Sampling-based learning control of inhomogeneous quantum ensembles

TL;DR

This paper introduces a sampling-based learning control method to effectively steer inhomogeneous quantum ensembles to a desired state, addressing parameter dispersion challenges in quantum control.

Contribution

The paper presents a systematic SLC methodology combining sampling, training, and testing to optimize control of inhomogeneous quantum systems, a novel approach in quantum control.

Findings

Successful control of quantum ensembles demonstrated through numerical simulations.

The SLC method effectively compensates for parameter dispersion.

Control performance validated across different quantum systems.

Abstract

Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present a systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\Lambda$ type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find the control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented showing the success of the SLC method.