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We prove that given the ability to make entangled measurements on at most $k$ replicas of an $n$-qubit state $\rho$ simultaneously, there is a property of $\rho$ which requires at least order $2^n$ measurements to learn.
Weak multiplicativity for random quantum channels
A. Montanaro · 2013
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Measuring entanglement entropy in a quantum many-body system
R. Islam, R. Ma, P. M. Preiss, M. E. Tai, A. Lukin, M. Rispoli, and M. Greiner · 2015
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Quantum spectrum testing
R. O’Donnell and J. Wright · 2015
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Local random quantum circuits are approximate polynomial-designs
F. G. Brandao, A. W. Harrow, and M. Horodecki · 2016
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Quantum thermalization through entanglement in an isolated many-body system
A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner · 2016
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Shadow tomography of quantum states
S. Aaronson · 2018
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A. Harrow and S. Mehraban · 2018
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Measuring the rényi entropy of a two-site fermi-hubbard model on a trapped ion quantum computer
N. M. Linke, S. Johri, C. Figgatt, K. A. Landsman, A. Y. Matsuura, and C. Monroe · 2018
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Quantum computing in the NISQ era and beyond
J. Preskill · 2018
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Gentle measurement of quantum states and differential privacy
S. Aaronson and G. N. Rothblum · 2019
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Quantum supremacy using a programmable superconducting processor
F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandão, D. A. Buell, et al · 2019
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Quantum virtual cooling
J. Cotler, S. Choi, A. Lukin, H. Gharibyan, T. Grover, M. E. Tai, M. Rispoli, R. Schittko, P. M. Preiss, A. M. Kaufman, et al · 2019
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Improved quantum data analysis
C. Bădescu and R. O’Donnell · 2020
Cited alongside, same era.
Entanglement is necessary for optimal quantum property testing
S. Bubeck, S. Chen, and J. Li · 2020
Computations with greater quantum depth are strictly more powerful (relative to an oracle)
M. Coudron and S. Menda · 2020
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Quantum homeopathy works: Efficient unitary designs with a system-size independent number of non-Clifford gates
J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, and I. Roth · 2020
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Quantum algorithmic measurement
D. Aharonov, J. Cotler, and X.-L. Qi · 2021
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Toward instance-optimal state certification with incoherent measurements
S. Chen, J. Li, and R. O’Donnell · 2021
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Approximate orthogonality of permutation operators
A. W. Harrow · 2021
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Cited alongside, same era.
On the need for large quantum depth
N.-H. Chia, K.-M. Chung, and C.-Y. Lai · 2020
Cited alongside, same era.
Exponential separations between learning with and without quantum memory
S. Chen, J. Cotler, H.-Y. Huang, and J. Li
Cited in the paper.
H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, R. Babbush, H. Neven, R. Kueng, J. Preskill, and J. McClean · 2021
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Information-theoretic bounds on quantum advantage in machine learning
H.-Y. Huang, R. Kueng, and J. Preskill · 2021
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