Abstract: Quantum shortcuts to adiabaticity (STA) constitutes a class of control protocols to reproduce the outcome of an adiabatic process within a finite evolution time. Among these control protocols, the inverse-engineering approach, based on the Lewis-Riesenfeld invariant theory, constructs an auxiliary Hamiltonian that satisfies the invariant equation and prescribes a time-dependent trajectory for the system parameters, thereby enabling precise steering of the quantum state to a desired target under specified boundary conditions. In this work, we apply the STA inverse-engineering approach to a quantized resistorinductor- capacitor (RLC) circuit. By accurately engineering the driving frequency, we achieve effective regulation of the quantum RLC circuit dynamics. Furthermore, the inverse-engineering approach framework is extended to memristive systems, where our results demonstrate that this approach can effectively stabilize the nonlinear output of a memristor and guide its dynamical evolution toward the prescribed state. Finally, based on this controllable memristor model, we construct memristor arrays and explore their implementation in reservoir computing, achieving efficient simulation and prediction of random input signals.

Key words: inverse-engineering, memristor, reservoir computing