Characterization of randomness in quantum circuits of continuous gate sets
In the accompanying paper [Y. Mitsuhashi, et al., Phys. Rev. Lett. 134, 180404 (2025)], we established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and explicitly specified the order in the cases of ${\mathbb{Z}}_{2}, \mathrm{U}(1)$, and $\mathrm{SU}(2)$ symmetries. Here, we provide full details on the derivation of the main theorems for general symmetry and for concrete symmetries. Furthermore, we consider a general framework where we have access to a finite set of connected compact unitary subgroups, which includes symmetric local unitary gate sets.
Authors
- Yosuke Mitsuhashi (ORCID: https://orcid.org/0000-0002-3315-4546)
- Tomohiro Soejima (ORCID: https://orcid.org/0000-0002-6542-597X)
- Nobuyuki Yoshioka (ORCID: https://orcid.org/0000-0001-6094-8635)
- Ryotaro Suzuki
Institutions
- Harvard University Press (US)
- RIKEN (JP)
- Judd Systems Technologies (United States) (US)
- The University of Tokyo (JP)
- Freie Universität Berlin (DE)
Publication Details
- Journal
- Physical review. A/Physical review, A
- Published
- 2025-05-07
- DOI
- https://doi.org/10.1103/physreva.111.052409
- Citations
- 7
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 17.37
Funders
- Gordon and Betty Moore Foundation
- Bundesministerium für Bildung und Forschung
- Japan Society for the Promotion of Science
- Japan Science and Technology Agency
- Core Research for Evolutional Science and Technology
- Precursory Research for Embryonic Science and Technology
- Exploratory Research for Advanced Technology