591a\u502b\u591a\u6642\u9593\u5167\u53ef\u89e3\u6c7a\u7684\u554f\u984c\u96c6\uff0c\u4ee5\u53ca BPP<\/b>\uff0c\u5b83\u5141\u8a31\u5728\u6982\u7387\u5716\u9748\u6a5f\u5668\u4e0a\u4ee5\u591a\u6578\u6b21\u6642\u9593\u9054\u5230\u6709\u754c\u932f\u8aa4\u3002BQP \u7684\u8a98\u4eba\u4e4b\u8655\u5728\u65bc\u5176\u5ee3\u6cdb\u7684\u80fd\u529b\uff0c\u65e2\u80fd\u7d50\u5408\u9019\u5169\u7a2e\u7d93\u5178\u6a21\u578b\u7684\u7279\u8cea\uff0c\u53c8\u80fd\u5728\u91cf\u5b50\u529b\u5b78\u7684\u7368\u7279\u9818\u57df\u4e2d\u904b\u4f5c\u3002\u9019\u7a2e\u7d9c\u5408\u80fd\u529b\u6a19\u8a8c\u8457\u8d85\u8d8a\u7d93\u5178\u8a08\u7b97\u80fd\u529b\u7684\u4e00\u5927\u8e8d\u9032\u3002<\/p>\n

    \u8a55\u4f30 BQP \u5728 PSPACE \u7b49\u8907\u96dc\u6027\u5b50\u96c6\u4e2d\u7684\u91cd\u8981\u6027<\/h3>\n

    \u5728\u8c50\u5bcc\u7684 \u8907\u96dc\u5ea6\u8ad6<\/b>BQP \u7a69\u5b9a\u5730\u5b9a\u4f4d\u5728 PSPACE<\/b>.\u9019\u4e00\u5927\u985e\u53ef\u4ee5\u7528\u591a\u9805\u7a7a\u9593\u6c42\u89e3\u7684\u554f\u984c\u9060\u9060\u8d85\u8d8a\u4e86 P \u7684\u7bc4\u570d\uff0c\u4e5f\u5305\u542b\u4e86 NP \u7684\u8907\u96dc\u6027\u3002\u5728\u9019\u4e9b\u5c64\u7d1a\u4e2d\u5206\u6790 BQP \u662f\u975e\u5e38\u6709\u50f9\u503c\u7684\uff0c\u56e0\u70ba\u5b83\u63ed\u793a\u4e86\u91cf\u5b50\u904b\u7b97\u7684\u7406\u8ad6\u57fa\u790e\u548c\u6f5b\u5728\u61c9\u7528\u3002\u6b64\u5916\uff0c\u5b83\u9084\u80fd\u63a8\u52d5\u7814\u7a76\u5411\u524d\u9081\u9032\uff0c\u63a2\u7d22\u6211\u5011\u8a8d\u70ba\u7406\u8ad6\u4e0a\u53ef\u80fd\u7684\u908a\u7de3\uff0c\u6709\u53ef\u80fd\u5fb9\u5e95\u6539\u8b8a\u6211\u5011\u8655\u7406\u8907\u96dc\u554f\u984c\u7684\u65b9\u6cd5\u3002 \u554f\u984c\u89e3\u6c7a<\/b>.<\/p>\n

    \u91cf\u5b50\u81f3\u4e0a\u5c0d BQP \u666f\u89c0\u7684\u5f71\u97ff<\/h2>\n

    \u91cf\u5b50\u512a\u8d8a\u6027\u7684\u9810\u5146\uff0c\u6a19\u8a8c\u8457 BQP\uff08\u6709\u754c\u932f\u8aa4\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593\uff09\u5728\u4e0d\u65b7\u6f14\u9032\u7684\u8a08\u7b97\u7406\u8ad6\u7e54\u9326\u4e2d\u6240\u626e\u6f14\u89d2\u8272\u7684\u5206\u6c34\u5dba\u6642\u523b\u3002\u7576\u6211\u5011\u6df1\u5165\u63a2\u8a0e\u91cf\u5b50\u904b\u7b97\u9019\u4e00\u7a81\u7834\u6027\u9032\u5c55\u6240\u5e36\u4f86\u7684\u6df1\u9060\u8f49\u8b8a\u6642\uff0c\u6211\u5011\u6703\u610f\u8b58\u5230\u5169\u65b9\u9762\u7684\u8f49\u8b8a--\u91cf\u5b50\u904b\u7b97\u7684\u8e8d\u9032\u8207\u91cf\u5b50\u6642\u4ee3\u7684\u4f86\u81e8\u3002 \u554f\u984c\u89e3\u6c7a<\/b> \u80fd\u529b\uff0c\u4e26\u632f\u8208\u91cf\u5b50\u932f\u8aa4\u4fee\u6b63\u65b9\u6cd5\u3002<\/p>\n

