Parameter estimation and system identification for continuously-observed quantum systems

TL;DR

This paper reviews methods for estimating parameters and identifying models of quantum systems through continuous measurement, highlighting recent advances in quantum Fisher information and black-box modeling techniques.

Contribution

It provides a comprehensive overview of quantum parameter estimation, system identification, and introduces empirical methods for black-box modeling of quantum systems.

Findings

Quantum Fisher information characterizes output sensitivity to parameters.

Continuous-time measurements relate to quantum Zakai equations.

Empirical methods enable black-box modeling of quantum systems.

Abstract

This paper gives an overview of parameter estimation and system identification for quantum input-output systems by continuous observation of the output field. We present recent results on the quantum Fisher information of the output with respect to unknown dynamical parameters. We discuss the structure of continuous-time measurements as solutions of the quantum Zakai equation, and their relationship to parameter estimation methods. Proceeding beyond parameter estimation, the paper also gives an overview of the emerging topic of quantum system identification for black-box modeling of quantum systems by continuous observation of a traveling wave probe, for the case of ergodic quantum input-output systems and linear quantum systems. Empirical methods for such black-box modeling are also discussed.