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We construct random walks on simple Lie groups that quickly converge to the Haar measure for all moments up to order $t$.
“Counting and recounting: The aftermath”
Marta Sved · 1984
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“Classical and Quantum Computation”
A.. Kitaev, A.. Shen and M.. Vyalyi · 2002
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“Derandomized Squaring of Graphs”
Eyal Rozenman and Salil Vadhan · 2005
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“Evenly distributed unitaries: On the structure of unitary designs”
D. Gross, K. Audenaert and J. Eisert · 2007
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“Simple permutations mix even better”
Alex Brodsky and Shlomo Hoory · 2008
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“Exact and approximate unitary 2-designs and their application to fidelity estimation”
Christoph Dankert, Richard Cleve, Joseph Emerson and Etera Livine · 2009
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“Random Quantum Circuits are Approximate 2-designs”
Aram. Harrow and Richard. Low · 2009
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“Unitary designs and codes”
Aidan Roy and A.. Scott · 2009
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“Pseudo-randomness and Learning in Quantum Computation”, 2010
Richard. Low · 2010
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William Fulton and Joe Harris · 2013
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“Local Random Quantum Circuits are Approximate Polynomial-Designs”
Fernando… Brandão, Aram. Harrow and Michał Horodecki · 2016
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Fernando.S.L. Brandão et al · 2021
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“Random quantum circuits are approximate unitary t t -designs in depth O ( n t 5 + o ( 1 ) ) O\left(nt^{5+o(1)}\right) ”
Jonas Haferkamp · 2022
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“Efficient Unitary Designs with a System-Size Independent Number of Non-Clifford Gates”
J. Haferkamp et al · 2022
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“On the moments of random quantum circuits and robust quantum complexity”, 2023
Jonas Haferkamp · 2023
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“Explicit orthogonal and unitary designs”
R. O’Donnell, R.. Servedio and P. Paredes · 2023
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“to appear”, 2024
Adam Bouland et al · 2024
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