Quantumness and Learning Performance in Reservoir Computing with a Single Oscillator

We explore the power of reservoir computing with a single oscillator in learning time series using quantum and classical models. We demonstrate that this scheme learns the Mackey--Glass (MG) chaotic time series, a solution to a delay differential equation. Our results suggest that the quantum nonlinear model is more effective in terms of learning performance compared to a classical non-linear oscillator. We develop approaches for measuring the quantumness of the reservoir during the process, proving that Lee-Jeong's measure of macroscopicity is a non-classicality measure. We note that the evaluation of the Lee-Jeong measure is computationally more efficient than the Wigner negativity. Exploring the relationship between quantumness and performance by examining a broad range of initial states and varying hyperparameters, we observe that quantumness in some cases improves the learning performance. However, our investigation reveals that an indiscriminate increase in quantumness does not consistently lead to improved outcomes, necessitating caution in its application. We discuss this phenomenon and attempt to identify conditions under which a high quantumness results in improved performance.