C. Kargi, J. P. Dehollain, F. Henriques, L. Sieberer, T. Olsacher, P. Hauke, M. Heyl, P. Zoller, N. Langford Quantum Chaos and Trotterisation Thresholds in Digital Quantum Simulations,
arXiv:2110.11113 arXiv:2110.11113 (ID: 720694)
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 DQS resource scaling. Moreover, recent theoretical studies of Trotterised Ising models suggest it also offers feasible performance for unexpectedly large step sizes up to a sharp breakdown threshold, but demonstrations and characterisation have been limited, and the question of whether this behaviour applies as a general principle has remained open. Here, we study a set of paradigmatic and experimentally realisable DQS models, and show that a range of Trotterisation performance behaviours, including the existence of a sharp threshold, are remarkably universal. Carrying out a detailed characterisation of a range of performance signatures, we demonstrate that it is the onset of digitisation-induced quantum chaos at this threshold that underlies the breakdown of Trotterisation. Specifically, combining analysis of detailed dynamics with conclusive, global static signatures based on random matrix theory, we observe clear signatures of regular behaviour pre-threshold, and conclusive, initial-state-independent evidence for the onset of quantum chaotic dynamics beyond the threshold. We also show how this behaviour consistently emerges as a function of system size for sizes and times already relevant for current experimental DQS platforms. The advances in this work open up many important questions about the algorithm performance and general shared features of sufficiently complex Trotterisation-based DQS. Answering these will be crucial for extracting the maximum simulation power from future quantum processors.