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We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state.
1905
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1905
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1908
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Mikel Sanz, Tensor Networks in Condensed Matter , Ph.D. thesis (2011)
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R. O’Donnell and J. Wright, “Efficient quantum tomography,” in Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing , STOC ’16 (Association for Computing Machinery, New York, NY, USA, 2016) p. 899–912
2016
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J. Haah, A. W. Harrow, Z. Ji, X. Wu, and N. Yu, “Sample-optimal tomography of quantum states,” in Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing , STOC ’16 (Association for Computing Machinery, New York, NY, USA, 2016) p. 913–925
2016
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F. G. S. L. Brandao, A. W. Harrow, and M. Horodecki, “Local random quantum circuits are approximate polynomial-designs,” Commun. Math. Phys. 346
2016
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H. Zhu, “Multiqubit Clifford groups are unitary 3-designs,” Phys. Rev. A 96
2017
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A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller, “Rényi Entropies from random quenches in atomic Hubbard and spin models,” Phys. Rev. Lett. 120
2018
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S. Aaronson, “Shadow tomography of quantum states,” in Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing , STOC 2018 (Association for Computing Machinery, New York, NY, USA, 2018) p. 325–338
2018
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A. Nahum, S. Vijay, and J. Haah, “Operator spreading in random unitary circuits,” Phys. Rev. X 8
2018
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G. Lugosi and S. Mendelson, “Mean estimation and regression under heavy-tailed distributions: A survey,” Found. Comp. Math. 19
2019
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T. Zhou and A. Nahum, “Emergent statistical mechanics of entanglement in random unitary circuits,” Phys. Rev. B 99
2019
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H.-Y. Huang, R. Kueng, and J. Preskill, “Predicting many properties of a quantum system from very few measurements,” Nature Phys. 16
2020
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C. Hadfield, “Adaptive Pauli shadows for energy estimation,” (2021) , arXiv:2105.12207
2021
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2021
Sergey Bravyi and Dmitri Maslov, “Hadamard-free circuits expose the structure of the clifford group,” IEEE Transactions on Information Theory 67
2021
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2021
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C. Hadfield, S. Bravyi, R. Raymond, and A. Mezzacapo, “Measurements of quantum Hamiltonians with locally-biased classical shadows,” Commun. Math. Phys. 391
2022
Closest in time.
G. Boyd and B. Koczor, “Training variational quantum circuits with CoVaR: Covariance root finding with classical shadows,” Phys. Rev. X 12
2022
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S. H. Sack, R. A. Medina, A. A. Michailidis, R. Kueng, and M. Serbyn, “Avoiding barren plateaus using classical shadows,” PRX Quantum 3
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Cited alongside, same era.
2021
Cited alongside, same era.
A. Neven, J. Carrasco, V. Vitale, C. Kokail, A. Elben, M. Dalmonte, P. Calabrese, P. Zoller, B. Vermersch, R. Kueng, and B. Kraus, “Symmetry-resolved entanglement detection using partial transpose moments,” npj Quant. Inf. 7
2021
Cited alongside, same era.
A. Rath, C. Branciard, A. Minguzzi, and B. Vermersch, “Quantum fisher information from randomized measurements,” Phys. Rev. Lett. 127
2021
Cited alongside, same era.
R. J. Garcia, Y. Zhou, and A. Jaffe, “Quantum scrambling with classical shadows,” Phys. Rev. Res. 3
2021
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G. Li, Z. Song, and X. Wang, “VSQL: Variational shadow quantum learning for classification,” in Proceedings of the AAAI conference on artificial intelligence , Vol. 35 (2021) pp. 8357–8365
2021
Cited alongside, same era.
G. I. Struchalin, Y. A. Zagorovskii, E. V. Kovlakov, S. S. Straupe, and S. P. Kulik, “Experimental estimation of quantum state properties from classical shadows,” PRX Quantum 2
2021
Cited alongside, same era.
T. Zhang, J. Sun, X.-X. Fang, X.-M. Zhang, X. Yuan, and H. Lu, “Experimental quantum state measurement with classical shadows,” Phys. Rev. Lett. 127
2021
Cited alongside, same era.
2022
Closest in time.
W. J. Huggins, B. A. O’Gorman, N. C. Rubin, D. R. Reichman, R. Babbush, and J. Lee, “Unbiasing fermionic quantum Monte Carlo with a quantum computer,” Nature 603
2022
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D. E. Koh and S. Grewal, “Classical shadows with noise,” Quantum 6
2022
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2022
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2022
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2022
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2022
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2022
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H.-Y. Hu and Y.-Z. You, “Hamiltonian-driven shadow tomography of quantum states,” Phys. Rev. Res. 4
2022
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2022
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A. M. Dalzell, N. Hunter-Jones, and F. G. S. L. Brandão, “Random quantum circuits anticoncentrate in log depth,” PRX Quantum 3
2022
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A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, “The randomized measurement toolbox,” Nature Rev. Phys. 5
2023
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C. Bertoni, J. Haferkamp, M. Hinsche, M. Ioannou, J. Eisert, and H. Pashayan, “Shallow-shadows,” GitHub repository (2023)
2023
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