For random 1D brickwork circuits on qudits of dimension q, the spectral gap of the t-th moment is bounded below by a constant near the conjectured optimum whenever q ≥ t, improving t-design depth bounds dramatically.
Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G.S.L
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Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths
For random 1D brickwork circuits on qudits of dimension q, the spectral gap of the t-th moment is bounded below by a constant near the conjectured optimum whenever q ≥ t, improving t-design depth bounds dramatically.