Characterization of Randomness in Quantum Circuits of Continuous Gate Sets

• URL: http://arxiv.org/abs/2408.13475v2
• Date: Fri, 30 Aug 2024 16:32:21 GMT
• Title: Characterization of Randomness in Quantum Circuits of Continuous Gate Sets
• Authors: Yosuke Mitsuhashi, Ryotaro Suzuki, Tomohiro Soejima, Nobuyuki Yoshioka,
• Abstract summary: We have established the method of characterizing the maximal order of approximate unitary designs generated by symmetric local random circuits. Here, we provide details on the derivation of the main theorems for general symmetry and for concrete symmetries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of approximate unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the cases of $\mathbb{Z}_2$, U(1), and 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.

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