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Benchmarking quantum chaos from geometric complexity

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  • Published: 25 March 2025
  • Volume 2025, article number 177, (2025)
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Benchmarking quantum chaos from geometric complexity
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  • Arpan Bhattacharyya  ORCID: orcid.org/0000-0002-7933-64411,
  • Suddhasattwa Brahma  ORCID: orcid.org/0000-0003-4241-67012,
  • Satyaki Chowdhury  ORCID: orcid.org/0000-0002-8823-99343,4 &
  • …
  • Xiancong Luo  ORCID: orcid.org/0009-0004-9366-58682 

  • 158 Accesses

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A preprint version of the article is available at arXiv.

Abstract

Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to benchmark the quantum chaos in a well-known oscillator model. In particular, we study the circuit complexity for the unitary time-evolution operator of a non-Gaussian bosonic quantum mechanical system. Our results indicate that, within some limitations, geometric complexity can indeed be a good indicator of quantum chaos.

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Acknowledgments

We thank Bret Underwood for comments on an earlier version of this draft. AB is supported by the Core Research Grant (CRG/2023/001120) and Mathematical Research Impact Centric Support Grant (MTR/2021/000490) by the Department of Science and Technology Science and Engineering Research Board (India). SB is supported in part by the Higgs Fellowship and by the STFC Consolidated Grant “Particle Physics at the Higgs Centre”. SC would like to thank the doctoral school of Jagiellonian University for providing a fellowship during the course of the work. SC was supported by “Research support module” as part of the “Excellence Initiative — Research University” program at the Jagiellonian University in Kraków for this project. SC also acknowledges the hospitality of the Higgs Centre for Theoretical Physics at the University of Edinburgh during his visit where part of the work was conducted. XL is supported in part by the Program of China Scholarship Council (Grant No. 202208170014).

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Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology, Gandhinagar, Gujarat, 382355, India

    Arpan Bhattacharyya

  2. Higgs Centre for Theoretical Physics, School of Physics & Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, Scotland, UK

    Suddhasattwa Brahma & Xiancong Luo

  3. Institute of Theoretical Physics, Jagiellonian University, Lojasiewicza 11, 30-348, Cracow, Poland

    Satyaki Chowdhury

  4. Doctoral School of Exact and Natural Sciences, Jagiellonian University, Lojasiewicza 11, 30-348, Cracow, Poland

    Satyaki Chowdhury

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Bhattacharyya, A., Brahma, S., Chowdhury, S. et al. Benchmarking quantum chaos from geometric complexity. J. High Energ. Phys. 2025, 177 (2025). https://doi.org/10.1007/JHEP03(2025)177

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  • Received: 26 November 2024

  • Revised: 12 February 2025

  • Accepted: 28 February 2025

  • Published: 25 March 2025

  • DOI: https://doi.org/10.1007/JHEP03(2025)177

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Keywords

  • AdS-CFT Correspondence
  • Black Holes in String Theory
  • Holography and Hydrodynamics
  • Cosmological models

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