Quantum Chaos and Trotterisation Thresholds in Digital Quantum Simulations

Digital quantum simulation is one of the most promising paths for achieving useful real-world applications for industry-scale quantum processors. Yet even assuming continued rapid progress in device engineering, extensive resource optimisation will remain crucial to exploiting the full computational power of a device. In digital quantum simulations, Trotter step size has a profound impact on required qubit and gate numbers for each application. But contrary to standard rigorous bounds, recent theory results predict a performance threshold connecting simulation fidelity, system localisation and quantum chaos. Here, we numerically analyse several experimentally accessible digital simulation models, supporting and extending these predictions. In each case, we show that a range of numerical signatures share the same sharp threshold, at a step size that is largely independent of system size. We study in detail the relationship between the Trotterisation threshold and the onset of digitisation-induced quantum chaos. We show that chaotic dynamics can be conclusively observed down to modest system sizes, and that the same sharp threshold may even be observed in smaller systems which do not exhibit conclusive evidence of chaos.