    \u91cf\u5b50\u81f3\u4e0a\u5c0d\u554f\u984c\u89e3\u6c7a\u7684\u5f71\u97ff<\/h3>\n

    \u5728\u6578\u4f4d\u904b\u7b97\u7684\u53f2\u8a69\u50b3\u5947\u4e2d\uff0c\u91cf\u5b50\u512a\u52e2\u7684\u51fa\u73fe\u5df2\u958b\u59cb\u7de8\u5beb\u4e00\u500b\u6fc0\u9032\u7684\u7bc7\u7ae0\u3002\u91cf\u5b50\u512a\u52e2\u7684\u65b0\u6642\u4ee3\u7e2e\u5f71\u4e86\u91cf\u5b50\u96fb\u8166\u596e\u529b\u89e3\u6c7a BQP \u7d1a\u554f\u984c\u7684\u5178\u7bc4\uff0c\u800c\u9019\u4e9b\u554f\u984c\u537b\u8b93\u7d93\u5178\u96fb\u8166\u8655\u65bc\u4e4f\u5584\u53ef\u9673\u7684\u72c0\u614b\u3002\u9019\u4e0d\u50c5\u662f\u91cf\u7684\u8e8d\u9032\uff0c\u66f4\u662f\u8cea\u7684\u9032\u5316\u3002 \u554f\u984c\u89e3\u6c7a<\/b>\u91cf\u5b50\u6f14\u7b97\u6cd5\u80fd\u4ee5\u524d\u6240\u672a\u6709\u7684\u898f\u6a21\u548c\u901f\u5ea6\uff0c\u9748\u6d3b\u5730\u8655\u7406\u8907\u96dc\u7684\u554f\u984c\u3002<\/p>\n

    \u91cf\u5b50\u932f\u8aa4\u6821\u6b63\u5728 BQP \u4e2d\u7684\u6f5b\u5728\u9032\u5c55<\/h3>\n

    \u8981\u5145\u5206\u767c\u63ee\u91cf\u5b50\u904b\u7b97\u7684\u512a\u52e2\uff0c\u5c31\u5fc5\u9808\u638c\u63e1\u91cf\u5b50\u932f\u8aa4\u4fee\u6b63\u3002\u5b83\u662f\u62b5\u6297\u91cf\u5b50\u4f4d\u5143\u5bb9\u6613\u767c\u751f\u7684\u81ea\u7136\u9000\u76f8\u5e72\u548c\u64cd\u4f5c\u7f3a\u9677\u7684\u5821\u58d8\u3002\u5728\u8ffd\u6c42\u91cf\u5b50\u512a\u52e2\u7684\u904e\u7a0b\u4e2d\uff0c\u5b8c\u5584\u4e26\u52a0\u5f37\u932f\u8aa4\u4fee\u6b63\u5354\u5b9a\u7684\u63a8\u52d5\u529b\u662f\u4e0d\u8a00\u800c\u55bb\u7684\u3002\u6211\u5011\u898b\u8b49\u4e86\u91cf\u5b50\u5f48\u6027\u7684\u5354\u540c\u767c\u5c55\uff0c\u9019\u662f BQP \u9032\u5c55\u7684\u95dc\u9375\u4efb\u52d9\uff0c\u4e5f\u662f\u91cf\u5b50\u7cfb\u7d71\u5167\u7d50\u679c\u6e96\u78ba\u6027\u7684\u4fdd\u8b49\u3002<\/p>\n

