Stabilization of Time-Varying Perturbed Quantum Systems via Reduced Filters

TL;DR

This paper introduces a reduced quantum filter for stabilizing time-varying perturbed quantum systems, offering robustness, computational efficiency, and scalability without prior knowledge of system states or parameters.

Contribution

A novel reduced quantum filter that estimates only diagonal elements, simplifying computation while ensuring robustness and stability in quantum feedback control.

Findings

Achieves robustness against Hamiltonian perturbations and environmental noise.

Reduces computational complexity from O(N^2) to O(N) variables.

Ensures global exponential stability of the target subspace.

Abstract

In practical applications, quantum systems are inevitably subject to significant uncertainties, including unknown initial states, imprecise physical parameters, and unmodeled environmental noise, all of which pose major challenges to robust quantum feedback control. This paper proposes a feedback stabilization strategy based on a reduced quantum filter that achieves robustness against time-varying Hamiltonian perturbations and additional dissipative effects, without requiring prior knowledge of the initial state or exact system parameters. The proposed filter estimates only O(N) real variables corresponding to the diagonal elements of the system density matrix in a quantum non-demolition basis in contrast to the O(N^2) variables required by a full stochastic master equation, where N is the Hilbert space dimension. This dimensionality reduction substantially simplifies real-time computation and feedback implementation while preserving both convergence and robustness guarantees. Rigorous analysis further establishes global exponential stability of the target subspace. The results provide a scalable framework for robust and efficient measurement-based feedback control applicable to high-dimensional perturbed open quantum systems.