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Unitary Designs have become a vital tool for investigating pseudorandomness since they approximate the statistics of the uniform Haar ensemble.
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Fernando G. S. L. Brandão, Aram W. Harrow, and Michał Horodecki, “Efficient quantum pseudorandomness,” Phys. Rev. Lett. 116
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Hassan Shapourian, Shang Liu, Jonah Kudler-Flam, and Ashvin Vishwanath, “Entanglement negativity spectrum of random mixed states: A diagrammatic approach,” PRX Quantum 2
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2021
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2021
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Shao-Kai Jian and Brian Swingle, “Note on entropy dynamics in the brownian SYK model,” Journal of High Energy Physics 2021
2021
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M.S. Blok, V.V. Ramasesh, T. Schuster, K. O’Brien, J.M. Kreikebaum, D. Dahlen, A. Morvan, B. Yoshida, N.Y. Yao, and I. Siddiqi, “Quantum Information Scrambling on a Superconducting Qutrit Processor,” Physical Review X 11
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Pavan Hosur, Xiao-Liang Qi, Daniel A. Roberts, and Beni Yoshida, “Chaos in quantum channels,” Journal of High Energy Physics 2016
2016
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Kurusch Ebrahimi-Fard and Frédéric Patras, “The combinatorics of green’s functions in planar field theories,” Frontiers of Physics 11
2016
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Benoît Collins and Ion Nechita, “Random matrix techniques in quantum information theory,” Journal of Mathematical Physics 57
2016
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Yoshifumi Nakata, Christoph Hirche, Masato Koashi, and Andreas Winter, “Efficient quantum pseudorandomness with nearly time-independent hamiltonian dynamics,” Phys. Rev. X 7
2017
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Daniel A Roberts and Beni Yoshida, “Chaos and complexity by design,” Journal of High Energy Physics 2017
2017
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Julian Sonner and Manuel Vielma, “Eigenstate thermalization in the sachdev-ye-kitaev model,” Journal of High Energy Physics 2017
2017
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Michel Bauer, Denis Bernard, and Tony Jin, “Stochastic dissipative quantum spin chains (i) : Quantum fluctuating discrete hydrodynamics,” SciPost Physics 3
2017
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2021
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Andreas Elben, Steven T. Flammia, Hsin-Yuan Huang, Richard Kueng, John Preskill, Benoît Vermersch, and Peter Zoller, “The randomized measurement toolbox,” Nature Reviews Physics 5
2022
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Jonas Haferkamp, “Random quantum circuits are approximate unitary t t -designs in depth o ( n t 5 + o ( 1 ) ) o(nt^{5+o(1)}) ,” Quantum 6
2022
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Jonas Haferkamp, Philippe Faist, Naga B. T. Kothakonda, Jens Eisert, and Nicole Yunger Halpern, “Linear growth of quantum circuit complexity,” Nature Physics 18
2022
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2022
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Wen Wei Ho and Soonwon Choi, “Exact emergent quantum state designs from quantum chaotic dynamics,” Phys. Rev. Lett. 128
2022
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Pieter W Claeys and Austen Lamacraft, “Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics,” Quantum 6
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Anatoly Dymarsky, “Bound on eigenstate thermalization from transport,” Phys. Rev. Lett. 128
2022
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Zohar Nussinov and Saurish Chakrabarty, “Exact universal chaos, speed limit, acceleration, planckian transport coefficient,“collapse” to equilibrium, and other bounds in thermal quantum systems,” Annals of Physics 443
2022
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Giorgio Cipolloni, László Erdős, and Dominik Schröder, “Thermalisation for wigner matrices,” Journal of Functional Analysis 282
2022
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2022
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Aram W. Harrow and Saeed Mehraban, “Approximate unitary t-designs by short random quantum circuits using nearest-neighbor and long-range gates,” Communications in Mathematical Physics 401
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