Enhanced Nonlinear Capacity of a Trapped-Ion Quantum Memristor Reservoir

Abstract We present a numerical study of a quantum memristor (QM) reservoir based on a trapped-ion platform. The reservoir exploits nonlinear input-output mapping arising from Born-rule nonlinearity, quantum coherences, and feedback-induced fading memory to process classical time-series data.We benchmarked the performance of the QM reservoir on monomial approximation, NARMA, Mackey-Glass, and the Santa Fe time series, standard tasks in reservoir computing and quantum reservoir computing (QRC). The QM reservoir shows a clear memory-nonlinearity trade-off. Its nonlinear capacity scales favorably: two coupled QMs reproduce monomials xd up to degree d=100 with test MSE below 10-2, while classical echo state networks (ESNs) fail beyond d ≈ 40 and show no improvement with increasing size up to 2000 nodes. However, for memory-dominated tasks such as NARMA10, the same two-QM extension provides only marginal gains; the insensitivity of the test MSE to the memory decay parameter confirms that, in the present architecture, nonlinear expressivity rather than dynamical memory is the main computational resource. On standard time-series benchmarks, the QM reservoir matches the accuracy of small ESNs while using a comparable number of readout weights, and it remains robust against gate noise.Our results establish trapped-ion QMs as a competitive QRC platform with particular advantages in tasks dominated by strong nonlinearity.