Year: 2025
Type: article
Abstract: The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been extensively studied in previous works, it remains an open question how these rates are affected by the choice of local randomizers. In this Letter, we prove that the circuit depths required for general non-Haar random circuits to form unitary designs are upper bounded by those for the corresponding Haar random circuits, up to a constant factor independent of the system size. This result is derived in a broad range of circuit structures, including one- and higher-dimensional lattices, geometrically nonlocal configurations, and even extremely shallow circuits with patchwork architectures. We provide specific applications of these results in randomized benchmarking and random circuit sampling, and also discuss their implications for quantum many-body physics. Our results lays the foundation for flexible and robust randomness generation in real-world experiments, and offers new insights into chaotic dynamics in complex quantum systems.
Source: Physical Review Letters
DOI: 10.1103/q172-8cmt
Authors: Toshihiro Yada, Ryotaro Suzuki, Yosuke Mitsuhashi, Nobuyuki Yoshioka
Institutions: The University of Tokyo, Freie Universität Berlin
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Bundesministerium für Bildung und Forschung, University of Tokyo, Japan Society for the Promotion of Science, Japan Science and Technology Agency, Division of Materials Research, Core Research for Evolutional Science and Technology, Precursory Research for Embryonic Science and Technology, Exploratory Research for Advanced Technology
OpenAlex ID: W4417279927