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\u5728\u901a\u5e38\u7684\u7ecf\u5178\u7edf\u8ba1\u6a21\u578b\u4e2d\uff0c(1)\u5f0f\u4e2d\u7684\u5f20\u91cf T  \u662f\u5177\u6709\u5e73\u79fb\u4e0d\u53d8\u6027\u7684\uff0c\u5373\u5b58\u5728\u4e00\u4e2a\u6709\u9650\u7684\u5143\u80de\uff0c\u5728\u5143\u80de\u5185\u90e8T\u662f\u4f9d\u8d56\u4e8e\u683c\u70b9\u7684\uff0c\u6574\u4e2a\u7cfb\u7edf\u662f\u7531\u8be5\u5143\u80de\u8fdb\u884c\u5468\u671f\u6027\u5e73\u79fb\u5f97\u5230\uff0c\u56e0\u6b64\u5f20\u91cf\u7f51\u7edc\u53ef\u4ee5\u76f4\u63a5\u5904\u7406\u70ed\u529b\u5b66\u6781\u9650\u3002\u4f46\u5bf9\u4e8e\u6ca1\u6709\u5e73\u79fb\u4e0d\u53d8\u6027\u7684\u7cfb\u7edf\uff0c\u5219\u9700\u8981\u727a\u7272\u6389\u5e73\u79fb\u4e0d\u53d8\u6027\uff0c\u5904\u7406\u6709\u9650\u6676\u683c\u7cfb\u7edf\uff0c\u5f20\u91cf\u7f51\u7edc\u5728\u8fd9\u65b9\u9762\u4e5f\u6709\u6210\u529f\u7684\u5e94\u7528\uff0c\u5982Edward\u2014Anderson \u6a21\u578b\u548c Biroli\u2014Mezard \u6a21\u578b\u7b49\u7ecf\u5178\u81ea\u65cb\u73bb\u7483\u7cfb\u7edf[15]\u3002
\u5f20\u91cf\u7f51\u7edc\u7684\u6c42\u548c\u662f\u5f20\u91cf\u91cd\u6b63\u5316\u7fa4\u7684\u6838\u5fc3\u5185\u5bb9\u4e4b\u4e00\uff0c\u4e0d\u4ec5\u7ecf\u5178\u6a21\u578b\u9700\u8981\u6c42\u548c\u7f51\u7edc\uff0c\u91cf\u5b50\u683c\u70b9\u6a21\u578b\u7684\u7269\u7406\u91cf\u548c\u6ce2\u51fd\u6570\u7684\u7cbe\u786e\u6c42\u89e3\uff0c\u4e5f\u90fd\u9700\u8981\u6c42\u548c\u7f51\u7edc\u3002\u7269\u7406\u5b66\u5bb6\u57fa\u4e8e\u91cd\u6b63\u5316\u7fa4\u7684\u601d\u60f3\u53d1\u5c55\u4e86\u5f88\u591a\u79cd\u65b9\u6cd5\u8fdb\u884c\u7f51\u7edc\u6c42\u548c\uff0c\u611f\u5174\u8da3\u7684\u8bfb\u8005\u53ef\u4ee5\u53c2\u8003\u6587\u732e[1\uff0c3\uff0c16]\uff0c\u5728\u8fd9\u91cc\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n


2.2 \u5f20\u91cf\u7f51\u7edc\u5728\u91cf\u5b50\u683c\u70b9\u6a21\u578b\u4e2d\u7684\u5e94\u7528