    \u91cf\u5b50\u904b\u7b97\u7684\u5927\u5716\u666f\uff1a\u8d85\u8d8a BQP<\/h2>\n

    \u7576\u6211\u5011\u6df1\u5165\u63a2\u7d22\u91cf\u5b50\u904b\u7b97\u7684\u5ee3\u95ca\u9818\u57df\u6642\uff0c\u6211\u5011\u610f\u8b58\u5230 BQP (Bounded-error Quantum Polynomial Time) \u53ea\u662f\u756b\u5e03\u7684\u4e00\u89d2\uff0c\u52fe\u52d2\u51fa\u91cf\u5b50\u56f0\u96e3\u8207\u52dd\u5229\u7684\u57fa\u672c\u9762\u8c8c\u3002\u5c0d BQP \u7684\u63a2\u7d22\u70ba\u6211\u5011\u5960\u5b9a\u4e86\u5805\u5be6\u7684\u57fa\u790e\uff0c\u63ed\u793a\u4e86\u91cf\u5b50\u6f14\u7b97\u6cd5\u7684\u8907\u96dc\u6027\u8207\u512a\u52e2\uff0c\u4ee5\u53ca\u5b83\u5011\u4e4b\u9593\u7684\u4e92\u52d5\u95dc\u4fc2\u3002 \u91cf\u5b50\u8907\u96dc\u6027\u7406\u8ad6<\/b>.\u7136\u800c\uff0c\u91cf\u5b50\u8a08\u7b97\u7684\u7bc4\u570d\u9060\u9060\u8d85\u904e\u9019\u500b\u57fa\u790e\u985e\u5225\uff0c\u56e0\u70ba\u6301\u7e8c\u7684\u9032\u6b65\u6b63\u5f15\u9818\u6211\u5011\u671d\u5411\u4ee5\u4e0b\u7406\u8ad6\u9818\u57df\u524d\u9032 BQP\u5f8c<\/b> \u8907\u96dc\u6027\u7b49\u7d1a\u3002<\/p>\n

    \u5c55\u671b\u5f8c BQP \u8907\u96dc\u6027\u985e\u5225<\/h3>\n

    \u7684\u6982\u5ff5\u3002 BQP\u5f8c<\/b> \u8907\u96dc\u6027\u7b49\u7d1a\u4ee3\u8868\u8457\u667a\u6167\u7684\u524d\u6cbf\uff0c\u5145\u6eff\u6311\u6230\u8207\u7cbe\u5bc6\u7684\u6a5f\u5236\uff0c\u5c1a\u672a\u88ab\u767c\u73fe\u6216\u5b8c\u5168\u7406\u89e3\u3002\u5728\u91cf\u5b50\u8a08\u7b97\u7684\u65c5\u7a0b\u4e2d\u3001 BQP \u9032\u5c55<\/b> \u7167\u4eae\u4e86\u4e00\u689d\u901a\u5f80\u5145\u6eff\u589e\u5f37\u904b\u7b97\u80fd\u529b\u8207\u795e\u79d8\u91cf\u5b50\u73fe\u8c61\u9818\u57df\u7684\u9053\u8def\u3002\u8eab\u70ba\u7814\u7a76\u4eba\u54e1\uff0c\u6211\u5011\u70af\u70af\u6709\u795e\u5730\u671b\u8457\u5730\u5e73\u7dda\uff0c\u56e0\u70ba\u6211\u5011\u77e5\u9053\u8d85\u8d8a BQP \u6240\u5e36\u4f86\u7684\u5f71\u97ff\uff0c\u4e0d\u50c5\u6703\u91cd\u65b0\u5b9a\u7fa9\u6211\u5011\u89e3\u6c7a\u554f\u984c\u7684\u65b9\u5f0f\uff0c\u4e5f\u6703\u91cd\u65b0\u5b9a\u7fa9\u6211\u5011\u5c0d\u8a08\u7b97\u73fe\u5be6\u672c\u8eab\u7d50\u69cb\u7684\u770b\u6cd5\u3002<\/p>\n

    \u4ee5 BQP \u70ba\u57fa\u790e\u7684\u91cf\u5b50\u904b\u7b97\u6240\u5e36\u4f86\u7684\u5be6\u969b\u61c9\u7528<\/h3>\n

