Robust Learning Control Design for Quantum Unitary Transformations

TL;DR

This paper introduces an extended sampling-based learning control method with gradient flow to design robust quantum unitary transformations, effectively handling uncertainties in quantum systems.

Contribution

It develops a systematic SLC approach with gradient flow for robust quantum control, applicable to various quantum systems and uncertainties.

Findings

Effective in three different quantum systems

Improves fidelity under uncertainties

Demonstrates potential for practical quantum control

Abstract

Robust control design for quantum unitary transformations has been recognized as a fundamental and challenging task in the development of quantum information processing due to unavoidable decoherence or operational errors in the experimental implementation of quantum operations. In this paper, we extend the systematic methodology of sampling-based learning control (SLC) approach with a gradient flow algorithm for the design of robust quantum unitary transformations. The SLC approach first uses a "training" process to find an optimal control strategy robust against certain ranges of uncertainties. Then a number of randomly selected samples are tested and the performance is evaluated according to their average fidelity. The approach is applied to three typical examples of robust quantum transformation problems including robust quantum transformations in a three-level quantum system, in a superconducting quantum circuit, and in a spin chain system. Numerical results demonstrate the effectiveness of the SLC approach and show its potential applications in various implementation of quantum unitary transformations.