HIGHLIGHTS
SUMMARY
The authors find that it suffices to inject O(t 4 log2 (t) log(1/ε)) many non-Clifford gates into a polynomial-depth random Clifford circuit to obtain an ε-approximate tdesign. The authors also derive novel bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group. Designs consisting of Clifford operations would be particular attractive from various points of view: (i) Because the Clifford unitaries form a finite group, elements can be represented exactly using a small number (O(n 2 )) of . . .
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