2026-01-22 東京大学
量子回路における大規模な量子ランダムネス生成の概念図。構成要素として不完全なランダムネスを用いた場合でも、完全なランダムネスを用いた場合と同程度に速く大規模なランダムネスを生成できることを示した。
＜関連情報＞
- https://www.t.u-tokyo.ac.jp/press/pr2026-01-22-001
- https://www.t.u-tokyo.ac.jp/hubfs/press-release/2026/0122/001/text.pdf
- https://journals.aps.org/prl/abstract/10.1103/q172-8cmt
非ハールランダム回路はハールランダム回路と同じ速度でユニタリー設計を形成します Non-Haar Random Circuits form Unitary Designs as Fast as Haar Random Circuits
Toshihiro Yada, Ryotaro Suzuki, Yosuke Mitsuhashi, and Nobuyuki Yoshioka
Physical Review Letters Published: 20 January, 2026
DOI: https://doi.org/10.1103/q172-8cmt
Abstract
The unitary design formation in random circuits has attracted considerable attention due to its wide range of practical applications and relevance to fundamental physics. While the formation rates in Haar random circuits have been extensively studied in previous works, it remains an open question how these rates are affected by the choice of local randomizers. In this Letter, we prove that the circuit depths required for general non-Haar random circuits to form unitary designs are upper bounded by those for the corresponding Haar random circuits, up to a constant factor independent of the system size. This result is derived in a broad range of circuit structures, including one- and higher-dimensional lattices, geometrically nonlocal configurations, and even extremely shallow circuits with patchwork architectures. We provide specific applications of these results in randomized benchmarking and random circuit sampling, and also discuss their implications for quantum many-body physics. Our results lays the foundation for flexible and robust randomness generation in real-world experiments, and offers new insights into chaotic dynamics in complex quantum systems.