    \u7136\u800c\uff0c\u5373\u4f7f\u6211\u5011\u5c55\u671b\u672a\u4f86\uff0cBQP \u7684\u80a5\u6c83\u571f\u58e4\u5df2\u7d93\u5728\u91cf\u5b50\u904b\u7b97\u4e2d\u7d50\u51fa\u8c50\u78a9\u7684\u679c\u5be6\u3002 \u5be6\u969b\u61c9\u7528<\/b> BQP \u7684\u6210\u5c31\u6b63\u5728\u5d1b\u8d77\uff0c\u5c0d\u5bc6\u78bc\u5b78\u3001\u900f\u904e\u7121\u6cd5\u7834\u89e3\u7684\u52a0\u5bc6\u4fdd\u8b77\u8cc7\u6599\u3001\u900f\u904e\u52a0\u901f\u85e5\u7269\u767c\u73fe\u6539\u8b8a\u88fd\u85e5\uff0c\u4ee5\u53ca\u900f\u904e\u91cf\u5b50\u6a5f\u5668\u5b78\u7fd2\u8e8d\u9032\u4eba\u5de5\u667a\u6167\u7b49\u9818\u57df\u7522\u751f\u91cd\u5927\u5f71\u97ff\u3002\u9019\u4e9b\u5728 \u5be6\u969b\u61c9\u7528<\/b> \u91cd\u7533\u4e86 BQP \u4f5c\u70ba\u71c8\u5854\u7684\u95dc\u9375\u89d2\u8272\uff0c\u70ba\u6211\u5011\u6307\u51fa\u4e86\u4e00\u500b\u5145\u6eff\u53ef\u80fd\u6027\u548c\u7121\u8207\u502b\u6bd4\u7684\u8a08\u7b97\u80fd\u529b\u7684\u672a\u4f86\u3002<\/p>\n

    \n

    \u5e38\u898b\u554f\u984c<\/h2>\n
    \n

    \u4ec0\u9ebc\u662f\u91cf\u5b50\u904b\u7b97\u4e2d\u7684 BQP\uff1f<\/h3>\n
    \n
    \n

    BQP \u6216 Bounded-error Quantum Polynomial Time\uff0c\u662f\u91cf\u5b50\u96fb\u8166\u80fd\u4ee5\u9ad8\u6210\u529f\u6982\u7387 (\u81f3\u5c11 2\/3)\u3001\u591a\u9805\u5f0f\u6642\u9593\u89e3\u6c7a\u7684\u6c7a\u7b56\u554f\u984c\u7684\u8907\u96dc\u6027\u985e\u5225\u3002\u5b83\u985e\u4f3c\u65bc\u7d93\u5178\u8907\u96dc\u6027\u985e\u5225 BPP<\/b> \u4f46\u5c08\u70ba\u91cf\u5b50\u904b\u7b97\u91cf\u8eab\u6253\u9020\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    BQP \u5982\u4f55\u5b9a\u7fa9\u6c7a\u7b56\u554f\u984c\uff1f<\/h3>\n
    \n
    \n

    BQP \u4e2d\u7684\u6c7a\u7b56\u554f\u984c\u662f\u4ee5\u5176\u53ef\u89e3\u7a0b\u5ea6\u4f86\u5b9a\u7fa9\u7684\uff0c\u91cf\u5b50\u6f14\u7b97\u6cd5\u53ef\u5728\u591a\u9805\u5f0f\u6642\u9593\u5167\u904b\u4f5c\uff0c\u4e26\u5728\u6bcf\u500b\u554f\u984c\u5be6\u4f8b\u7684\u932f\u8aa4\u6982\u7387\u4e0d\u8d85\u904e 1\/3 \u7684\u60c5\u6cc1\u4e0b\u63d0\u4f9b\u6b63\u78ba\u7b54\u6848\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    BQP \u80fd\u5426\u64f4\u5c55\u7d93\u5178\u8907\u96dc\u6027\u7406\u8ad6\u7684\u80fd\u529b\uff1f<\/h3>\n
    \n
    \n

    \u662f\u7684\uff0cBQP \u5c07\u91cf\u5b50\u529b\u5b78\u539f\u7406\u5e36\u5165\u8a08\u7b97\u8907\u96dc\u6027\u7406\u8ad6\u9818\u57df\uff0c\u6709\u53ef\u80fd\u8b93\u91cf\u5b50\u96fb\u8166\u89e3\u6c7a\u7d93\u5178\u96fb\u8166\u96e3\u4ee5\u89e3\u6c7a\u7684\u554f\u984c\uff0c\u9032\u800c\u64f4\u5c55\u7d93\u5178\u8a08\u7b97\u7684\u6975\u9650\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u91cf\u5b50\u96fb\u8def\u5728 BQP \u6f14\u7b97\u6cd5\u4e2d\u626e\u6f14\u4ec0\u9ebc\u89d2\u8272\uff1f<\/h3>\n
    \n
    \n

