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Realizing Unitary $k$-designs with a Single Quench

Quantum Physics 2026-03-17 v2 Quantum Gases Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory

Abstract

We present a single-quench protocol that generates unitary kk-designs with minimal control. A system first evolves under a random Hamiltonian H1H_1; at a switch time tstTht_s \geq t_{\mathrm{Th}} (the Thouless time), it is quenched to an independently drawn H2H_2 from the same ensemble and then evolves under H2H_2. 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 kk-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 tTht_{\mathrm{Th}} 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.

Keywords

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

R2 v1 2026-07-01T07:42:05.100Z