Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations
- Publisher:
- Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
- Publication Type:
- Journal Article
- Citation:
- Quantum, 2025, 9, pp. 1924
- Issue Date:
- 2025-01-01
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Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world ap-plications for industry-scale quantum processors. Yet even assuming continued rapid progress in device en-gineering 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-the-art resource scaling. And recent theoretical observa-tions of a distinct breakdown threshold in empirical performance for Trotterised Ising models suggest that even better performance than expected may be possi-ble prior to the threshold. Here, to start exploring this possibility, we study multiple paradigmatic DQS models with experimen-tally realisable Trotterisations, and provide strong evi-dence for universality of a range of Trotterisation per-formance 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 im-portant pre-threshold regime, we are able to identify new distinct regimes displaying qualitatively differ-ent 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.
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