Realizing Unitary $k$-designs with a Single Quench

• URL: http://arxiv.org/abs/2511.13829v1
• Date: Mon, 17 Nov 2025 19:00:04 GMT
• Title: Realizing Unitary $k$-designs with a Single Quench
• Authors: Yi-Neng Zhou, Robin Löwenberg, Julian Sonner,
• Abstract summary: We present a single-quench protocol that generates unitary $k$-designs with minimal control.<n>The protocol yields an operational, measurement-friendly definition of $t_mathrmTh$ and provides a quantitative diagnostic of chaoticity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a single-quench protocol that generates unitary $k$-designs with minimal control. A system first evolves under a random Hamiltonian $H_1$; at a switch time $t_s \geq t_{\mathrm{Th}}$ (the Thouless time), it is quenched to an independently drawn $H_2$ from the same ensemble and then evolves under $H_2$. 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 $k$-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 $t_{\mathrm{Th}}$ 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.

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