(2)\u5f0f\u4ee3\u8868\u7684\u91cf\u5b50\u6001\uff0c\u88ab\u79f0\u4e3a\u6295\u5f71\u7ea0\u7f20\u5bf9\u6001(projected entangled pair state\uff0cPEPS)[17]\uff0c\u5b83\u6ee1\u8db3\u7ea0\u7f20\u71b5\u7684\u9762\u79ef\u5b9a\u5f8b[18]\uff0c\u662f\u4e00\u7c7b\u6700\u65e9\u88ab\u5e7f\u6cdb\u5e94\u7528\u7684\u5f20\u91cf\u7f51\u7edc\u6001\u3002\u4e0d\u540c\u5f20\u91cf\u7f51\u7edc\u5bf9\u91cf\u5b50\u6001\u7684\u8868\u8fbe\u80fd\u529b\uff0c\u51b3\u5b9a\u4e8e\u5176\u5bf9\u7ea0\u7f20\u71b5\u7684\u523b\u753b\u80fd\u529b\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u77e9\u9635\u4e58\u79ef\u6001\u548c\u6811\u5f62\u5f20\u91cf\u7f51\u7edc\u6001\u6ee1\u8db3\u4e00\u7ef4\u9762\u79ef\u5f8b\uff0cPEPS\u548c\u5b83\u7684\u6295\u5f71\u7ea0\u7f20\u5355\u5f62\u6001\u63a8\u5e7f[19]\uff0c\u4ee5\u53ca\u4e8c\u7ef4\u591a\u5c3a\u5ea6\u7ea0\u7f20\u91cd\u6b63\u5316\u62df\u8bbe(multi-scale entanglement renormalization ansatz\uff0cMERA)[20]\uff0c\u6ee1\u8db3\u4e8c\u7ef4\u9762\u79ef\u5f8b\u3002\u8fd8\u6709\u4e00\u4e9b\u7279\u6b8a\u7684\u5f20\u91cf\u7f51\u7edc\u6001\uff0c\u53ef\u4ee5\u523b\u753b\u8d85\u8d8a\u5bf9\u5e94\u7ef4\u5ea6\u4e0b\u9762\u79ef\u5f8b\u7684\u7ea0\u7f20\u71b5\u884c\u4e3a\uff0c\u5982\u4e00\u7ef4MERA\u3001\u4e8c\u7ef4\u5e26\u6709\u5206\u652f\u7ed3\u6784\u7684MERA[21]\uff0c\u5177\u6709\u957f\u7a0b\u5173\u8054\u7684\u5173\u8054\u4e58\u79ef\u6001[22]\u7b49\u3002
\u4f7f\u7528\u5f20\u91cf\u7f51\u7edc\u6001\u6765\u7814\u7a76\u91cf\u5b50\u6a21\u578b\uff0c\u5c31\u9700\u8981\u9009\u53d6\u5177\u6709\u5408\u9002\u8868\u8fbe\u80fd\u529b\u7684\u6ce2\u51fd\u6570\u62df\u8bbe\uff0c\u6bd4\u5982\u5177\u6709\u5c40\u57df\u76f8\u4e92\u4f5c\u7528\u548c\u6709\u9650\u57fa\u6001\u7b80\u5e76\u5ea6\u7684\u4e8c\u7ef4\u91cf\u5b50\u81ea\u65cb\u6a21\u578b\uff0c\u5bf9\u4e8e\u6709\u80fd\u9699\u7cfb\u7edf\uff0c\u4eba\u4eec\u671f\u671b\u5176\u57fa\u6001\u662f\u6ee1\u8db3\u9762\u79ef\u5f8b\u7684\uff0c\u56e0\u6b64\u5c31\u53ef\u4ee5\u9009\u62e9\u6ee1\u8db3\u4e8c\u7ef4\u9762\u79ef\u5f8b\u7684\u6ce2\u51fd\u6570\u62df\u8bbe\uff1b\u5bf9\u4e8e\u65e0\u80fd\u9699\u7cfb\u7edf\uff0c\u5176\u57fa\u6001\u4f1a\u8d85\u8d8a\u9762\u79ef\u5f8b\uff0c\u53ef\u6839\u636e\u8ba1\u7b97\u8d44\u6e90\u9009\u53d6\u6ee1\u8db3\u6216\u8005\u8d85\u8d8a\u4e8c\u7ef4\u9762\u79ef\u5f8b\u7684\u62df\u8bbe\u3002\u9664\u4e86\u5c11\u6570\u7cfb\u7edf\u6bd4\u8f83\u6e05\u695a\u4ee5\u5916\uff0c\u5173\u4e8e\u7ea0\u7f20\u71b5\u7684\u4e00\u822c\u6027\u8ba8\u8bba\uff0c\u76ee\u524d\u8fd8\u662f\u4e00\u4e2a\u5f00\u653e\u6027\u8bfe\u9898\uff0c\u5177\u4f53\u53ef\u4ee5\u53c2\u8003\u6587\u732e[18]\u3002
