{"id":24129,"date":"2021-02-28T22:10:09","date_gmt":"2021-02-28T14:10:09","guid":{"rendered":"https:\/\/swarma.org\/?p=24129"},"modified":"2021-02-28T22:10:09","modified_gmt":"2021-02-28T14:10:09","slug":"%e8%a7%a3%e5%af%86%e7%a5%9e%e5%a5%87%e7%9a%84%e9%87%8f%e5%ad%90%e9%bb%91%e7%9b%92","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=24129","title":{"rendered":"\u89e3\u5bc6\u795e\u5947\u7684\u91cf\u5b50\u9ed1\u76d2"},"content":{"rendered":"
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\u5bfc\u8bed<\/p>\n

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\u6248\u9e3f\u4e1a | \u4f5c\u8005<\/p>\n

\u5b59\u5b87 | \u8bd1\u8005
\u9093\u4e00\u96ea | \u7f16\u8f91<\/p>\n

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1. \u4e8b\u7269\u80fd\u591f\u4ee5\u53e0\u52a0\u6001\u7684\u65b9\u5f0f\u5b58\u5728<\/p>\n


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 <\/p>\n

2. \u4e8b\u7269\u7684\u4e0d\u540c\u65b9\u9762\u65e0\u6cd5\u88ab\u540c\u65f6\u6d4b\u5b9a<\/p>\n


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\u901a\u4fd7\u4e00\u70b9\u6765\u8bb2\uff0c \u5c31\u597d\u6bd4\u6211\u4eec\u6709\u4e00\u5757\u91cf\u5b50\u86cb\u7cd5\u76db\u653e\u5728\u91cf\u5b50\u9b54\u672f\u5e08\u7684\u9ed1\u7bb1\u4e2d\uff0c\u8fd9\u5757\u86cb\u7cd5\u7684\u5f62\u72b6\u53ef\u80fd\u662f\u5706\u4e5f\u53ef\u80fd\u662f\u65b9\uff0c \u989c\u8272\u53ef\u80fd\u662f\u7ea2\u4e5f\u53ef\u80fd\u662f\u84dd\u3002\u4e00\u4e2a\u8bda\u5b9e\u7684\u5b88\u62a4\u7cbe\u7075\u770b\u5b88\u7740\u8fd9\u5757\u86cb\u7cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u95ee\u8fd9\u4e2a\u5b88\u62a4\u7cbe\u7075\u201c\u86cb\u7cd5\u662f\u4ec0\u4e48\u5f62\u72b6\u7684\u201d\u6216\u8005\u201c\u86cb\u7cd5\u662f\u4ec0\u4e48\u989c\u8272\u7684\u201d\u3002\u4e0d\u8fc7\u8fd9\u4e2a\u7cbe\u7075\u4e0d\u5141\u8bb8\u6211\u4eec\u9488\u5bf9\u8fd9\u4e24\u4e2a\u95ee\u9898\u540c\u65f6\u53d1\u95ee\u3002\u4f60\u6216\u8bb8\u4f1a\u60f3\uff0c \u597d\u5427\uff0c\u5982\u679c\u771f\u662f\u8fd9\u6837\uff0c \u6211\u53ef\u4ee5\u5148\u95ee\u5f62\u72b6\u518d\u95ee\u989c\u8272\uff0c\u7136\u540e\u6211\u4eec\u5c31\u81ea\u7136\u77e5\u9053\u5168\u90e8\u4fe1\u606f\u5566\u3002\u4e0d\u8fc7\u5f88\u53ef\u60dc\uff0c \u91cf\u5b50\u9b54\u672f\u5e08\u6bd4\u6211\u4eec\u60f3\u7684\u8fd8\u8981\u72e1\u733e\u3002\u771f\u5b9e\u60c5\u5f62\u5f88\u53ef\u80fd\u662f\u8fd9\u6837\uff1a\u5148\u95ee\u5f62\u72b6\uff0c \u5b88\u62a4\u7cbe\u7075\u8bf4\u201c\u5706\u5f62\u201d\uff1b\u7136\u540e\u95ee\u989c\u8272\uff0c\u5b88\u62a4\u7cbe\u7075\u8bf4\u201c\u7ea2\u8272” \uff1b\u5230\u76ee\u524d\u8fd8\u6bd4\u8f83\u6ee1\u610f\uff0c \u8ba9\u6211\u4eec\u518d\u548c\u5b88\u62a4\u7cbe\u7075\u6838\u5bf9\u4e00\u4e0b\u5427\uff0c \u518d\u95ee\u4e0b\u86cb\u7cd5\u7684\u5f62\u72b6\uff0c \u4ec0\u4e48\uff01\u5b88\u62a4\u7cbe\u7075\u7adf\u7136\u8bf4\u662f\u201c\u65b9\u5f62\u201d\uff01\u5b88\u62a4\u7cbe\u7075\u53ef\u662f\u4ece\u6765\u4e0d\u8bf4\u8c0e\u7684\uff0c\u4e3a\u4ec0\u4e48\u4f1a\u662f\u65b9\u5f62\uff01\u770b\u5230\u4e86\u5427\uff0c \u8fd9\u5c31\u662f\u91cf\u5b50\u9b54\u672f\u5e08\u7684\u72e1\u733e\u3002\u8fd9\u4e2a\u9b54\u672f\u7684\u80cc\u540e\u4e0e\u91cf\u5b50\u5bf9\u8c61\u7684\u72b6\u6001\u53e0\u52a0\u7279\u6027\u5b58\u5728\u67d0\u79cd\u5173\u7cfb\u3002\u5927\u6982\u8fd9\u4e2a\u91cf\u5b50\u9b54\u672f\u5e08\u7684\u7ae5\u8bdd\u5df2\u7ecf\u6216\u591a\u6216\u5c11\u8ba9\u4f60\u4f53\u4f1a\u5230\u91cf\u5b50\u4e16\u754c\u4ee4\u4eba\u8d39\u89e3\u7684\u53e4\u602a\u79bb\u5947\u3002 <\/p>\n


