Bilinear dynamic mode decomposition for quantum control

TL;DR

This paper introduces bilinear dynamic mode decomposition (biDMD), a data-driven, physics-informed regression method for quantum system identification and optimal control, capable of real-time adaptation with minimal data.

Contribution

The paper develops biDMD, a novel regression framework leveraging Hamiltonian structure for quantum control, integrating stroboscopic sampling and strong theoretical foundations in Koopman theory.

Findings

biDMD accurately models quantum dynamics

It requires minimal data compared to machine learning methods

The approach matches experimental results on quantum systems

Abstract

Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates non-linear dynamics with linear operators. In comparison with many machine learning paradigms, it requires minimal data and the biDMD model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.