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• W2059045419 abstract "We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the resulting unitary converge to Haar measure averages. This is accomplished by establishing an exact mapping between the superoperator that describes t-order moments on n qubits and a multilevel SU(4^t) Lipkin-Meshkov-Glick Hamiltonian. For arbitrary fixed t, we find that the spectral gap scales as 1/n in the thermodynamic limit. Our results imply that random quantum circuits yield an efficient implementation of epsilon-approximate unitary t-designs." @default.
• W2059045419 created "2016-06-24" @default.
• W2059045419 creator A5034282266 @default.
• W2059045419 creator A5036492578 @default.
• W2059045419 date "2010-06-21" @default.
• W2059045419 modified "2023-09-27" @default.
• W2059045419 title "Convergence Rates for Arbitrary Statistical Moments of Random Quantum Circuits" @default.
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• W2059045419 doi "https://doi.org/10.1103/physrevlett.104.250501" @default.
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• W2059045419 hasPublicationYear "2010" @default.
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