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quant-ph2025
Apparent Universal Behavior in Second Moments of Random Quantum Circuits
Daniel Belkin, James Allen, Bryan K. Clark
Just how fast does the brickwork circuit form an approximate 2-design? Is there any difference between anticoncentration and being a 2-design? Does geometry matter? How deep a circ…
quant-ph2025
Absence of censoring inequalities in random quantum circuits
Daniel Belkin, James Allen, Bryan K. Clark
Ref. 1 asked whether deleting gates from a random quantum circuit architecture can ever make the architecture a better approximate -design. We show that it can. In particular, w…
quant-ph2025
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths
James Allen, Daniel Belkin, Bryan K. Clark
A fundamental question is understanding the rate at which random quantum circuits converge to the Haar measure. One quantity which is important in establishing this rate is the spe…