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arXiv · 2408.13475

Characterization of randomness in quantum circuits of continuous gate sets

Yosuke Mitsuhashi·Ryotaro Suzuki·Tomohiro Soejima·Nobuyuki Yoshioka
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Abstract

In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic 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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Yosuke Mitsuhashi, Ryotaro Suzuki, Tomohiro Soejima, Nobuyuki Yoshioka. 2024-08-24. Characterization of randomness in quantum circuits of continuous gate sets. https://doi.org/10.1103/physreva.111.052409

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