随机单位是量子技术和复杂量子多体物理学研究的核心。然而，用于生成随机单位的现有协议需要较长的演化时间和深层电路。研究组证明了局域量子电路可以在任何几何形状上形成极低深度的随机单位。这些浅电路的复杂性较低，只产生短程相关性，但与指数复杂性的随机单位无法区分。
这一发现与经典系统形成鲜明对比，在经典系统中，需要很长的进化时间才能出现随机性。该研究结果在量子科学领域有着广泛的应用，从设备基准测试到量子优势。此外，他们揭示了基本的物理性质（包括进化时间、因果结构和物质的相位）很难学习。
附：英文原文
Title: Random unitaries in extremely low depth
Author: Thomas Schuster, Jonas Haferkamp, Hsin-Yuan Huang
Issue&Volume: 2025-07-03
Abstract: Random unitaries are central to quantum technologies and the study of complex quantum many-body physics. However, existing protocols for generating random unitaries require long evolution times and deep circuits. In this work, we prove that local quantum circuits can form random unitaries in extremely low depth on any geometry. These shallow circuits have low complexity and create only short-range correlations, yet are indistinguishable from random unitaries with exponential complexity. This finding contrasts sharply with classical systems, in which a long evolution time is required to appear random. Our results have widespread applications across quantum science, from device benchmarking to quantum advantages. Moreover, they reveal that fundamental physical properties—including evolution time, causal structure, and phases of matter—are provably hard to learn.
DOI: adv8590
Source: https://www.science.org/doi/10.1126/science.adv8590