Quantum model reduction for continuous-time quantum filters

TL;DR

This paper introduces a systematic method for deriving exact reduced-order quantum filters that preserve the evolution of specific expectation values, enhancing efficiency in quantum system simulation and control.

Contribution

It presents a novel, exact reduction technique for quantum filters using minimal realization and non-commutative expectations, unlike prior approximate methods.

Findings

Successfully applied to prototypical examples

Enables smaller, exact quantum filters

Facilitates quantum trajectory simulation and feedback control

Abstract

The use of quantum stochastic models is widespread in dynamical reduction, simulation of open systems, feedback control and adaptive estimation. In many applications only part of the information contained in the filter's state is actually needed to reconstruct the target observable quantities; thus, filters of smaller dimensions could be in principle implemented to perform the same task.In this work, we propose a systematic method to find, when possible, reduced-order quantum filters that are capable of exactly reproducing the evolution of expectation values of interest. In contrast with existing reduction techniques, the reduced model we obtain is exact and in the form of a Belavkin filtering equation, ensuring physical interpretability.This is attained by leveraging tools from the theory of both minimal realization and non-commutative conditional expectations. The proposed procedure is tested on prototypical examples, laying the groundwork for applications in quantum trajectory simulation and quantum feedback control.