Tight bounds on the convergence of noisy random circuits to the uniform distribution

Understand

We study the properties of output distributions of noisy, random circuits.

• We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution.
• These bounds are tight with respect to the dependence on circuit depth.
• Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits.