Convergence rates for arbitrary statistical moments of random quantum circuits

Details Convergence rates for arbitrary statistical moments of random quantum circuits Convergence rates for arbitrary statistical moments of random quantum circuits

2009-10-06

arxiv.org/abs/0910.0913v3

Physics

Quantum Physics

4 pages, 1 figure 2nd revised version with supplementary material

Scientific paper

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.

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