\u5f20\u91cf\u7f51\u7edc\u6001\u6700\u91cd\u8981\u7684\u5e94\u7528\u573a\u666f\u4e4b\u4e00\uff0c\u662f\u8fd1\u4f3c\u4e00\u4e2a\u7ed9\u5b9a\u683c\u70b9\u6a21\u578b\u7684\u57fa\u6001\u6ce2\u51fd\u6570\u3002\u4e00\u822c\u5730\uff0c\u53ea\u8981\u76f8\u4e92\u4f5c\u7528\u662f\u5b9e\u7a7a\u95f4\u5c40\u57df\u7684\uff0c\u603b\u53ef\u4ee5\u4f7f\u7528\u5f20\u91cf\u7f51\u7edc\u6001\u6765\u903c\u8fd1\u4e00\u4e2a\u6709\u80fd\u9699\u7cfb\u7edf\u7684\u57fa\u6001\u3002\u901a\u8fc7\u865a\u65f6\u6f14\u5316\u548c\u80fd\u91cf\u4f18\u5316\uff0c\u5b83\u6700\u521d\u88ab\u5e94\u7528\u5728\u65e0\u963b\u632b\u81ea\u65cb\u7cfb\u7edf[23,24]\uff0c\u800c\u540e\u53c8\u88ab\u63a8\u5e7f\u81f3\u5f3a\u963b\u632b\u81ea\u65cb\u7cfb\u7edf[19,25,26]\u3002\u8fd9\u65b9\u9762\u6709\u4ef7\u503c\u7684\u5de5\u4f5c\u975e\u5e38\u591a\uff0c\u5728\u6b64\u4e0d\u80fd\u4f5c\u9010\u4e00\u8bf4\u660e\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u6709\u4e00\u4e2a\u4e0d\u540c\u4f46\u76f8\u5173\u7684\u7814\u7a76\u65b9\u5411\uff0c\u5373\u4e0d\u4ece\u5177\u4f53\u54c8\u5bc6\u987f\u91cf\u51fa\u53d1\uff0c\u800c\u662f\u7528\u5f20\u91cf\u7f51\u7edc\u6001\u6765\u6784\u9020\u7269\u7406\u4e0a\u611f\u5174\u8da3\u7684\u91cf\u5b50\u6001\uff0c\u5982\u5bf9\u79f0\u4fdd\u62a4\u6001\u548c\u62d3\u6251\u76f8\uff0c\u4ece\u800c\u7814\u7a76\u8fd9\u4e9b\u6001\u548c\u5bf9\u5e94\u54c8\u5bc6\u987f\u7cfb\u7edf\u7684\u65b0\u5947\u6027\u8d28\uff0c\u8fd9\u4e2a\u65b9\u5411\u4e0a\u6709\u5f88\u591a\u6709\u8da3\u7684\u5de5\u4f5c[27,28]\u3002\u5982\u679c\u5047\u8bbe\u7cfb\u7edf\u7684\u4f4e\u80fd\u6fc0\u53d1\u6001\u4e5f\u6ee1\u8db3\u9762\u79ef\u5f8b\uff0c\u5219\u8fd8\u53ef\u4ee5\u5728\u5f97\u5230\u57fa\u6001\u6ce2\u51fd\u6570\u4e4b\u540e\uff0c\u91c7\u7528\u5355\u6a21\u8fd1\u4f3c\u7684\u601d\u60f3\uff0c\u4f7f\u7528\u57fa\u6001\u7684\u5c40\u57df\u6270\u52a8\u6765\u6784\u9020\u57fa\u6001\u7684\u6b63\u4ea4\u7a7a\u95f4\uff0c\u5728\u8be5\u6b63\u4ea4\u7a7a\u95f4\u6c42\u89e3\u4f7f\u80fd\u91cf\u6781\u5c0f\u7684\u91cf\u5b50\u6001\uff0c\u4ece\u800c\u5f97\u5230\u8be5\u7cfb\u7edf\u7684\u4f4e\u80fd\u5355\u7c92\u5b50\u6fc0\u53d1\u6001[29]\u3002
