{"id":63255,"date":"2025-04-14T20:36:46","date_gmt":"2025-04-14T20:36:46","guid":{"rendered":""},"modified":"2025-04-14T20:36:46","modified_gmt":"2025-04-14T20:36:46","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nStabilizer bootstrapping: A recipe for efficient agnostic tomography and magic estimation<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nSitan Chen, Weiyuan Gong, Qi Ye, Zhihan Zhang<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n68<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nQuantum Physics,Computational Complexity,Data Structures and Algorithms,Machine Learning,\u0641\u06cc\u0632\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc , \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc , \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0648 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645 \u0647\u0627 , \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0645\u0627\u0634\u06cc\u0646<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 13 August, 2024; originally announced August 2024. , Comments: 68 pages<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 13 \u0627\u0648\u062a 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0648\u062a 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f. \u060c \u0646\u0638\u0631\u0627\u062a: 68 \u0635\u0641\u062d\u0647<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

We study the task of agnostic tomography: given copies of an unknown $n$-qubit state $\u03c1$ which has fidelity $\u03c4$ with some state in a given class $C$, find a state which has fidelity $\\ge \u03c4- \u03b5$ with $\u03c1$. We give a new framework, stabilizer bootstrapping, for designing computationally efficient protocols for this task, and use this to get new agnostic tomography protocols for the following classes: Stabilizer states: We give a protocol that runs in time $\\mathrm{poly}(n,1\/\u03b5)\\cdot (1\/\u03c4)^{O(\\log(1\/\u03c4))}$, answering an open question posed by Grewal, Iyer, Kretschmer, Liang [40] and Anshu and Arunachalam [6]. Previous protocols ran in time $\\mathrm{exp}(\u0398(n))$ or required $\u03c4>\\cos^2(\u03c0\/8)$. States with stabilizer dimension $n – t$: We give a protocol that runs in time $n^3\\cdot(2^t\/\u03c4)^{O(\\log(1\/\u03b5))}$, extending recent work on learning quantum states prepared by circuits with few non-Clifford gates, which only applied in the realizable setting where $\u03c4= 1$ [30, 37, 46, 61]. Discrete product states: If $C = K^{\\otimes n}$ for some $\u03bc$-separated discrete set $K$ of single-qubit states, we give a protocol that runs in time $(n\/\u03bc)^{O((1 + \\log (1\/\u03c4))\/\u03bc)}\/\u03b5^2$. This strictly generalizes a prior guarantee which applied to stabilizer product states [39]. For stabilizer product states, we give a further improved protocol that runs in time $(n^2\/\u03b5^2)\\cdot (1\/\u03c4)^{O(\\log(1\/\u03c4))}$. As a corollary, we give the first protocol for estimating stabilizer fidelity, a standard measure of magic for quantum states, to error $\u03b5$ in $n^3 \\mathrm{quasipoly}(1\/\u03b5)$ time.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0645\u0627 \u0648\u0638\u06cc\u0641\u0647 \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u0631\u0627 \u0645\u0637\u0627\u0644\u0639\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645: \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0646\u0633\u062e\u0647 \u0647\u0627\u06cc \u0646\u0627\u0634\u0646\u0627\u062e\u062a\u0647 $ n $ -qubit $ \u03c1 $ \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u0648\u0641\u0627\u062f\u0627\u0631\u06cc $ \u03c4 $ \u0628\u0627 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0627\u06cc\u0627\u0644\u062a \u0647\u0627 \u062f\u0631 \u06cc\u06a9 \u06a9\u0644\u0627\u0633 \u062e\u0627\u0635 $ c $ \u0627\u0633\u062a \u060c \u0648\u0636\u0639\u06cc\u062a\u06cc \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u0648\u0641\u0627\u062f\u0627\u0631\u06cc $ \\ ge \u03c4- \u0628\u0627\u0634\u062f\u03b5 $ \u0628\u0627 $ \u03c1 $.