Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system

Abstract

We analyze the control of the motion of a charged particle by means of an external electric field. The system is constrained to move along a given direction. The goal of the control is to change the speed of the particle in a fixed time with zero initial and final accelerations, while minimizing a cost functional in order to achieve a smooth transport of the system. We solve this linear control problem by using shortcut to adiabaticity methods and optimal control techniques. STA protocols are built upon local constraints. By extending the number of space variables, we explain how optimal control protocols can accommodate for such constraints and provide robust solutions against slight initial and final time uncertainties. Conversely, optimal control can guide the choice of the class of functions involved in STA processes. Such mutual benefices of the two approaches remain valid beyond the specific example studied here.

31 pages (with the supplementary material), 5 figures

References in corpus (5)

• Shortcut to adiabatic passage in two and three level atoms
• Modeling and Control of Quantum Systems: An Introduction
• Singular extremals for the time-optimal control of dissipative spin 1/2 particles
• Transport in a harmonic trap: shortcuts to adiabaticity and robust protocols
• Searching for quantum optimal controls in the presence of singular critical points

Cited by in corpus (4)

• Exploiting Landscape Geometry to Enhance Quantum Optimal Control
• Connection between inverse engineering and optimal control in shortcuts to adiabaticity
• Optimal control of uniformly heated granular fluids in linear response
• Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control