Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations

Cahit Kargi; Angsar Manatuly; Lukas M. Sieberer; Juan Pablo Dehollain; Fabio Henriques; Tobias Olsacher; Philipp Hauke; Markus Heyl; Peter Zoller; Nathan K. Langford

doi:10.22331/q-2025-12-02-1924

Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations

Cahit Kargi^1,2, Angsar Manatuly^1,2, Lukas M. Sieberer³, Juan Pablo Dehollain¹, Fabio Henriques^1,2, Tobias Olsacher^4,5, Philipp Hauke⁶, Markus Heyl^7,8, Peter Zoller^4,5, and Nathan K. Langford¹

¹Centre for Quantum Software and Information & School of Mathematical and Physical Sciences, Faculty of Science, University of Technology Sydney, New South Wales 2007, Australia
²Sydney Quantum Academy, Sydney, New South Wales, Australia
³Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
⁴Center for Quantum Physics, University of Innsbruck, 6020 Innsbruck, Austria
⁵Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
⁶INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
⁷Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
⁸Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany

Published:	2025-12-02, volume 9, page 1924
Editor:	Álvaro Alhambra
Eprint:	arXiv:2110.11113v6
Doi:	https://doi.org/10.22331/q-2025-12-02-1924
Citation:	Quantum 9, 1924 (2025).

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Abstract

Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world applications for quantum processors. Yet even assuming rapid progress in device engineering and development of fault-tolerant quantum processors, algorithmic resource optimisation will long remain crucial to exploit their full power. Currently, Trotterisation provides state-of-the-art resource scaling. And recent theoretical studies of Trotterised Ising models suggest that even better performance than expected may be possible up to a distinct breakdown threshold in empirical performance. Here, we study multiple paradigmatic DQS models with experimentally realisable Trotterisations, and evidence the universality of a range of Trotterisation performance behaviours, including not only the threshold, but also new features in the pre-threshold regime that is most important for practical applications. In each model, we observe a distinct Trotterisation threshold shared across widely varying performance signatures; we further show that an onset of quantum chaotic dynamics causes the performance breakdown and is directly induced by digitisation errors. In the important pre-threshold regime, we are able to identify new distinct regimes displaying qualitatively different quasiperiodic performance behaviours, and show analytic behaviour for properly defined operational Trotter errors. Our results rely crucially on diverse new analytical tools, and provide a previously missing unified picture of Trotterisation behaviour across local observables, the global quantum state, and the full Trotterised unitary. This work provides new insights and tools for addressing important questions about the algorithm performance and underlying theoretical principles of sufficiently complex Trotterisation-based DQS, that will help in extracting maximum simulation power from future quantum processors.

Featured image: Digitisation of unitary time evolution with small Trotter step sizes leads to regular dynamics with perturbatively small Trotter errors. At larger Trotter step sizes, quantum chaotic dynamics causes a proliferation of Trotter errors. A pronounced threshold separates the regular and quantum chaotic regimes. We observe this phenomenology universally across various models, including the XYZ Heisenberg model (bottom left), the Ising model with all-to-all interactions (bottom right), and the Dicke model of spins immersed in a cavity (top right).

Popular summary

Quantum simulation offers exciting opportunities for quantum processors to carry out "in-silico" modelling of quantum systems too complex for simulation by classical computing technology. In digital quantum simulation (DQS), complex target dynamics is constructed in discrete time steps from the elementary gates of a quantum processor. This approach offers great flexibility, and compatibility with future universal quantum computers, but inevitably introduces digitisation or Trotter errors. A key goal of DQS research is to better understand the computational performance of these algorithms with a view to improving the power of practical quantum processors. Recent studies have observed a rather sharp performance threshold eparating a regime of regular dynamics and controllable Trotter errors, from quantum chaotic dynamics. In this work, we study empirical Trotterisation performance systematically across diverse, paradigmatic models, and we demonstrate marked universality for a range of performance behaviours, including both the threshold itself and new features in the pre- and post-threshold regimes. We obtain our results using various new analytical tools, including new Trotter error metrics and quantitatively rigorous global signatures of quantum chaos.

► BibTeX data

@article{Kargi2025quantumchaos,
  doi = {10.22331/q-2025-12-02-1924},
  url = {https://doi.org/10.22331/q-2025-12-02-1924},
  title = {Quantum {C}haos and {U}niversal {T}rotterisation {B}ehaviours in {D}igital {Q}uantum {S}imulations},
  author = {Kargi, Cahit and Manatuly, Angsar and Sieberer, Lukas M. and Dehollain, Juan Pablo and Henriques, Fabio and Olsacher, Tobias and Hauke, Philipp and Heyl, Markus and Zoller, Peter and Langford, Nathan K.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1924},
  month = dec,
  year = {2025}
}

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