# Stochastic learning control of inhomogeneous quantum ensembles

## TL;DR

This paper explores stochastic optimization methods like stochastic gradient descent and Adam for controlling inhomogeneous quantum ensembles, demonstrating their effectiveness in high-dimensional uncertainty scenarios.

## Contribution

It introduces stochastic search procedures for quantum control that handle high-dimensional uncertainties, improving upon fixed-grid approaches.

## Key findings

- Algorithms perform well against benchmarks
- Effective in 3D and 6D parameter spaces
- Handle high-dimensional uncertainties efficiently

## Abstract

In quantum control, the robustness with respect to uncertainties in the system's parameters or driving field characteristics is of paramount importance and has been studied theoretically, numerically and experimentally. We test in this paper stochastic search procedures (Stochastic gradient descent and the Adam algorithm) that sample, at each iteration, from the distribution of the parameter uncertainty, as opposed to previous approaches that use a fixed grid. We show that both algorithms behave well with respect to benchmarks and discuss their relative merits. In addition the methodology allows to address high dimensional parameter uncertainty; we implement numerically, with good results, a 3D and a 6D case.