Optimal control with a multidimensional quantum invariant

TL;DR

This paper introduces a Gaussian invariant approach to optimize control in high-dimensional quantum systems, specifically for quadratic Hamiltonians, simplifying complex problems like ion shuttling.

Contribution

It proposes a new Gaussian invariant method compatible with quadratic Hamiltonians to enhance quantum optimal control in high-dimensional systems.

Findings

Gaussian invariant reduces computational complexity

Applicable to systems with multiple motional degrees of freedom

Facilitates ground-state-to-ground-state shuttling in trapped ions

Abstract

Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity of such problems, but it requires the knowledge of an invariant compatible with the Hamiltonian of the system in question. We explore the potential of a Gaussian invariant that is suitable for quadratic Hamiltonians with any given number of motional degrees of freedom for quantum optimal control problems that are inspired by current challenges in ground-state-to-ground-state shuttling of trapped-ions.