3. \u4e3a\u4ec0\u4e48\u6211\u4eec\u9700\u8981\u5173\u6ce8\u91cf\u5b50\u6001\u5c42\u6790\u6210\u50cf\u6280\u672f<\/p>\n

\u867d\u7136\u91cf\u5b50\u4e16\u754c\u53e4\u602a\u79bb\u5947\uff0c \u79d1\u5b66\u5bb6\u4ecd\u7136\u80fd\u591f\u8bbe\u8ba1\u5b9e\u9a8c\u6765\u5b8c\u5168\u5730\u63ed\u793a\u91cf\u5b50\u9ed1\u7bb1\u7684\u771f\u9762\u76ee\uff0c \u5e76\u7406\u89e3\u91cf\u5b50\u9ed1\u7bb1\u4e2d\u90a3\u53ea\u91cf\u5b50\u732b\u201c\u65e2\u751f\u53c8\u6b7b\u201d\u7684\u751f\u5b58\u72b6\u6001\u3002\u8fd9\u4e2a\u624b\u6bb5\u5c31\u662f\u91cf\u5b50\u6001\u5c42\u6790\u6210\u50cf\u6280\u672f\uff08Quantum state tomography\uff09\uff0c \u7b80\u79f0QST\u3002\u91cf\u5b50\u6001\u5c42\u6790\u6210\u50cf\u6280\u672f\u5f88\u91cd\u8981\u3002\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u60f3\u8981\u4ece\u79d1\u5b66\u7684\u89d2\u5ea6\u51fa\u53d1\u7406\u89e3\u8fd9\u4e9b\u91cf\u5b50\u7cfb\u7edf\u3002\u6bd4\u5982\uff0c\u91cf\u5b50\u6750\u6599\uff08\u4f8b\u5982\u8d85\u5bfc\u4f53\uff09\u5c55\u73b0\u51fa\u8ff7\u4eba\u800c\u8be1\u5f02\u7684\u7279\u6027\uff0c\u4e00\u65e6\u6211\u4eec\u7406\u89e3\u8fd9\u4e9b\u6027\u8d28\uff0c \u6211\u4eec\u5c31\u80fd\u591f\u5229\u7528\u5b83\u4eec\u7684\u7279\u6027\u6765\u9020\u798f\u793e\u4f1a\u3002

\u53e6\u4e00\u65b9\u9762\uff0c\u4eba\u7c7b\u5bf9\u4e8e\u91cf\u5b50\u4fe1\u606f\u7684\u9a7e\u9a6d\u4e0e\u64cd\u63a7\u7a0b\u5ea6\u6807\u5fd7\u7740\u6211\u4eec\u7684\u6280\u672f\u6c34\u5e73\u3002\u6211\u4eec\u5e0c\u671b\u81ea\u5df1\u8bbe\u8ba1\u91cf\u5b50\u6750\u6599\u3001\u64cd\u63a7\u91cf\u5b50\u4fe1\u606f\u80fd\u591f\u50cf\u5efa\u9020\u8ba1\u7b97\u673a\u3001\u64cd\u63a7\u4f20\u7edf\u4fe1\u606f\u90a3\u6837\u968f\u5fc3\u81ea\u5982 \u3002\u5728\u4f20\u7edf\u8ba1\u7b97\u7684\u65f6\u4ee3\uff0c \u6211\u4eec\u5236\u9020\u4e86\u8ba1\u7b97\u673a\u5668\uff0c\u8fd9\u4e9b\u673a\u5668\u4ee5\u4e8c\u8fdb\u5236\u6570\u4f4d\u4e32\uff08bit string\uff09\u7684\u5f62\u5f0f\u5b58\u50a8\u4fe1\u606f\uff0c \u5e76\u4ee5\u6b64\u4e3a\u57fa\u7840\u8fdb\u884c\u5404\u79cd\u8fd0\u7b97\u6216\u4fe1\u606f\u4ea4\u4e92\uff1a\u7f16\u5199\u7a0b\u5e8f\u8fdb\u884c\u6570\u503c\u6a21\u62df\u3001\u7f51\u4e0a\u8d2d\u7269\u7b49\u7b49\u3002\u7ecf\u5178\u4fe1\u606f\u65f6\u4ee3\u7684\u5230\u6765\u5bf9\u6211\u4eec\u7684\u751f\u6d3b\u572821\u4e16\u7eaa\u4ea7\u751f\u4e86\u91cd\u5927\u7684\u5f71\u54cd\u3002\u5047\u5982\u6709\u671d\u4e00\u65e5\u6211\u4eec\u771f\u7684\u642d\u5efa\u51fa\u4e00\u53f0\u91cf\u5b50\u673a\u5668\uff08\u6bd4\u5982\u91cf\u5b50\u8ba1\u7b97\u673a\uff0c\u6216\u8005\u91cf\u5b50\u6a21\u62df\u5668\uff09\uff0c \u8fd9\u53f0\u91cf\u5b50\u673a\u5668\u5c06\u4f1a\u4ee5\u91cf\u5b50\u6570\u4f4d\u4e32\uff08qbit string\uff09\u505a\u4e3a\u57fa\u7840\u3002\u5230\u90a3\u65f6\u6211\u4eec\u53ef\u80fd\u5c31\u9700\u8981\u7528\u91cf\u5b50\u6001\u5c42\u6790\u6210\u50cf\u6280\u672f\u6765\u5b9e\u73b0\u5bf9\u8fd9\u4e9b\u91cf\u5b50\u4fe1\u606f\u7684\u8bfb\u53d6\u4e86\uff0c \u90a3\u5c06\u4f1a\u662f\u4e00\u4e2a\u5168\u65b0\u7684\u91cf\u5b50\u4fe1\u606f\u4eba\u7c7b\u65f6\u4ee3\u3002 <\/p>\n


