Unitary Designs of Symmetric Local Random Circuits
We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is given by simple integer optimization for general symmetry and locality. By using the result, we explicitly give the maximal order of unitary design under the Z_{2}, U(1), and SU(2) symmetries for general locality. This work reveals the relation between the fundamental notions of symmetry and locality in terms of randomness.
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 Letters
- Published
- 2025-05-07
- DOI
- https://doi.org/10.1103/physrevlett.134.180404
- Citations
- 7
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 17.37
Funders
- Gordon and Betty Moore Foundation
- International Business Machines Corporation
- 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