Gradient flow for controlling quantum ensemble

TL;DR

This paper introduces a gradient-based dynamical system to optimize quantum observables in finite-dimensional quantum ensembles, analyzing its convergence and addressing challenges posed by singular controls.

Contribution

It presents a novel gradient flow approach for quantum control problems and analyzes its convergence properties under regularity assumptions.

Findings

The dynamical system converges to solutions of the maximization problem under certain conditions.

The paper identifies difficulties caused by singular controls in the convergence process.

Convergence analysis provides insights into quantum control optimization.

Abstract

We propose in this paper a gradient-type dynamical system to solve the problem of maximizing quantum observables for finite dimensional closed quantum ensembles governed by the controlled Liouville-von Neumann equation. The asymptotic behavior is analyzed: we show that under the regularity assumption on the controls the dynamical system almost always converges to a solution of the maximization problem; we also detail the difficulties related to the occurrence of singular controls.