4. \u91cf\u5b50\u6001\u5c42\u6790\u6210\u50cf\u6280\u672f\u6709\u591a\u56f0\u96be<\/p>\n

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\u4f46\u662f\u771f\u7684\u5c31\u6beb\u65e0\u529e\u6cd5\u4e48\uff1f\u5982\u679c\u6211\u4eec\u7684\u786e\u662f\u5bf9\u8fd9\u4e2a\u91cf\u5b50\u7cfb\u7edf\u4e00\u65e0\u6240\u77e5\uff0c \u800c\u53c8\u60f3\u4e86\u89e3\u5b83\u7684\u6240\u6709\u7279\u6027\uff0c \u6211\u4eec\u771f\u7684\u6beb\u65e0\u529e\u6cd5\u3002\u8fd8\u597d\uff0c \u5bf9\u4e8e\u67d0\u4e9b\u60c5\u5f62\uff0c\u6211\u4eec\u8fd8\u6709\u5546\u91cf\u7684\u4f59\u5730\u3002 1. \u65b9\u6848\u4e00\uff1a\u5047\u5982\u6211\u4eec\u5bf9\u8fd9\u4e2a\u91cf\u5b50\u7cfb\u7edf\u6709\u4e00\u4e9b\u4e86\u89e3\uff0c\u6211\u4eec\u53ef\u4ee5\u57fa\u4e8e\u8fd9\u4e9b\u4fe1\u606f\u505a\u51fa\u67d0\u4e9b\u7b26\u5408\u5b9e\u9645\u60c5\u5f62\u7684\u5047\u8bbe\uff0c \u57fa\u4e8e\u8fd9\u4e9b\u5047\u8bbe\u8fdb\u884c\u5c42\u6790\u6210\u50cf\u5b9e\u9a8c\uff0c \u8fd9\u65f6\u6240\u9700\u5b9e\u9a8c\u6570\u91cf\u5c31\u4e0d\u518d\u662f\u6307\u6570\u91cf\u7ea7\u90a3\u4e48\u6050\u6016\u4e86\u3002\u77e9\u9635\u76f4\u57fa\u6001\u6001\u5c42\u6790\u6210\u50cf\u6280\u672f\uff08 matrix product state tomography\uff09\u3001\u7ea6\u5316\u5bc6\u5ea6\u77e9\u9635\u5c42\u6790\u6210\u50cf\u6280\u672f\uff08reduced density matrix tomography\uff09 \u8fd8\u6709\u4e00\u4e9b\u65b0\u5174\u7684\u673a\u5668\u5b66\u4e60\u5c42\u6790\u6210\u50cf\u672f\u90fd\u662f\u9075\u5faa\u8fd9\u4e00\u601d\u8def\u7684\u5b9e\u9645\u5c42\u6790\u6210\u50cf\u6280\u672f\u3002\uff08\u5982\u679c\u6709\u4eba\u60f3\u4e86\u89e3\u7528\u4fe1\u606f\u5b8c\u5907\u7684POVM\u6d4b\u91cf\u5b9e\u73b0\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u5c42\u6790\u6210\u50cf\u672f\uff0c \u53ef\u4ee5\u53c2\u8003\u6211\u7684\u516c\u5f00\u7a0b\u5e8f\uff08repo\uff1ahttps:\/\/github.com\/hongyehu\/Machine_Learning_Quantum_State_Tomography\uff09\uff0c\u90a3\u91cc\u6709\u6211\u7528pytorch\u8bed\u8a00\u7f16\u5199\u7684\u4e00\u4e9b\u76f8\u5173\u7a0b\u5e8f\u6a21\u62df\u548c\u5b9e\u73b0\u3002\uff09 
\u7b2c\u4e00\u79cd\u65b9\u6848\u5f88\u4f18\u79c0\u3002\u4f46\u662f\u4e0d\u53ef\u907f\u514d\u53ef\u80fd\u4f1a\u5e26\u6765\u4e00\u4e9b\u5c0f\u5c0f\u7684\u504f\u5dee\uff0c \u56e0\u4e3a\u5047\u8bbe\u5e76\u4e0d\u4e00\u5b9a\u603b\u662f\u51c6\u786e\u65e0\u8bef\u7684\u3002\u6700\u8fd1\u51fa\u73b0\u4e86\u53e6\u4e00\u79cd\u4f18\u79c0\u7684\u5c42\u6790\u6210\u50cf\u65b9\u6848\u3002\u6211\u4eec\u79f0\u4e4b\u4e3a\u9634\u5f71\u5c42\u6790\u6210\u50cf\uff08shadow tomography\uff09\u3002\u8fd9\u4e00\u6210\u50cf\u65b9\u6848\u662f\u6211\u4eec\u8fd9\u7bc7\u7814\u7a76\u8bba\u6587\u7684\u4e3b\u8981\u5173\u6ce8\u70b9\u3002\u6211\u4eec\u5c06\u4f1a\u5728\u4e0b\u9762\u7684\u7ae0\u8282\u4e2d\u4ecb\u7ecd\u8fd9\u79cd\u65b9\u6848\u3002