    \u91cf\u5b50\u96fb\u8def\u662f BQP \u6f14\u7b97\u6cd5\u7684\u57fa\u790e\uff0c\u56e0\u70ba\u91cf\u5b50\u96fb\u8def\u662f\u7531\u91cf\u5b50\u9598\u9580\u6240\u7d44\u6210\uff0c\u91cf\u5b50\u9598\u9580\u53ef\u4ee5\u64cd\u63a7\u91cf\u5b50\u4f4d\u5143\u4f86\u6709\u6548\u7387\u5730\u5be6\u4f5c\u9019\u4e9b\u6f14\u7b97\u6cd5\uff0c\u76f4\u63a5\u5f71\u97ff\u91cf\u5b50\u96fb\u8166\u89e3\u6c7a BQP \u67b6\u69cb\u5167\u554f\u984c\u7684\u80fd\u529b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u4ec0\u9ebc\u662f\u91cf\u5b50\u96fb\u8def\u7684\u300c\u7d71\u4e00\u65cf\u300d\uff1f<\/h3>\n
    \n
    \n

    \u91cf\u5b50\u96fb\u8def\u7684\u7d71\u4e00\u65cf\u6307\u7684\u662f\u53ef\u4ee5\u7531\u7d93\u5178\u96fb\u8166\u6709\u6548\u7387\u5730\u7522\u751f\u7684\u96fb\u8def\u96c6\uff0c\u5176\u96fb\u8def\u8a2d\u8a08\u7684\u5927\u5c0f\u4ee5\u8f38\u5165\u9577\u5ea6\u7684\u51fd\u6578\u591a\u9879\u5f0f\u7e2e\u653e\uff0c\u78ba\u4fdd BQP \u6f14\u7b97\u6cd5\u6240\u9700\u7684\u4e00\u81f4\u6027\u8207\u6a19\u6e96\u5316\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u91cf\u5b50\u6f14\u7b97\u6cd5\u8207 BQP \u6709\u4f55\u95dc\u806f\uff1f<\/h3>\n
    \n
    \n

    \u91cf\u5b50\u6f14\u7b97\u6cd5\u63d0\u4f9b\u89e3\u6c7a BQP \u985e\u554f\u984c\u7684\u65b9\u6cd5\uff0c\u904b\u7528\u91cf\u5b50\u529b\u5b78\u7279\u6027\u548c\u5148\u9032\u7684\u8a08\u7b97\u7b56\u7565\uff0c\u4ee5\u9054\u5230\u4f4e\u5230\u8db3\u4ee5\u7b26\u5408 BQP \u6a19\u6e96\u7684\u932f\u8aa4\u6982\u7387\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    BQP \u8207 BPP\u3001RP \u548c ZPP \u6709\u4f55\u4e0d\u540c\uff1f<\/h3>\n
    \n
    \n

    BQP \u662f\u5c08\u70ba\u91cf\u5b50\u8a08\u7b97\u800c\u8a2d\u8a08\uff0c\u5176\u7368\u7279\u7684\u80fd\u529b\uff0c\u5982\u758a\u52a0\u548c\u7e8f\u7d50\uff0c\u4f7f\u5176\u6709\u53ef\u80fd\u89e3\u6c7a\u7d93\u5178\u8a08\u7b97\u7bc4\u570d\u4e4b\u5916\u7684\u554f\u984c\u3002 \u6982\u7387\u985e\u5225<\/b> \u559c BPP<\/b>, RP<\/b>\u4ee5\u53ca ZPP<\/b>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u91cf\u5b50\u8cc7\u8a0a\u7406\u8ad6\u4e2d\u7684 BQP \u6709\u4f55\u7368\u7279\u4e4b\u8655\uff1f<\/h3>\n
    \n
    \n

    \u5167 \u91cf\u5b50\u8cc7\u8a0a\u8ad6<\/b>BQP \u7684\u7279\u9ede\u662f\u5229\u7528\u91cf\u5b50\u8a08\u7b97\u6a21\u578b\uff0c\u4ee5\u9ad8\u6e96\u78ba\u5ea6\u548c\u9ad8\u901f\u5ea6\u4f86\u89e3\u6c7a\u6c7a\u7b56\u554f\u984c\uff0c\u5229\u7528\u91cf\u5b50\u529b\u5b78\u7684\u7279\u6b8a\u6027\u4f86\u8d85\u8d8a\u7d93\u5178\u6a21\u578b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u4ec0\u9ebc\u662f Promise-BQP\uff1f<\/h3>\n
    \n
    \n

