Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations
Year: 2025
Authors: Kargi C., Manatuly A., Sieberer L.M., Dehollain J.P., Henriques F., Olsacher T., Hauke P., Heyl M., Zoller P., Langford N.K.
Autors Affiliation: Univ Technol Sydney, Ctr Quantum Software & Informat, Sydney, NSW 2007, Australia; Univ Technol Sydney, Fac Sci, Sch Math & Phys Sci, Sydney, NSW 2007, Australia; Sydney Quantum Acad, Sydney, NSW, Australia; Univ Innsbruck, Inst Theoret Phys, A-6020 Innsbruck, Austria; Univ Innsbruck, Ctr Quantum Phys, A-6020 Innsbruck, Austria; Austrian Acad Sci, Inst Quantum Opt & Quantum Informat, A-6020 Innsbruck, Austria; Univ Trento, INO CNR BEC Ctr, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dept Phys, Via Sommar 14, I-38123 Trento, Italy; Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany; Univ Augsburg, Inst Phys, Ctr Elect Correlat & Magnetism, Theoret Phys 3, D-86135 Augsburg, Germany.
Abstract: Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world applications for industry-scale quantum processors. Yet even assuming continued rapid progress in device engineering and successful development of fault-tolerant quantum processors, extensive algorithmic resource optimisation will long remain crucial to exploit their full computational power. Currently, among leading DQS algorithms, Trotterisation provides state-of-theart resource scaling. And recent theoretical observations of a distinct breakdown threshold in empirical performance for Trotterised Ising models suggest that even better performance than expected may be possible prior to the threshold. Here, to start exploring this possibility, we study multiple paradigmatic DQS models with experimentally realisable Trotterisations, and provide strong evidence for 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.
Journal/Review: QUANTUM
Volume: 9 Pages from: 1 to: 52
More Information: Authors thanks G. J. Milburn, R. L. Mann, M. J. Bremner, T. Srivipat, K. Modi, D. Braak, J. F. Ralph, and D. W. Berry for useful discussions. Numerical simulations are realised using a Python library, called QuanGuru [105] , developed in our group at UTS. The data and the Python code that support the findings of this study are available from the corresponding authors upon reasonable request.This work has been funded by the Australian Research Council Future Fellowship of N.K.L. (FT170100399) and Discovery Project (DP210101367) . C.K., A.M. and F.H. acknowledge the supports from UTS President’s scholarship, international research scholarship, and Sydney Quantum Academy. J.P.D. acknowledges support from the University of Technology Sydney, Chancellor’s Post-doctoral Research Fellowship (UTS, CPRDF) . L.M.S. acknowledges support from the Austrian Science Fund (FWF) : P 33741-N. P.H. acknowledges support from Provincia Autonoma di Trento, the ERC Starting Grant StrEnQTh (project ID 804305) , the Google Research Scholar Award ProGauge. This project has benefited from Q@TN, the joint lab between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics and CNR- National Research Council. M.H. and P.Z. both acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, under grant agreements No. 853443 and No. 817482 (Pasquans) , respectively. M.H. also acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) via the Gottfried Wilhelm Leibniz Prize program. P.Z. also acknowledges support by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, P.Z.) .KeyWords: Many-body Theories; Exponential Operators; Statistical-mechanics; Level Statistics; Gauge-invariance; Dynamics; Thermalization; Decomposition; Convergence; Algorithms
