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?

References

In fact, this suggests a more general open question: Is it possible for the deletion of random quantum gates to speed up the formation of unitary designs?

— Random unitaries in extremely low depth  (2407.07754 - Schuster et al., 2024) in Discussion

In particular, it remains to determine when the stronger convergence enabled by local invariance translates into lower design orders or more efficient circuit constructions for such tasks.

— Random Quantum Circuits Beyond Moment Matching  (2610.02135 - Hung, 1 Oct 2026) in Section 1, Discussion