Robust control of linear systems and shortcut to adiabaticity based on superoscillations

TL;DR

This paper develops a novel control framework for linear quantum systems using superoscillations, enhancing robustness and energy efficiency, with applications in quantum control, sensing, and thermodynamics.

Contribution

It introduces a generalized inverse engineering formalism based on superoscillations for robust quantum control under energy and Fourier space constraints.

Findings

Effective control strategies for quantum systems demonstrated.

Enhanced sensing capabilities through optimized control.

Applicable to both dissipative and non-dissipative quantum regimes.

Abstract

With the advent of quantum technologies, control issues are becoming increasingly important. In this article, we address the control in phase space under a global constraint provided by a minimal energy-like cost function and a local (in Fourier space) constraint resulting from a robustness criterion. The inverse engineering Lagrangian formalism developed here generalizes the one commonly used to describe the superoscillation phenomenon. It is applied to both non-dissipative and dissipative quantum mechanics, and extended to stochastic thermodynamics. Interestingly, our approach also allows to improve the sensing capabilities by an appropriate control of the system.