Sampling-based Learning Control for Quantum Systems with Uncertainties

TL;DR

This paper introduces a sampling-based learning control method for quantum systems with uncertainties, employing a training and testing process to enhance robustness in quantum control tasks.

Contribution

It presents a systematic numerical approach combining sampling and gradient flow learning for robust quantum control design under uncertainties.

Findings

Effective control performance with large uncertainties

Successful application to quantum state preparation, entanglement generation, and entanglement control

Demonstrated robustness and potential for practical quantum system control

Abstract

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with uncertainties. The SLC method includes two steps of "training" and "testing". In the training step, an augmented system is constructed using artificial samples generated by sampling uncertainty parameters according to a given distribution. A gradient flow based learning algorithm is developed to find the control for the augmented system. In the process of testing, a number of additional samples are tested to evaluate the control performance where these samples are obtained through sampling the uncertainty parameters according to a possible distribution. The SLC method is applied to three significant examples of quantum robust control including state preparation in a three-level quantum system, robust entanglement generation in a two-qubit superconducting circuit and quantum entanglement control in a two-atom system interacting with a quantized field in a cavity. Numerical results demonstrate the effectiveness of the SLC approach even when uncertainties are quite large, and show its potential for robust control design of quantum systems.