Optimal Quantum Filtering and Quantum Feedback Control

TL;DR

This paper develops a theory of nonlinear optimal quantum feedback control using quantum noise models, deriving a quantum Bellman equation and applying it to a solvable quantum LQG problem, highlighting parallels with classical control.

Contribution

It introduces a comprehensive framework for quantum feedback control based on quantum noise models and derives a quantum Bellman equation for optimal control.

Findings

Quantum Bellman equation formulated for quantum feedback control

Explicit solution for quantum linear-quadratic-Gaussian problem

Demonstrates similarities between quantum and classical control theories

Abstract

Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic control theory, we present the theory of nonlinear optimal quantum feedback control. The resulting quantum Bellman equation is then applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem which emphasizes many similarities with the corresponding classical control problem.