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Random unitaries in extremely low depth.

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Title: Random unitaries in extremely low depth.
Authors: Schuster, Thomas, Haferkamp, Jonas, Huang, Hsin-Yuan
Source: Science. 7/3/2025, Vol. 389 Issue 6755, p92-96. 5p.
Subjects: Unitary dynamics, Quantum theory, Randomization (Statistics), Polynomials, Geometry
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. Editor's summary: Understanding random processes in nature is important across a range of science and engineering fields. In quantum science, randomization is achieved by the generation of Haar unitary matrices. However, present protocols for the generation of random unitary operations is thought to take long evolution times and require deep circuits. By contrast, Schuster et al. found that local quantum circuits can form random unitaries in exponentially lower depths rather than in the polynomial depths seen in classical dynamics (see the Perspective by Yamamoto and Wada). Such a speedup will be important for benchmarking quantum technologies and probing complex quantum dynamics. —Ian S. Osborne [ABSTRACT FROM AUTHOR]
Copyright of Science is the property of American Association for the Advancement of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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. Editor's summary: Understanding random processes in nature is important across a range of science and engineering fields. In quantum science, randomization is achieved by the generation of Haar unitary matrices. However, present protocols for the generation of random unitary operations is thought to take long evolution times and require deep circuits. By contrast, Schuster et al. found that local quantum circuits can form random unitaries in exponentially lower depths rather than in the polynomial depths seen in classical dynamics (see the Perspective by Yamamoto and Wada). Such a speedup will be important for benchmarking quantum technologies and probing complex quantum dynamics. —Ian S. Osborne [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Science is the property of American Association for the Advancement of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: 7/3/2025
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