2. \u65b9\u6848\u4e8c\uff1a\u9634\u5f71\u5c42\u6790\u6210\u50cf\u3002\u5728\u8bb8\u591a\u4efb\u52a1\u4e2d\uff0c \u6211\u4eec\u4e4b\u6240\u4ee5\u8fd0\u7528\u5c42\u6790\u6210\u50cf\u6280\u672f\u662f\u56e0\u4e3a\u6211\u4eec\u60f3\u8981\u9884\u6d4b\u91cf\u5b50\u7cfb\u7edf\u4e4b\u540e\u7684\u67d0\u4e9b\u884c\u4e3a\u6216\u7279\u6027\u3002\u4e3a\u4e86\u5b9e\u73b0\u51c6\u786e\u9884\u6d4b\u8fd9\u4e9b\u7cfb\u7edf\u884c\u4e3a\u7684\u76ee\u7684\uff0c \u6709\u65f6\u5019\u6211\u4eec\u4e0d\u5fc5\u5b8c\u5168\u4e86\u89e3\u8fd9\u4e2a\u91cf\u5b50\u7cfb\u7edf\u7684\u5168\u90e8\u7279\u5f81\u3002
\u63a5\u4e0b\u6765\uff0c \u6211\u4eec\u5c06\u5411\u5927\u5bb6\u5c55\u793a\u4f20\u7edf\u9634\u5f71\u5c42\u6790\u6210\u50cf\u7684\u57fa\u672c\u601d\u60f3\uff0c\u5e76\u5bf9\u6211\u4eec\u5728\u201c\u54c8\u5bc6\u987f\u91cf\u9a71\u4f7f\u7684\u9634\u5f71\u5c42\u6790\u6210\u50cf\u201d\u300aHamiltonian-driven shadow tomography\u300b[3]\u4e2d\u7684\u7ed3\u679c\u8fdb\u884c\u4e00\u4e9b\u4ecb\u7ecd\u3002<\/p>\n

5. \u91cf\u5b50\u6001\u9634\u5f71\u5c42\u6790\u6210\u50cf<\/p>\n


\u4e3a\u4e86\u7406\u89e3\u91cf\u5b50\u6001\u9634\u5f71\u5c42\u6790\u6210\u50cf\u7684\u6982\u5ff5\uff0c \u5148\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u7ecf\u5178\u7cfb\u7edf\u4e2d\u7684\u4f8b\u5b50\u3002\u5047\u5982\u5728\u4e00\u4e2a\u623f\u95f4\u91cc\u5b58\u5728\u67d0\u4e2a\u7269\u4f53\u3002\u6211\u4eec\u60f3\u8981\u77e5\u9053\u8fd9\u4e2a\u7269\u4f53\u7684\u5f62\u72b6\uff0c \u4f46\u6211\u4eec\u6ca1\u6709\u529e\u6cd5\u89e6\u78b0\u5b83\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6295\u5c04\u5149\u7ebf\u7684\u5f62\u5f0f\u89c2\u5bdf\u8fd9\u4e2a\u7269\u4f53\u7684\u9634\u5f71\u3002\u4e3a\u4e86\u5927\u81f4\u4f30\u6d4b\u7269\u4f53\u7684\u5f62\u72b6\uff0c \u4e00\u79cd\u6709\u6548\u7684\u65b9\u5f0f\u5c31\u662f\u4ece\u4e0d\u540c\u7684\u89d2\u5ea6\u8fdb\u884c\u5149\u7ebf\u6295\u5c04\uff0c \u5e76\u6536\u96c6\u5404\u4e2a\u89d2\u5ea6\u4e0b\u7684\u9634\u5f71\u5f62\u72b6\u3002\u901a\u8fc7\u8fd9\u4e00\u7cfb\u5217\u6295\u5f71\uff0c \u6211\u4eec\u53ef\u4ee5\u5927\u81f4\u91cd\u6784\u51fa\u8fd9\u4e2a\u7269\u4f53\u7684\u5f62\u72b6\u3002\u4e0d\u5f97\u4e0d\u63d0\u53ca\u7684\u4e00\u70b9\u662f\uff0c \u6700\u9ad8\u6548\u51c6\u786e\u7684\u6295\u5f71\u65b9\u5f0f\u7adf\u7136\u662f\u9009\u53d6\u4e00\u7ec4\u968f\u673a\u7684\u6295\u5f71\u65b9\u5411\uff01

