Unitary Designs of Symmetric Local Random Circuits

• URL: http://arxiv.org/abs/2408.13472v2
• Date: Fri, 30 Aug 2024 16:27:14 GMT
• Title: Unitary Designs of Symmetric Local Random Circuits
• Authors: Yosuke Mitsuhashi, Ryotaro Suzuki, Tomohiro Soejima, Nobuyuki Yoshioka,
• Abstract summary: We show that the necessary and sufficient condition for the circuit forming an approximate t-design is given by simple integer optimization for general symmetry and locality. This work reveals the relation between the fundamental notions of symmetry and locality in terms of randomness.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 forming an approximate 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 $\mathbb{Z}_2$, 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.

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