Trapped-ion quantum memristor reservoir reaches degree-100 monomials while classical echo state networks stall past 40

A trapped-ion quantum memristor can serve as the core element of a reservoir computer, mapping an input sequence into a high-dimensional quantum state for readout. Quantum memristors had largely remained device proposals or demonstrations on photonic and superconducting platforms, without evaluation inside a full reservoir-computing framework for nonlinear capacity. The reservoir is compared against classical echo state networks and cubic regression with memory across monomial approximation, NARMA2, NARMA10, NARMA10-st, Mackey–Glass and Santa Fe benchmarks.

The advantage of the quantum memristor reservoir widens as the degree of the monomial target grows. Classical echo state networks match quantum accuracy with small reservoirs at low degrees, but the required size rises quickly with degree. Two coupled quantum memristors with two chip passes keep test MSE below 10^-2 up to d=100, raising readout weights from 25 to 50, while classical echo state networks fail beyond about d=40 even at 2000 nodes and show no improvement with increasing size.

The reservoir's computational resource is mainly nonlinear mapping rather than dynamical memory. On the memory-dominated NARMA10 and NARMA10-st tasks, adding coherences, extra unitaries or two-memristor architectures brings almost no gain. Scanning the exponential smoothing parameter m from 1.01 to 1000 while re-optimizing all other parameters leaves test MSE essentially stable, with only shallow minima at small m for NARMA2 and Mackey–Glass.

Sensitivity to gate-angle noise depends on the task type. Monomial approximation needs precise gate control, whereas time-series tasks carry intrinsic temporal redundancy. Across 20 independent simulations at each noise level from 0 to 0.2 rad, time-series test MSE stays stable over a wide range, while monomial accuracy degrades rapidly with noise, especially at high degrees.

The conclusions rest on numerical simulation covering monomial approximation, the NARMA family, Mackey–Glass and Santa Fe benchmarks; the authors note that an experimental implementation would still require repeated projective measurements and re-initialization at each time step and depends on composite laser pulses of finite fidelity.

The authors frame the work as a numerical proof of principle and note that a theoretical characterization of the functional basis spanned by the quantum memristor readout is still missing, and that scaling memory capacity remains an open question.