\u91cf\u5b50\u7cfb\u7edf\u7684\u9634\u5f71\u5c42\u6790\u6210\u50cf[1,2]\u6cbf\u7528\u76f8\u540c\u7684\u601d\u8def\u3002\u53ea\u4e0d\u8fc7\u8fd9\u56de\u6211\u4eec\u8981\u7814\u7a76\u7684\u5bf9\u8c61\u7531\u7ecf\u5178\u7269\u4f53\u6362\u6210\u4e86\u6570\u5b66\u4e0a\u7531\u5bc6\u5ea6\u77e9\u9635\u8868\u793a\u7684\u91cf\u5b50\u7269\u4f53\u3002\u4e3a\u4e86\u83b7\u5f97\u5bf9\u91cf\u5b50\u6001\u7684\u6709\u6548\u4f30\u8ba1,  \u5728\u5b9e\u9a8c\u4e2d\u6211\u4eec\u968f\u673a\u9009\u62e9\u6295\u5f71\u7684\u89d2\u5ea6\u8fdb\u884c\u6d4b\u91cf\u3002\u6211\u4eec\u6536\u96c6\u8fd9\u4e9b\u91cf\u5b50\u6001\u7684\u7ecf\u5178\u9634\u5f71\uff0c \u5e76\u7528\u8ba1\u7b97\u673a\u5bf9\u8fd9\u4e9b\u9634\u5f71\u4fe1\u606f\u8fdb\u884c\u5206\u6790\u4e0e\u5904\u7406\u3002\uff08\u4e0a\u56fe\u5c31\u662f\u4e00\u4e9b\u91cf\u5b50\u6001\u7ecf\u5178\u9634\u5f71\u7684\u793a\u4f8b\uff09
 \u4e00\u65e6\u6211\u4eec\u5f97\u5230\u8fd9\u4e9b\u9634\u5f71\u4fe1\u606f\uff0c \u6211\u4eec\u53ef\u4ee5\u5bf9\u8fd9\u4e9b\u9634\u5f71\u8fdb\u884c\u4e00\u4e9b\u7279\u6b8a\u7684\u7ebf\u6027\u7ec4\u5408\u4ece\u800c\u5f97\u5230\u5bf9\u5e94\u91cf\u5b50\u6001\u7684\u4fe1\u606f\u3002\u5982\u5728\u56fe\u4e2d\u6240\u5c55\u793a\u7684\uff0c \u901a\u8fc7\u5904\u7406\u4e00\u7ec4\u9634\u5f71\u4fe1\u606f\uff0c\u6211\u4eec\u91cd\u6784\u51fa\u91cf\u5b50\u7cfb\u7edf\u7684\u732b\u6001\/GHZ\u6001\u3002 \u7814\u7a76\u8005\u4eec\u4e4b\u6240\u4ee5\u559c\u6b22\u9634\u5f71\u5c42\u6790\u6210\u50cf\u7684\u4e00\u4e2a\u539f\u56e0\u662f\uff0c \u8fd9\u79cd\u5c42\u6790\u6210\u50cf\u65b9\u6848\u662f\u80fd\u591f\u505a\u5230\u6700\u9ad8\u6548\u7684\u5c42\u6790\u6210\u50cf\u65b9\u6848\u4e4b\u4e00\uff08maximal efficiency bound\uff09[2]\u3002\u5b9e\u9645\u4e0a\uff0c \u5982\u679c\u6211\u4eec\u6240\u5173\u5fc3\u7684\u7269\u7406\u91cf\u662f\u91cf\u5b50\u4fdd\u771f\u5ea6\uff08quantum fidelity\uff09\u8fd9\u6837\u7684\u5355\u79e9\u91cf\uff08rank-1 observable\uff09\uff0c \u6211\u4eec\u53ea\u9700\u8981\u8fdb\u884c\u56fa\u5b9a\u6570\u91cf\u7684\u9634\u5f71\u5c42\u6790\u6210\u50cf\u5b9e\u9a8c\u5c31\u53ef\u4ee5\u83b7\u5f97\u7279\u5b9a\u7684\u7cbe\u51c6\u5ea6\uff0c \u65e0\u8bba\u7cfb\u7edf\u5c3a\u5bf8\u6709\u591a\u5927\uff01\u8fd9\u771f\u662f\u592a\u795e\u5947\u4e86\uff01 <\/p>\n