\u0645\u0627 \u0628\u0631\u0627\u06cc \u0637\u0631\u0627\u062d\u06cc \u067e\u0631\u0648\u062a\u06a9\u0644 \u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u060c \u06cc\u06a9 \u0686\u0627\u0631\u0686\u0648\u0628 \u062c\u062f\u06cc\u062f \u060c Bootstrapping \u062a\u062b\u0628\u06cc\u062a \u06a9\u0646\u0646\u062f\u0647 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0648 \u0627\u0632 \u0627\u06cc\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u067e\u0631\u0648\u062a\u06a9\u0644 \u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u0631\u0627 \u0628\u0631\u0627\u06cc \u06a9\u0644\u0627\u0633\u0647\u0627\u06cc \u0632\u06cc\u0631 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645: \u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u062a\u062b\u0628\u06cc\u062a \u06a9\u0646\u0646\u062f\u0647: \u0645\u0627 \u067e\u0631\u0648\u062a\u06a9\u0644 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0645\u0648\u0642\u0639 $ \\ Mathrm {Poly} \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f (n \u060c 1\/\u03b5) \\ cdot (1\/\u03c4)^{o (\\ log (1\/\u03c4))} $ \u060c \u067e\u0627\u0633\u062e \u062f\u0627\u062f\u0646 \u0628\u0647 \u06cc\u06a9 \u0633\u0624\u0627\u0644 \u0628\u0627\u0632 \u0645\u0637\u0631\u062d \u0634\u062f\u0647 \u062a\u0648\u0633\u0637 Grewal \u060c Iyer \u060c Kretschmer \u060c Liang [40] \u0648 Anshu \u0648 Arunachalam [6].\u067e\u0631\u0648\u062a\u06a9\u0644 \u0647\u0627\u06cc \u0642\u0628\u0644\u06cc \u0628\u0647 \u0645\u0648\u0642\u0639 $ \\ mathrm {exp} (\u03b8 (n)) $ \u06cc\u0627 $ \u03c4> \\ cos^2 (\u03c0\/8) $ \u0646\u06cc\u0627\u0632 \u062f\u0627\u0634\u062a\u0646\u062f.\u0627\u06cc\u0627\u0644\u0627\u062a \u0628\u0627 \u0627\u0628\u0639\u0627\u062f \u062a\u062b\u0628\u06cc\u062a \u06a9\u0646\u0646\u062f\u0647 $ n – t $: \u0645\u0627 \u067e\u0631\u0648\u062a\u06a9\u0644 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0645\u0648\u0642\u0639 $ n^3 \\ cdot (2^t\/\u03c4)^{o (\\ log (1\/\u03b5))} $ \u060c \u06a9\u0627\u0631 \u0627\u062e\u06cc\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645.\u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u062d\u0627\u0644\u062a\u0647\u0627\u06cc \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u062a\u0647\u06cc\u0647 \u0634\u062f\u0647 \u062a\u0648\u0633\u0637 \u0645\u062f\u0627\u0631\u0647\u0627 \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u06a9\u0645\u06cc \u0627\u0632 \u062f\u0631\u0648\u0627\u0632\u0647 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u06a9\u06cc\u0641\u0648\u0631\u062f \u060c \u06a9\u0647 \u0641\u0642\u0637 \u062f\u0631 \u0645\u062d\u06cc\u0637 \u0642\u0627\u0628\u0644 \u062a\u062d\u0642\u0642 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 $ \u03c4 = 1 $ [30 \u060c 37 \u060c 46 \u060c 61].\u0645\u062d\u0635\u0648\u0644 \u06af\u0633\u0633\u062a\u0647: \u0627\u06af\u0631 $ c = k^{\\ otimes n} $ \u0628\u0631\u0627\u06cc \u0628\u0631\u062e\u06cc \u0627\u0632 $ $ $ \u062c\u062f\u0627 \u0634\u062f\u0647 $ $ k $ \u0627\u0632 \u0627\u06cc\u0627\u0644\u062a \u0647\u0627\u06cc \u062a\u06a9 \u06a9\u0628\u0648\u062a\u0631 \u060c \u0645\u0627 \u06cc\u06a9 \u067e\u0631\u0648\u062a\u06a9\u0644 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0645\u0648\u0642\u0639 $ (n\/\u03bc)^{\u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f.o ((1 + \\ log (1\/\u03c4))\/\u03bc)}\/\u03b5^2 $.\u0627\u06cc\u0646 \u0628\u0647 \u0634\u062f\u062a \u0636\u0645\u0627\u0646\u062a \u0642\u0628\u0644\u06cc \u0631\u0627 \u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u0645\u062d\u0635\u0648\u0644 \u062a\u062b\u0628\u06cc\u062a \u06a9\u0646\u0646\u062f\u0647 \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc \u0634\u0648\u062f \u060c \u062a\u0639\u0645\u06cc\u0645 \u0645\u06cc \u062f\u0647\u062f [39].\u0628\u0631\u0627\u06cc \u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u0645\u062d\u0635\u0648\u0644 \u062a\u062b\u0628\u06cc\u062a \u06a9\u0646\u0646\u062f\u0647 \u060c \u0645\u0627 \u06cc\u06a9 \u067e\u0631\u0648\u062a\u06a9\u0644 \u0628\u0647\u0628\u0648\u062f \u06cc\u0627\u0641\u062a\u0647 \u0628\u06cc\u0634\u062a\u0631 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0645\u0648\u0642\u0639 $ (n^2\/\u03b5^2) \\ cdot (1\/\u03c4)^{o (\\ log (1\/\u03c4))} $.\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0646\u062a\u06cc\u062c\u0647 \u060c \u0645\u0627 \u0627\u0648\u0644\u06cc\u0646 \u067e\u0631\u0648\u062a\u06a9\u0644 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0628\u0631\u0622\u0648\u0631\u062f \u0648\u0641\u0627\u062f\u0627\u0631\u06cc \u062a\u062b\u0628\u06cc\u062a \u06a9\u0646\u0646\u062f\u0647 \u060c \u06cc\u06a9 \u0645\u0639\u06cc\u0627\u0631 \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f \u0627\u0632 \u062c\u0627\u062f\u0648 \u0628\u0631\u0627\u06cc \u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u060c \u0628\u0631\u0627\u06cc \u062e\u0637\u0627 $ \u03b5 $ \u062f\u0631 $ n^3 \\ mathrm {quasipoly} (1\/\u03b5) $.