Unitary designs from perturbed time evolutions of a chaotic Hamiltonian
Abstract
Unitary designs provide efficient substitutes for Haar-random unitaries in quantum information processing, randomized measurements, and many-body quantum dynamics. We propose a protocol based on time evolutions of a single chaotic Hamiltonian interleaved with unitary perturbations to generate unitary designs. We derive the frame potential of the resulting ensemble in terms of those of the intermediate ensemble. The intermediate ensemble need not itself be Haar random or exhibit Haar-level frame potentials, provided that its trace moments and frame-potential growth are sufficiently suppressed. The nontrivial Pauli set and the Clifford ensemble are simple examples, whereas ensembles whose cardinality does not grow with the Hilbert-space dimension generally fail. We further establish a frame-potential correspondence between multi-Hamiltonian temporal protocols and one-Hamiltonian protocols interleaved with repeated fixed trace-suppressed perturbations, showing that two perturbations suffice to recover Haar-level frame potentials. For local Hamiltonians, we derive a lower bound on the space--depth control resource, while more generally we establish a universal finite-window bound that constrains the required temporal sampling range. Together, these results identify complementary spatial and temporal resource requirements for perturbation-assisted randomness generation.
Related
- Superposed quantum evolutions across chaotic and regular regimes
- Generating random unitaries by products of conjugated Hamiltonian evolutions
- Near-Optimal Ground-State Preparation without Controlled Hamiltonian Evolutions
- Nonintegrability theorem on perturbed integrable Hamiltonian dynamical systems with two independent resonances
- Unitary Designs from Doped Matchgate Circuits
BibTeX
@misc{yang2026unitary,
title = {{Unitary designs from perturbed time evolutions of a chaotic Hamiltonian}},
author = {Zhongyi Yang and Biao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.24851},
eprint = {2607.24851},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24851},
}
RIS
TY - UNPB
TI - Unitary designs from perturbed time evolutions of a chaotic Hamiltonian
AU - Zhongyi Yang
AU - Biao Wu
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2607.24851
UR - https://arxiv.org/abs/2607.24851
AB - Unitary designs provide efficient substitutes for Haar-random unitaries in quantum information processing, randomized measurements, and many-body quantum dynamics. We propose a protocol based on time evolutions of a single chaotic Hamiltonian interleaved with unitary perturbations to generate unitary designs. We derive the frame potential of the resulting ensemble in terms of those of the intermediate ensemble. The intermediate ensemble need not itself be Haar random or exhibit Haar-level frame potentials, provided that its trace moments and frame-potential growth are sufficiently suppressed. The nontrivial Pauli set and the Clifford ensemble are simple examples, whereas ensembles whose cardinality does not grow with the Hilbert-space dimension generally fail. We further establish a frame-potential correspondence between multi-Hamiltonian temporal protocols and one-Hamiltonian protocols interleaved with repeated fixed trace-suppressed perturbations, showing that two perturbations suffice to recover Haar-level frame potentials. For local Hamiltonians, we derive a lower bound on the space--depth control resource, while more generally we establish a universal finite-window bound that constrains the required temporal sampling range. Together, these results identify complementary spatial and temporal resource requirements for perturbation-assisted randomness generation.
ER -