Speaker
Description
Unitary k-designs efficiently reproduce Haar-random statistics up to the k-th moment. In this talk, we show that Hamiltonian randomness is not required: a single chaotic Hamiltonian, including deterministic local systems, can generate approximate unitary k-designs. We introduce a two-Pauli-kick (2PK) protocol, where evolution under one fixed Hamiltonian is interspersed with two Pauli kicks, with randomness arising solely from the evolution times. The resulting frame potential approaches the Haar value at long times, with finite-size deviations suppressed by the inverse Hilbert-space dimension. We demonstrate this mechanism analytically and numerically for a single realisation of random matrices, SYK models, and deterministic local quantum spin chains, establishing a simple route to unitary designs without Hamiltonian disorder.