    Promise-BQP \u662f BQP \u4e2d\u7684\u4e00\u500b\u5b50\u985e\uff0c\u5305\u542b\u4e86\u88ab\u8996\u70ba\u5b8c\u5168\u91cf\u5b50\u5316\u7684\u554f\u984c\uff0c\u610f\u5373 BQP \u4e2d\u7684\u6240\u6709\u5176\u4ed6\u554f\u984c\u90fd\u53ef\u4ee5\u5728\u591a\u6578\u6b21\u6642\u9593\u5167\u9084\u539f\u70ba\u9019\u4e9b\u554f\u984c\uff0c\u7a81\u986f\u4e86\u91cf\u5b50\u8a08\u7b97\u8907\u96dc\u6027\u7684\u7d50\u69cb\u6838\u5fc3\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    BQP \u5982\u4f55\u7d50\u5408 P \u548c BPP \u7b49\u7d93\u5178\u8907\u96dc\u6027\u985e\u5225\uff1f<\/h3>\n
    \n
    \n

    BQP \u5305\u542b P\uff08\u53ef\u7531\u78ba\u5b9a\u5f0f\u5716\u9748\u6a5f\u5668\u5728\u591a\u6578\u6b21\u6642\u9593\u5167\u89e3\u6c7a\u7684\u554f\u984c\uff09\u548c BPP\uff08\u53ef\u4f7f\u7528\u6982\u7387\u6f14\u7b97\u6cd5\u5728\u591a\u6578\u6b21\u6642\u9593\u5167\u89e3\u6c7a\u7684\u554f\u984c\uff09\uff0c\u986f\u793a\u91cf\u5b50\u96fb\u8166\u7684\u6548\u80fd\u81f3\u5c11\u53ef\u5ab2\u7f8e\u78ba\u5b9a\u5f0f\u548c\u96a8\u6a5f\u5316\u7684\u7d93\u5178\u96fb\u8166\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u70ba\u4ec0\u9ebc BQP \u5728 PSPACE \u5167\u7684\u4f4d\u7f6e\u5f88\u91cd\u8981\uff1f<\/h3>\n
    \n
    \n

    \u81ea PSPACE<\/b> \u5305\u62ec P \u548c NP \u5728\u5167\u7684\u6240\u6709\u53ef\u7528\u591a\u6578\u8a18\u61b6\u9ad4\u7a7a\u9593\u6c42\u89e3\u7684\u554f\u984c\u3002 PSPACE<\/b> \u986f\u793a\u91cf\u5b50\u96fb\u8166\u53ef\u80fd\u6709\u6548\u7387\u5730\u89e3\u6c7a\u5404\u7a2e\u8907\u96dc\u554f\u984c\uff0c\u800c\u4e0d\u9700\u8981\u6307\u6578\u7d1a\u7684\u7a7a\u9593\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u91cf\u5b50\u81f3\u4e0a\u5982\u4f55\u5f71\u97ff BQP \u7684\u683c\u5c40\uff1f<\/h3>\n
    \n
    \n

    \u91cf\u5b50\u512a\u8d8a\u6027\u8aaa\u660e\u91cf\u5b50\u96fb\u8166\u53ef\u4ee5\u89e3\u6c7a\u67d0\u4e9b\u7d93\u5178\u6a5f\u5668\u7121\u6cd5\u89e3\u6c7a\u7684\u554f\u984c\u3002\u9019\u500b\u73fe\u8c61\u9a57\u8b49\u4e86 BQP \u554f\u984c\u7684\u91cd\u8981\u6027\uff0c\u4e26\u63a8\u52d5\u4e86\u91cf\u5b50\u932f\u8aa4\u4fee\u6b63\u7b49\u9032\u6b65\uff0c\u9019\u4e9b\u5c0d\u65bc\u91cf\u5b50\u904b\u7b97\u7684\u7a69\u5b9a\u6027\u548c\u7cbe\u78ba\u5ea6\u662f\u975e\u5e38\u91cd\u8981\u7684\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u91cf\u5b50\u932f\u8aa4\u4fee\u6b63\u5c0d BQP \u6709\u4f55\u5f71\u97ff\uff1f<\/h3>\n
    \n
    \n

