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Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements.
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2021
Cited alongside, same era.
G. Struchalin, Y. A. Zagorovskii, E. Kovlakov, S. Straupe, and S. Kulik, Experimental estimation of quantum state properties from classical shadows, PRX Quantum 2
2021
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D. Gross, S. Nezami, and M. Walter, Schur-Weyl duality for the Clifford group with applications: Property testing, a robust Hudson theorem, and de Finetti representations, Communications in Mathematical Physics , 1 (2021)
2021
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The name being derived from a more theoretical proposal due to Aaronson [ 21 ]
Cited in the paper.
The quantum channel ℱ \mathcal{F} is also called a frame operator . While it need not be invertible in general, it is invertible for all circuit sets considered in this Letter (as well as those considered in all other shadow tomography protocols that we are aware of)
Cited in the paper.
This is a subject of active research, and thus this scaling might improve further
Cited in the paper.
This follows from [ 16 , Example 4.27 and Theorem 4.24] . Observe that the stabilizer of the left multiplication action of S 4 S_{4} on R T 4 R_{T_{4}} is the Klein four-group K 4 = ⟨ ( 12 ) ( 34 ) , ( 13 ) ( 24 ) ⟩ K_{4}=\langle(12)(34),(13)(24)\rangle , with quotient S 4 / K 4 S_{4}/K_{4} is isomorphic to S 3 S_{3}
Cited in the paper.
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2022
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B. Collins, S. Matsumoto, and J. Novak, The Weingarten calculus, Notices of the AMS 69
2022
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