Realizing Unitary $k$-designs with a Single Quench
Abstract
We present a single-quench protocol that generates unitary -designs with minimal control. A system first evolves under a random Hamiltonian ; at a switch time (the Thouless time), it is quenched to an independently drawn from the same ensemble and then evolves under . This single quench breaks residual spectral correlations that prevent strictly time-independent chaotic dynamics from forming higher-order designs. The resulting ensemble approaches a unitary -design using only a single control operation -- far simpler than Brownian schemes with continuously randomized couplings or protocols that apply random quenches at short time intervals. Beyond offering a direct route to Haar-like randomness, the protocol yields an operational, measurement-friendly definition of and provides a quantitative diagnostic of chaoticity. It further enables symmetry-resolved and open-system extensions, circuit-level single-quench analogs, and immediate applications to randomized measurements, benchmarking, and tomography.
Cite
@article{arxiv.2511.13829,
title = {Realizing Unitary $k$-designs with a Single Quench},
author = {Yi-Neng Zhou and Robin Löwenberg and Julian Sonner},
journal= {arXiv preprint arXiv:2511.13829},
year = {2026}
}
Comments
5 pages, 4 figures, appendix 12 pages