    \u91cf\u5b50\u932f\u8aa4\u6821\u6b63\u5c0d\u7dad\u6301\u91cf\u5b50\u8a08\u7b97\u7684\u4e00\u81f4\u6027\u548c\u7cbe\u78ba\u5ea6\u81f3\u95dc\u91cd\u8981\u3002\u5b83\u7684\u6539\u9032\u8207\u61c9\u7528\u5c0d\u65bc\u53ef\u9760\u7684\u91cf\u5b50\u904b\u7b97\u662f\u4e0d\u53ef\u6216\u7f3a\u7684\uff0c\u800c\u53ef\u9760\u7684\u91cf\u5b50\u904b\u7b97\u5c0d\u65bc\u5728\u73fe\u5be6\u4e16\u754c\u5834\u666f\u4e2d\u6709\u6548\u89e3\u6c7a BQP \u5167\u7684\u554f\u984c\u662f\u5fc5\u8981\u7684\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u5728\u91cf\u5b50\u8a08\u7b97\u8907\u96dc\u6027\u65b9\u9762\uff0cBQP \u9084\u6709\u54ea\u4e9b\u8d85\u8d8a\u4e4b\u8655\uff1f<\/h3>\n
    \n
    \n

    Post-BQP<\/b> \u8907\u96dc\u6027\u985e\u5225\u53ef\u80fd\u5305\u542b\u76ee\u524d\u91cf\u5b50\u6a21\u578b\u7121\u6cd5\u89e3\u6c7a\u7684\u554f\u984c\uff0c\u63a8\u9032\u8a08\u7b97\u4e0a\u53ef\u80fd\u7684\u908a\u754c\uff0c\u4e26\u555f\u767c\u65b0\u7684\u91cf\u5b50\u6f14\u7b97\u6cd5\u8207\u6280\u8853\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n

    \u57fa\u65bc BQP \u7684\u91cf\u5b50\u904b\u7b97\u6709\u54ea\u4e9b\u5be6\u969b\u61c9\u7528\uff1f<\/h3>\n
    \n
    \n

    \u57fa\u65bc BQP \u7684\u91cf\u5b50\u8a08\u7b97\u6b63\u5728\u767c\u73fe \u5be6\u969b\u61c9\u7528<\/b> \u5728\u5404\u500b\u9818\u57df\uff0c\u4f8b\u5982\u5bc6\u78bc\u5b78\uff0c\u7528\u65bc\u5b89\u5168\u901a\u8a0a\uff1b\u85e5\u7269\u767c\u73fe\u548c\u6750\u6599\u79d1\u5b78\uff0c\u900f\u904e\u6a21\u64ec\u5206\u5b50\u7d50\u69cb\uff1b\u4ee5\u53ca\u6a5f\u5668\u5b78\u7fd2\uff0c\u589e\u5f37\u8cc7\u6599\u5206\u6790\u548c\u4eba\u5de5\u667a\u6167\u6f14\u7b97\u6cd5\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>","protected":false},"excerpt":{"rendered":"

    \u5728\u63a2\u7d22\u91cf\u5b50\u904b\u7b97\u4e0d\u65b7\u6f14\u9032\u7684\u904e\u7a0b\u4e2d\uff0c\u6211\u5011\u6df1\u5165\u63a2\u8a0e\u4e86 BQP (Bounded-error Quantum Polynomial Time\uff0c\u6709\u754c\u932f\u91cf\u5b50\u591a\u9879\u5f0f\u6642\u9593) \u7684\u8907\u96dc\u6027\u3002\u9019\u500b\u57fa\u77f3\u6982\u5ff5\u662f\u91cf\u5b50\u904b\u7b97\u7684\u6838\u5fc3\u3002\u7e7c\u7e8c\u95b1\u8b80 “Understanding BQP in Quantum Computing”<\/span><\/a><\/p>","protected":false},"author":1,"featured_media":505500,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-505499","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"acf":[],"_links":{"self":[{"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/posts\/505499","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/comments?post=505499"}],"version-history":[{"count":0,"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/posts\/505499\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/media\/505500"}],"wp:attachment":[{"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/media?parent=505499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/categories?post=505499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumaieu.com\/zh\/wp-json\/wp\/v2\/tags?post=505499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}