Unitary Designs from Two Chaotic Hamiltonians and a Random Pauli Operation

Quantum Physics [Submitted on 11 Apr 2026] Unitary Designs from Two Chaotic Hamiltonians and a Random Pauli Operation Ning Sun, Pengfei Zhang The realization of unitary designs is of fundamental interest in quantum science and typically requires the ability to implement structured quantum circuits. Recent developments have explored the possibility of generating unitary designs using only a small number of quantum quenches, in which the evolution during each interval is governed by a static Hamiltonian. In particular, it has been established that at least three chaotic Hamiltonians are required when only Hamiltonian evolutions are employed. In this work, we propose the emergence of unitary designs in the temporal ensemble of qubit systems evolved under two distinct chaotic Hamiltonians for sufficiently long times, supplemented by an intermediate random Pauli operation inserted between them. This result follows from the universal Pauli spectrum of chaotic Hamiltonians, a central concept in the study of non-stabilizerness. Our theoretical predictions are verified numerically using explicit examples, including Gaussian unitary ensemble Hamiltonians and random spin models. We further investigate finite-time and finite-size corrections to the protocol. Our results provide new insights into the dynamical generation of quantum randomness and offer a new route toward realizing unitary designs in chaotic systems. Comments: 6 pages, 3 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.10122 [quant-ph]   (or arXiv:2604.10122v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.10122 Focus to learn more Submission history From: Ning Sun [view email] [v1] Sat, 11 Apr 2026 09:35:45 UTC (610 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)