Optimal Control of Quantum Spin Systems with Non-Zero Impulsive Control Costs

Pradip Das

Vasileios Evangelakos, Emmanuel Paspalakis, Dionisis Stefanatos

We derive STIRAP (stimulated Raman adiabatic passage) shortcuts to adiabaticity maximizing population transfer in a three-level $\mathrm{\ensuremath{\Lambda}}$ quantum system, using spin-to-spring mapping to formulate the corresponding optimal control problem on the simpler system of a classical driven dissipative harmonic oscillator. We solve the spring optimal control problem and obtain analytical expressions for the impulses, the durations of the zero control intervals, and the singular control, which are the elements composing the optimal pulse sequence. We also derive suboptimal solutions for the spring problem, one with less impulses than the optimal and others with smoother polynomial controls. We then apply the solutions derived for the spring system to the original system, and compare the population transfer efficiency with that obtained for the original system using numerical optimal control. For all dissipation rates used, the efficiency of the optimal spring control approaches that of the numerical optimal solution for longer durations, with the approach accomplished earlier for smaller decay rates. The efficiency achieved with the suboptimal spring control with less impulses is very close to that of the optimal spring control in all cases, while that obtained with polynomial controls lies below, and this is the price paid for not using impulses, which can quickly build a nonzero population in the intermediate state. The analysis of the optimal solution for the classical driven dissipative oscillator is not restricted to the system at hand but can also be applied in the transport of a coherent state trapped in a moving harmonic potential and the transport of a mesoscopic object in stochastic thermodynamics.

Kaspar Schmerling, Andreas Kugi, Andreas Deutschmann-Olek

We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for linear Gaussian systems to collect information from the temporal vicinity of the disturbance, we cast the minimization of disturbance estimation uncertainty as a nonlinear optimal control problem over time-dependent system parameters. The resulting method dynamically shapes the estimation covariances through parametric modulation, maximizing information gain at a known impulse time. This differs fundamentally from conventional squeezing protocols using periodic modulation that effectively degrade inference of impulse-like disturbances. Applied to nanomechanical resonators and levitated nanoparticles, optimal parametric driving reduces estimation variance by up to a factor of two relative to steady-state operation

Seth Merkel, Souma Chaudhury, Andrew Silberfarb +3 more

Victor Mukherjee, Vittorio Giovannetti, Rosario Fazio +3 more

M. R. James

This article explains some fundamental ideas concerning the optimal control of quantum systems through the study of a relatively simple two-level system coupled to optical fields. The model for this system includes both continuous and impulsive dynamics. Topics covered include open- and closed-loop control, impulsive control, open-loop optimal control, quantum filtering, and measurement feedback optimal control.