6. \u54c8\u5bc6\u987f\u91cf\u9a71\u52a8\u7684\u91cf\u5b50\u6001\u9634\u5f71\u5c42\u6790\u6210\u50cf<\/p>\n

\u5728\u524d\u9762\u7684\u90e8\u5206\uff0c \u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u5230\uff0c \u9634\u5f71\u5c42\u6790\u6210\u50cf\u5229\u7528\u968f\u673a\u6295\u5f71\u6d4b\u91cf\u7684\u65b9\u5f0f\u6765\u6536\u96c6\u91cf\u5b50\u6001\u7684\u7ecf\u5178\u9634\u5f71\u3002\u968f\u673a\u7684\u6295\u5f71\u65b9\u5411\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u8d77\u5230\u4e86\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002\u56e0\u4e3a\u5b83\u4ee5\u4e00\u79cd\u65e0\u504f\u7684\u65b9\u5f0f\u6293\u53d6\u51fa\u6700\u91cd\u8981\u7684\u4fe1\u606f\u3002\u5728\u5b9e\u9a8c\u4e2d\uff0c \u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u901a\u8fc7\u5168\u5c40\u968f\u673aClifford \u95e8\uff08global random Clifford gates\uff09\u6765\u6539\u53d8\u91cf\u5b50\u6001\u5e76\u5728\u8ba1\u7b97\u57fa\u5e95\uff08computional basis\uff09\u4e0a\u8fdb\u884c\u6d4b\u91cf\u3002\u5168\u5c40\u968f\u673aClifford\u95e8\u80fd\u591f\u4ee5\u6700\u9ad8\u6548\u7684\u65b9\u5f0f\u6270\u4e71\u4fe1\u606f\u4ee5\u4fbf\u4e8e\u8ba1\u7b97\u57fa\u5e95\u6d4b\u91cf\u80fd\u591f\u6293\u53d6\u5230\u6240\u6709\u4fe1\u606f\u3002\u867d\u7136\u8fd9\u4e2a\u65b9\u6848\u5728\u5b9e\u9645\u5b9e\u9a8c\u4e2d\u5b9e\u73b0\u8d77\u6765\u6709\u4e00\u70b9\u56f0\u96be\u3002
 \u6211\u4eec\u5728\u8bba\u6587\u4e2d\u63d0\u4f9b\u4e86\u601d\u8003\u8fd9\u4e2a\u95ee\u9898\u7684\u53e6\u5916\u4e00\u79cd\u65b9\u6848\u3002\u5982\u56fe\u6240\u793a\uff0c \u6211\u4eec\u5728\u8fd9\u4e00\u65b9\u6848\u4e2d\u5229\u7528\u4e00\u822c\u7684\u5177\u6709\u6df7\u6c8c\u6027\u8d28\u7684\u54c8\u5bc6\u987f\u91cf\uff08\u54c8\u5bc6\u987f\u91cf\uff1a\u51b3\u5b9a\u7269\u7406\u4f53\u7cfb\u5982\u4f55\u6f14\u5316\u7684\u4e00\u79cd\u6570\u5b66\u63cf\u8ff0\uff09\u6765\u5bf9\u7cfb\u7edf\u8fdb\u884c\u6f14\u5316\uff0c \u8fdb\u800c\u5728\u8ba1\u7b97\u57fa\u5e95\u4e2d\u8fdb\u884c\u6295\u5f71\u6d4b\u91cf\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u8fd9\u4e9b\u6295\u5f71\u89d2\u5ea6\u7531\u968f\u673a\u6f14\u5316\u6240\u51b3\u5b9a\u3002\u5728\u6211\u4eec\u7684\u8fd9\u4e2a\u65b9\u6848\u4e2d\uff0c \u6211\u4eec\u8ba4\u4e3a\u5728\u8fd1\u671f\u5177\u6709\u566a\u58f0\u7684\u4e2d\u578b\u89c4\u6a21\u91cf\u5b50\u673a\u5668\uff08noisy intermediate-scale quantum\uff09\u4e2d\u54c8\u5bc6\u987f\u91cf\u9a71\u52a8\u7684\u91cf\u5b50\u6001\u9634\u5f71\u5c42\u6790\u6210\u50cf\u53ef\u80fd\u4f1a\u662f\u4e00\u79cd\u66f4\u4e3a\u53ef\u884c\u7684\u65b9\u6848\u3002\u6b64\u5916\u8fd9\u4e2a\u65b9\u6848\u8fd8\u80fd\u4e3a\u6211\u4eec\u63d0\u4f9b\u7cfb\u7edf\u7684\u4fe1\u606f\u52a8\u529b\u5b66\uff0c\u5e76\u5141\u8bb8\u6211\u4eec\u5728\u5c42\u6790\u6210\u50cf\u4e2d\u5bf9\u91cf\u5b50\u4fe1\u606f\u5982\u4f55\u6f14\u5316\u548c\u8fdb\u884c\u4fe1\u606f\u6df7\u6742\uff08scrambling of quantum informations\uff09\u8fdb\u884c\u4e00\u4e9b\u63a2\u7a76\u3002 \u6d4b\u91cf\u6548\u7387\u4e0e\u4fe1\u606f\u8109\u52a8\uff08scrambling beat\uff09
\u5728\u6211\u4eec\u7684\u8bba\u6587\u4e2d[3]\uff0c\u6211\u4eec\u4ece\u7406\u8bba\u4e0a\u8ba1\u7b97\u4e86\u57fa\u4e8e\u54c8\u5bc6\u987f\u91cf\u6f14\u5316\u7684\u91cf\u5b50\u6001\u9634\u5f71\u5c42\u6790\u6210\u50cf\u7684\u91cd\u6784\u901a\u9053\uff0c \u8fd9\u4e00\u901a\u9053\u80fd\u591f\u628a\u771f\u5b9e\u91cf\u5b50\u6001\u501f\u52a9\u7ecf\u5178\u9634\u5f71\u91cd\u65b0\u6784\u9020\u51fa\u6765\u3002\u6211\u4eec\u8fd8\u4ece\u7406\u8bba\u4e0a\u63a2\u7d22\u4e86\u6211\u4eec\u8fd9\u4e00\u65b9\u6848\u7684\u6548\u7387\u3002\u9996\u5148\uff0c\u5728\u4f53\u7cfb\u6f14\u5316\u65f6\u95f4\u5206\u522b\u8d8b\u4e8e\u96f6\u6216\u65e0\u7a77\u5927\u7684\u6781\u9650\u4e0b\uff0c\u6211\u4eec\u5f88\u5bb9\u6613\u7406\u89e3\u8fd9\u4e24\u4e2a\u6781\u9650\u3002
\u65f6\u95f4\u8d8b\u8fd1\u4e8e\u96f6\u7684\u6781\u9650
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\u5728\u8fd9\u4e00\u6781\u9650\u4e0b\uff0c \u6df7\u6c8c\u54c8\u5bc6\u987f\u91cf\u4f7f\u91cf\u5b50\u6001\u5b8c\u5168\u6df7\u4e71\uff0c \u8fd9\u65f6\u6211\u4eec\u7684\u65b9\u6848\u5c31\u4e0e\u6700\u4f18\u5316\u6548\u7387\u7684\u968f\u673aClifford\u9634\u5f71\u5c42\u6790\u6210\u50cf\u65b9\u6848[2]\u7b49\u4ef7\u3002 \u8fc7\u6e21\u65f6\u95f4\u7a97\u53e3\u548c\u4fe1\u606f\u8109\u52a8

