An Improved Quantum Projection Filter

TL;DR

This paper introduces an improved quantum projection filter with an optimality analysis, enhancing approximation accuracy for open quantum systems using quantum information geometry techniques.

Contribution

It extends previous quantum projection filtering schemes by incorporating an optimality analysis through a reformulation based on minimizing a stochastic Taylor expansion.

Findings

Better approximation performance demonstrated in qubit simulations

Reformulation reduces the difference between true and approximate quantum trajectories

Utilizes quantum information geometric techniques for filter optimization

Abstract

This work extends the previous quantum projection filtering scheme in [Gao Q., Zhang G., & Petersen I. R. (2019). An exponential quantum projection filter for open quantum systems. \emph{Automatica}, 99, 59-68.], by adding an optimality analysis result. A reformulation of the quantum projection filter is derived by minimizing the truncated Stratonovich stochastic Taylor expansion of the difference between the true quantum trajectory and its approximation on a lower-dimensional submanifold through quantum information geometric techniques. Simulation results for a qubit example demonstrate better approximation performance for the new quantum projection filter.