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Stabilizer bootstrapping: A recipe for efficient agnostic tomography and magic estimation \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"open","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[21],"product_tag":[],"class_list":{"0":"post-63255","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-21","7":"pmpro-has-access","8":"desktop-align-left","9":"tablet-align-left","10":"mobile-align-left","12":"first","13":"instock","14":"downloadable","15":"shipping-taxable","16":"purchasable","17":"product-type-simple"},"yoast_head":"\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63255\/\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"og:description\" content=\"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Stabilizer bootstrapping: A recipe for efficient agnostic tomography and magic estimation \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63255\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\" \/>\n<meta property=\"og:image\" content=\"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png\" \/>\n\t<meta property=\"og:image:width\" content=\"440\" \/>\n\t<meta property=\"og:image:height\" content=\"486\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/\",\"url\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/\",\"name\":\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"isPartOf\":{\"@id\":\"https:\/\/express24.ir\/d\/#website\"},\"datePublished\":\"2025-04-14T20:36:46+00:00\",\"dateModified\":\"2025-04-14T20:36:46+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/#breadcrumb\"},\"inLanguage\":\"fa-IR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u062e\u0627\u0646\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647\",\"item\":\"https:\/\/express24.ir\/d\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/express24.ir\/d\/#website\",\"url\":\"https:\/\/express24.ir\/d\/\",\"name\":\"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/express24.ir\/d\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fa-IR\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63255\/","og_locale":"fa_IR","og_type":"article","og_title":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","og_description":"\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Stabilizer bootstrapping: A recipe for efficient agnostic tomography and magic estimation \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 […]","og_url":"https:\/\/express24.ir\/d\/product\/\u062a\u0631\u062c\u0645\u0647-\u0641\u0627\u0631\u0633\u06cc-\u0645\u0642\u0627\u0644\u0647-63255\/","og_site_name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","og_image":[{"width":440,"height":486,"url":"https:\/\/express24.ir\/d\/wp-content\/uploads\/2024\/02\/Elsevier_logo_2019.svg_.png","type":"image\/png"}],"twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/","url":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/","name":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","isPartOf":{"@id":"https:\/\/express24.ir\/d\/#website"},"datePublished":"2025-04-14T20:36:46+00:00","dateModified":"2025-04-14T20:36:46+00:00","breadcrumb":{"@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/#breadcrumb"},"inLanguage":"fa-IR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-63255\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u062e\u0627\u0646\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":2,"name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647","item":"https:\/\/express24.ir\/d\/"},{"@type":"ListItem","position":3,"name":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0627\u0633\u062a\u0627\u0628\u0644\u0627\u06cc\u0632\u0631 \u0628\u0648\u062a \u0627\u0633\u062a\u0631\u067e\u06cc\u0646\u06af: \u062f\u0633\u062a\u0648\u0631 \u0627\u0644\u0639\u0645\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0648\u0645\u0648\u06af\u0631\u0627\u0641\u06cc \u0622\u06af\u0646\u0648\u0633\u062a\u06cc\u06a9 \u06a9\u0627\u0631\u0622\u0645\u062f \u0648 \u062a\u062e\u0645\u06cc\u0646 \u062c\u0627\u062f\u0648\u06cc\u06cc"}]},{"@type":"WebSite","@id":"https:\/\/express24.ir\/d\/#website","url":"https:\/\/express24.ir\/d\/","name":"\u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/express24.ir\/d\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"fa-IR"}]}},"_links":{"self":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product\/63255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/types\/product"}],"replies":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/comments?post=63255"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media\/27"}],"wp:attachment":[{"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/media?parent=63255"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_cat?post=63255"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/express24.ir\/d\/wp-json\/wp\/v2\/product_tag?post=63255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}