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\u6709\u8da3\u7684\u662f\uff0c \u5728Fd(t)\u9971\u548c\u4e8e\u5b83\u7684\u957f\u65f6\u6781\u9650\u4e4b\u524d\uff0c Fd(t)\u5468\u671f\u6027\u7684\u51fa\u73b0\u6781\u5927\u503c\u5c16\u5cf0\uff08\u5982\u4e0a\u65b9\u53f3\u56fe\u6240\u793a\uff09\u3002\u5728\u8fd9\u4e9b\u5c16\u5cf0\u5904\uff0c \u5bf9\u89d2\u4fe1\u606f\u88ab\u6781\u5927\u7a0b\u5ea6\u7684\u6270\u4e71\uff0c\u7136\u540e\u53c8\u4f1a\u51fa\u73b0\u4fe1\u606f\u56de\u6eaf\u7684\u73b0\u8c61\uff0c \u56e0\u6b64\u6211\u4eec\u5c06\u8fd9\u4e00\u73b0\u8c61\u547d\u540d\u4e3a\u4fe1\u606f\u8109\u52a8\uff08scrambling beat\uff09\u3002\u5728\u76f8\u5e72\u54c8\u5bc6\u987f\u91cf\u6f14\u5316\u4e0b\u7684\u6709\u9650\u5c3a\u5bf8\u7cfb\u7edf\u4e2d\uff0c \u53d7\u6270\u52a8\u7684\u4fe1\u606f\u4f1a\u51fa\u73b0\u5468\u671f\u6027\u7684\u53cd\u5f39\uff0c \u8fdb\u800c\u5bfc\u81f4Fd(t)\u7684\u8109\u52a8\u884c\u4e3a\u3002\u8fd9\u5f88\u7c7b\u4f3c\u4e8e\u5316\u5b66\u4e2d\u7684\u201c\u65f6\u949f\u6548\u5e94\u201d\uff08clock phenomenon\uff0c \u5bf9\u8fd9\u4e2a\u73b0\u8c61\u611f\u5174\u8da3\u7684\u53ef\u4ee5\u89c2\u770b\u8fd9\u4e2a\u89c6\u9891\uff1ahttps:\/\/www.youtube.com\/watch?v=WpBwlSn1XPQ\uff09\u3002\u4e0d\u8fc7\uff0c \u8fd9\u79cd\u4fe1\u606f\u8109\u52a8\u7684\u6301\u7eed\u65f6\u95f4\u662f\u4f9d\u8d56\u4e8e\u7cfb\u7edf\u5c3a\u5bf8\u7684\u3002\u8868\u5f81\u4fe1\u606f\u8109\u52a8\u65f6\u957f\u7684\u7279\u5f81\u65f6\u95f4\u5c3a\u5ea6\u5728 td~ D1\/6=2N\/6\u8fd9\u4e2a\u91cf\u7ea7\u3002\u5728\u8fd9\u4e2a\u65f6\u95f4\u5c3a\u5ea6\u4e4b\u524d\uff0c\u6211\u4eec\u53ef\u4ee5\u6293\u4f4f\u4fe1\u606f\u8109\u52a8\u5c16\u5cf0\u4e0e\u5c16\u5cf0\u4e4b\u95f4\u5b58\u5728\u65f6\u95f4\u7a97\u53e3\u671f\uff08\u5982\u4e0a\u56fe\u4e2d\u9ec4\u8272\u9634\u5f71\u6240\u793a\uff09\u5bf9\u4e0e\u5bf9\u89d2\u5143\u7d20\u7684\u89c2\u6d4b\u91cf\u8fdb\u884c\u6709\u6548\u7684\u9884\u6d4b\uff0c\u540c\u65f6\u5bf9\u975e\u5bf9\u89d2\u5143\u7d20\u7684\u89c2\u6d4b\u91cf\u4e5f\u8fbe\u5230\u6709\u6548\u7684\u9884\u6d4b\u3002 <\/p>\n

