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arXiv:1906.02991 · Physical Review A

Stochastic learning control of inhomogeneous quantum ensembles

Gabriel Turinici

Published Nov 8, 2019• 23 citations
arXivHTMLPDF

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 used 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 three-dimensional and a six-dimensional case.

DOI
10.1103/physreva.100.053403

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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 Hamiltonian uncertainties. The SLC method includes two steps of “training” and “testing and evaluation”. In the training step, an augmented system is constructed by sampling uncertainties according to possible distributions of uncertainty parameters. A gradient flow based learning and optimization algorithm is adopted to find the control for the augmented system. In the process of testing and evaluation, a number of samples obtained through sampling the uncertainties are tested to evaluate the control performance. Numerical results demonstrate the success of the SLC approach. The SLC method has potential applications for robust control design of quantum systems.
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