Correlations Between Quantumness and Learning Performance in Reservoir Computing with a Single Oscillator

Arsalan Motamedi, Hadi Zadeh-Haghighi, Christoph Simon

Abstract: 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. We prove that Lee-Jeong's measure of macroscopicity is a non-classicality measure, and use it along with the Wigner negativity in our study of quantumness. We note that the evaluation of the Lee-Jeong measure is computationally more efficient than the Wigner negativity. Interestingly, we observe correlations between non-classicality and training accuracy in learning the MG series, suggesting that quantumness could be a valuable resource in reservoir computing. We, moreover, discriminate quantumness from complexity (dimensionality), and show that quantumness correlates more strongly with learning performance.