The Role of Entanglement in Quantum Reservoir Computing with Coupled Kerr Nonlinear Oscillators

Quantum Reservoir Computing (QRC) uses quantum dynamics to efficiently process temporal data. In this work, we investigate a QRC framework based on two coupled Kerr nonlinear oscillators, a system well-suited for time-series prediction tasks due to its complex nonlinear interactions and potentially high-dimensional state space. We explore how its performance in forecasting both linear and nonlinear time-series depends on key physical parameters: input drive strength, Kerr nonlinearity, and oscillator coupling, and analyze the role of entanglement in improving the reservoir's computational performance, focusing on its effect on predicting non-trivial time series. Using logarithmic negativity to quantify entanglement and normalized root mean square error (NRMSE) to evaluate predictive accuracy, our results suggest that entanglement provides a computational advantage on average -- up to a threshold in the input frequency -- that persists under some levels of dissipation and dephasing. In particular, we find that higher dissipation rates can enhance performance. While the entanglement advantage manifests as improvements in both average and worst-case performance, it does not lead to improvements in the best-case error. These findings contribute to the broader understanding of quantum reservoirs for high performance, efficient quantum machine learning and time-series forecasting.