Feedback Stabilization of Perturbed Quantum Systems via Reduced Filters

In practical scenarios, quantum systems often encounter significant uncertainties-such as unknown initial states, imprecise physical parameters, and unmodeled noise that challenge robust quantum control. We propose a feedback approach leveraging a reduced quantum filter capable of handling both Hamiltonian perturbations and additional unmodeled dissipative dynamics, without requiring prior knowledge of initial states or precise system parameters. Notably, the reduced filter tracks only $\mathcal{O}(N)$ real parameters instead of $\mathcal{O}\left(N^{2}\right)$, where $N$ is the Hilbert space dimension. By substantially lowering the dimensionality of the filter, this method significantly simplifies real-time implementation and offers a scalable path to robust quantum control in uncertain environments.