The operational time window for quantum reservoir computing beyond the edge of chaos

Abstract

Quantum reservoir computing harnesses complex quantum dynamics to process temporal data; however, the selection of its hyperparameters, such as the system’s evolution time, is often heuristic and lacks a physical justification. This work investigates quantum chaotic behaviour as a criterion for selecting this evolution time, using a transverse-field Ising model as a reservoir. We find that, while performance peaks at the so-called edge of chaos in terms of magnetic field strength, the optimal evolution time lies within a functional window bounded by two distinct timescales: a newly introduced lower bound set by the temporal collapse of observable variances and an upper bound given by the Thouless time. Notably, the optimal time is consistently shorter than the Thouless time, establishing it as an upper bound rather than a direct target, contrary to what has been suggested in previous studies. Furthermore, introducing measurement back-action shifts this optimal regime, challenging the notion of a universal edge of chaos rule. Our results demonstrate that effective quantum reservoir computing requires a nuanced balance between chaos, evolution time, and measurement strength, with fully chaotic systems proving detrimental for memory tasks.