7. \u603b\u7ed3<\/p>\n

\u505a\u4e00\u4e2a\u7b80\u5355\u7684\u603b\u7ed3\uff0c \u6211\u4eec\u63d0\u51fa\u7528\u54c8\u5bc6\u987f\u91cf\u6240\u4ea7\u751f\u7684\u6f14\u5316\u6765\u5bf9\u91cf\u5b50\u4f53\u7cfb\u8fdb\u884c\u9634\u5f71\u5c42\u6790\u6210\u50cf\u3002\u6211\u4eec\u63a2\u7a76\u4e86\u54c8\u5bc6\u987f\u91cf\u9a71\u52a8\u7684\u9634\u5f71\u5c42\u6790\u6210\u50cf\u65b9\u6848\u7684\u6548\u7387\u5e76\u8868\u660e\u8fd9\u4e00\u65b9\u6848\u4f18\u4e8e\u4f20\u7edf\u7684\u9634\u5f71\u5c42\u6790\u6210\u50cf\u3002\u5c3d\u7ba1\u6211\u4eec\u7684\u5206\u6790\u76ee\u524d\u4ec5\u57fa\u4e8eGUE\u968f\u673a\u54c8\u5bc6\u987f\u91cf\uff0c \u6211\u4eec\u671f\u671b\u8fd9\u4e2a\u7ed3\u679c\u80fd\u591f\u88ab\u6269\u5c55\u5230\u5176\u4ed6\u7c7b\u578b\u7684\u91cf\u5b50\u6df7\u6c8c\u54c8\u5bc6\u987f\u91cf\u4e2d\u3002 \u5176\u4ed6\u8d44\u6e90\u5982\u679c\u4f60\u5bf9\u91cf\u5b50\u6001\u7684\u7ecf\u5178\u9634\u5f71\u5c42\u6790\u6210\u50cf\u6280\u672f\u611f\u5174\u8da3\uff0c\u6211\u63a8\u8350\u9ec4\u4fe1\u5143\u5728IQIM\u548cQIP2021\u7684\u62a5\u544a\uff1a\u94fe\u63a51\uff1ahttps:\/\/www.youtube.com\/watch?v=xRHXsPp1O0I&feature=youtu.be\u94fe\u63a52\uff1ahttps:\/\/www.youtube.com\/watch?v=d1_hBEJQUSA&feature=share \u81f4\u8c22\u672c\u6587\u4f5c\u8005\u611f\u8c22\u4e0e\u52a0\u5dde\u7406\u5de5\u7684\u9ec4\u4fe1\u5143\u548c\u5218\u4fca\u5b87\u5177\u6709\u542f\u53d1\u6027\u7684\u8ba8\u8bba*\u672c\u6587\u4f5c\u8005\u611f\u8c22\u5317\u4eac\u5927\u5b66\u7269\u7406\u5b66\u9662\u5434\u98d9\u6559\u6388\u7684\u5efa\u8bae\u4e0e\u8ba8\u8bba \u53c2\u8003\u6587\u732e[1]Scott Aaronson. arXiv:1711.01053. Shadow tomography of quantum states.[2]Hsin-Yuan Huang, Richard Kueng & John Preskill. Nature Physics volume 16, pages1050\u20131057(2020). Predicting many properties of a quantum system from very few measurements.[3]Hong-Ye Hu, Yi-Zhuang You. arXiv:2102.10132. Hamiltonian-driven shadow tomography of quantum states.<\/p>\n

\u539f\u6587\u94fe\u63a5\uff1ahttps:\/\/hongyehu.github.io\/Hamiltonian-driven-shadow-tomography-page\/<\/p>\n

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<\/a>
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