Random unitaries in extremely low depth

IF 45.8 1区综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES

Science Pub Date : 2025-07-03 DOI:10.1126/science.adv8590

Thomas Schuster, Jonas Haferkamp, Hsin-Yuan Huang

引用次数: 0

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.

查看原文本刊更多论文

深度极低的随机单位

随机一元是量子技术和复杂量子多体物理研究的核心。然而，现有的生成随机酉元的协议需要较长的进化时间和较深的电路。在这项工作中，我们证明了局部量子电路可以在任何几何形状的极低深度上形成随机酉。这些浅层电路具有较低的复杂性，并且仅产生短距离相关性，但与具有指数复杂度的随机酉元难以区分。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显得随机。我们的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，它们揭示了基本的物理性质——包括进化时间、因果结构和物质的阶段——被证明是很难学习的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Science 综合性期刊-综合性期刊

CiteScore

61.10

自引率

0.90%

发文量

审稿时长

2.1 months

期刊介绍： Science is a leading outlet for scientific news, commentary, and cutting-edge research. Through its print and online incarnations, Science reaches an estimated worldwide readership of more than one million. Science’s authorship is global too, and its articles consistently rank among the world's most cited research. Science serves as a forum for discussion of important issues related to the advancement of science by publishing material on which a consensus has been reached as well as including the presentation of minority or conflicting points of view. Accordingly, all articles published in Science—including editorials, news and comment, and book reviews—are signed and reflect the individual views of the authors and not official points of view adopted by AAAS or the institutions with which the authors are affiliated. Science seeks to publish those papers that are most influential in their fields or across fields and that will significantly advance scientific understanding. Selected papers should present novel and broadly important data, syntheses, or concepts. They should merit recognition by the wider scientific community and general public provided by publication in Science, beyond that provided by specialty journals. Science welcomes submissions from all fields of science and from any source. The editors are committed to the prompt evaluation and publication of submitted papers while upholding high standards that support reproducibility of published research. Science is published weekly; selected papers are published online ahead of print.