\u5728\u5f20\u91cf\u7f51\u7edc\u6846\u67b6\u4e0b\uff0c\u53ef\u4ee5\u975e\u5e38\u76f4\u89c2\u5730\u7406\u89e3d\u7ef4\u91cf\u5b50\u6a21\u578b\u548cd+1\u7ef4\u7ecf\u5178\u6a21\u578b\u6c42\u89e3\u7684\u7b49\u4ef7\u6027\uff0c\u914d\u5206\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u6210\u4e3a d \u7ef4\u8f6c\u79fb\u77e9\u9635\u7684\u5e42\u6b21\u6c42\u8ff9\u3002\u56e0\u6b64\uff0c\u5982\u679c\u5c06\u865a\u65f6\u6f14\u5316\u65b9\u6cd5\u5728\u6709\u9650\u6e29\u5ea6\u622a\u6b62\uff0c\u5219\u53ef\u4ee5\u901a\u8fc7\u6c42\u548c\u4e00\u4e2a\u5355\u65b9\u5411\u6709\u9650\u7684\u5f20\u91cf\u7f51\u7edc\u6765\u7814\u7a76\u91cf\u5b50\u7cfb\u7edf\u7684\u70ed\u529b\u5b66\u6027\u8d28[30]\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u7531\u4e8e\u5177\u6709\u76f8\u5bf9\u4f4e\u7684\u590d\u6742\u5ea6\u548c\u76f8\u5bf9\u6210\u719f\u7684\u8ba1\u7b97\u624b\u6bb5\uff0c\u77e9\u9635\u4e58\u79ef\u6001\u548c\u6811\u5f62\u5f20\u91cf\u7f51\u7edc\u6001\uff0c\u8fd8\u88ab\u6210\u529f\u7528\u4e8e\u5176\u4ed6\u8f83\u4e3a\u68d8\u624b\u7684\u5e94\u7528\u573a\u666f\u4e2d\uff0c\u5982\u591a\u4f53\u5c40\u57df\u5316[31]\u3001\u90e8\u5206\u5b50(parton)\u8868\u793a[32]\u548c\u5f00\u653e\u7cfb\u7edf\u52a8\u529b\u5b66[33]\u7b49\u3002
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2.3 \u5f20\u91cf\u7f51\u7edc\u5728\u5176\u4ed6\u76f8\u5173\u9886\u57df\u7684\u5e94\u7528
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3.\u795e\u7ecf\u7f51\u7edc\u5728\u7269\u7406\u5b66\u4e2d\u7684\u5e94\u7528<\/p>\n

\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a(restricted boltzmann machine\uff0cRBM)[4]\uff0c\u662f\u88ab\u7269\u7406\u5b66\u5bb6\u7814\u7a76\u548c\u5e94\u7528\u6700\u591a\u7684\u795e\u7ecf\u7f51\u7edc\u4e4b\u4e00\u3002\u5982\u56fe3\u6240\u793a\uff0c\u5b83\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u53ea\u6709\u4e24\u5c42\u795e\u7ecf\u5143\u7684\u6d45\u5c42\u795e\u7ecf\u7f51\u7edc\uff0c\u5176\u4e2d\u4e00\u5c42\u662f\u8f93\u5165\u53d8\u91cf \u03bd\uff0c\u4e00\u5c42\u662f\u9700\u8981\u88ab\u6c42\u548c\u6389\u7684\u9690\u53d8\u91cf h \uff0c\u5176\u8f93\u51fa\u662f\u4e00\u4e2a\u5982\u4e0b\u7cbe\u5de7\u8bbe\u8ba1\u7684\u51fd\u6570\uff1a\u5176\u4e2da\uff0cb \u4ee3\u8868\u504f\u7f6e\u53c2\u6570\uff0cW \u662f\u6743\u91cd\u53c2\u6570\uff0c\u5b83\u4eec\u90fd\u9700\u8981\u901a\u8fc7\u7b97\u6cd5\u5b66\u4e60\u5f97\u5230\u3002P(\u03bd)\u5728\u5f62\u5f0f\u4e0a\u5f52\u4e00\u5316\u4e4b\u540e\uff0c\u53ef\u4ee5\u89c6\u4e3a\u4e00\u4e2a\u6982\u7387\u51fd\u6570\u3002\u901a\u8fc7\u8bad\u7ec3\uff0c\u8be5\u6a21\u578b\u53ef\u4ee5\u627e\u5230\u4e00\u7ec4\u6700\u4f18\u7684\u53c2\u6570\uff0c\u4f7f\u5f97\u751f\u6210\u7684\u6982\u7387\u51fd\u6570P(\u03bd)\u5c3d\u53ef\u80fd\u5730\u63a5\u8fd1\u771f\u5b9e\u6216\u8005\u671f\u671b\u7684\u6982\u7387\u5206\u5e03\u3002\u7531\u4e8e\u4e0e\u7edf\u8ba1\u7269\u7406\u5b66\u7406\u8bba\u7684\u6df1\u523b\u76f8\u4f3c\u6027\uff0cRBM\u5f88\u5feb\u88ab\u7269\u7406\u5b66\u5bb6\u6240\u7406\u89e3\uff0c\u7528\u4e8e\u8bf8\u5982\u8868\u5f81\u5e73\u8861\u6001\u7684\u7edf\u8ba1\u6a21\u578b[52]\uff0c\u91cf\u5b50\u591a\u4f53\u7cfb\u7edf\u7684\u57fa\u6001\u6ce2\u51fd\u6570[53]\uff0c\u6df7\u91cf\u5b50\u6001\u7684\u5bc6\u5ea6\u77e9\u9635\u63cf\u8ff0[54]\uff0c\u548c\u62d3\u6251\u91cf\u5b50\u6001[55]\u7b49\u7814\u7a76\u4e2d\u3002\u5b9e\u9645\u4e0a\uff0c\u4eba\u4eec\u53d1\u73b0\uff0c\u5728\u5927\u591a\u6570\u6761\u4ef6\u4e0b\uff0cRBM\u548c\u5f20\u91cf\u7f51\u7edc\u6001\u53ef\u4ee5\u76f8\u4e92\u8f6c\u5316[56]\uff0c\u800c\u4e14\u8ddf\u5173\u8054\u4e58\u79ef\u6001\u6ce2\u51fd\u6570\u5b58\u5728\u975e\u5e38\u5f3a\u7684\u8054\u7cfb[57]\uff0c\u8fd9\u8ddf\u6587\u732e[58]\u4e2d\u5b58\u5728\u957f\u7a0b\u8fde\u63a5\u7684RBM\u8868\u793a\u53ef\u4ee5\u523b\u753b\u4f53\u79ef\u7387\u7684\u7ea0\u7f20\u71b5\uff0c\u4ee5\u53ca\u6587\u732e[59]\u4e2dRBM\u53ef\u4ee5\u63a2\u6d4b\u5230\u8d1d\u5c14\u975e\u5c40\u57df\u6027\u7684\u7ed3\u8bba\uff0c\u662f\u76f8\u543b\u5408\u7684\u3002
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4.\u5f20\u91cf\u7f51\u7edc\u548c\u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u5408<\/p>\n

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