Magic spreading in random quantum circuits

Year: 2025

Authors: Turkeshi X., Tirrito E., Sierant P.

Autors Affiliation: Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany; Abdus Salam Int Ctr Theoret Phys ICTP, Trieste, Italy; Univ Trento, Pitaevskii BEC Ctr, CNR INO, Trento, Italy; Univ Trento, Dipartimento Fis, Trento, Italy; Barcelona Inst Sci & Technol, Inst Ciencies Foton, ICFO, Barcelona 08860, Spain; Barcelona Supercomp Ctr, Barcelona, Spain.

Abstract: Magic is the resource that quantifies the amount of beyond-Clifford operations necessary for universal quantum computing. It bounds the cost of classically simulating quantum systems via stabilizer circuits central to quantum error correction and computation. In this paper, we investigate how fast generic many-body dynamics generate magic resources under the constraints of locality and unitarity, focusing on magic spreading in brick-wall random unitary circuits. We explore scalable magic measures intimately connected to the algebraic structure of the Clifford group. These metrics enable the investigation of the spreading of magic for system sizes of up to N = 1024 qudits, surpassing the previous state-of-the-art, which was restricted to about a dozen qudits. We demonstrate that magic resources equilibrate on timescales logarithmic in the system size, akin to anti-concentration and Hilbert space delocalization phenomena, but qualitatively different from the spreading of entanglement entropy. As random circuits are minimal models for chaotic dynamics, we conjecture that our findings describe the phenomenology of magic resources growth in a broad class of chaotic many-body systems.

Journal/Review: NATURE COMMUNICATIONS

Volume: 16 (1)      Pages from: 2575-1  to: 2575-8

More Information: We are grateful to D. Gross, L. Leone, and A. Hamma for enlightening discussions, R. Fazio for valuable collaborations and comments, and M. Lewenstein for collaborations on related topics. X.T. acknowledges DFG under Germany’s Excellence Strategy – Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1 – 390534769, and DFG Collaborative Research Center (CRC) 183 Project No. 277101999 – project B01. E.T. was supported by the MIUR Programme FARE (MEPH), by QUANTERA DYNAMITE PCI2022-132919, and by the EU-Flagship programme Pasquans2. E.T. acknowledge the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support. P.S. acknowledges support from the European Research Council AdG NOQIA; MCIN/AEI (PGC2018-0910.13039/501100011033, CEX2019-000910-S/10.13039/501100011033; Plan National STAMEENA PID2022-139099NB; Ministry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call – Quantum Spain project, and by the European Union through the Recovery, Transformation and Resilience Plan – NextGenerationEU within the framework of the Digital Spain 2026 Agenda; Fundacio Cellex; Fundacio Mir-Puig; the computing resources at Urederra and technical support provided by NASERTIC (RES-FI-2024-1-0043). P.S. acknowledges fellowship within the -Generacion D initiative, Red.es, Ministerio para la Transformacion Digital y de la Funcion Publica, for talent atraction (C005/24-ED CV1), funded by the European Union NextGenerationEU funds, through PRTR. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union, or any other granting authority.
KeyWords: Entanglement
DOI: 10.1038/s41467-025-57704-x