Effect of gate deletion on the speed of forming unitary designs

Investigate whether deleting (censoring) a subset of gates in local random quantum circuits can strictly accelerate convergence to approximate unitary designs compared to circuits with fully i.i.d. Haar-random two-qubit gates, and establish rigorous conditions under which such deletion speeds up or cannot speed up design formation.

Background

Their construction of shallow designs effectively sets a subset of gates to identity on a brickwork architecture, raising the question of whether the same depth guarantees extend to standard i.i.d. Haar-random local circuits without gate deletions. The authors highlight a broader question inspired by censoring inequalities for Markov chains: can removing random gates ever improve mixing to a unitary design?