Dynamic Programming Principle and Stabilization for Mean-Field Quantum Filtering Systems

TL;DR

This paper develops a dynamic programming approach for mean-field quantum filtering systems and demonstrates stabilization and exponential convergence to target states in monitored qubit networks.

Contribution

It introduces a dynamic programming principle in an infinite-dimensional setting and proves stabilization results for mean-field quantum systems.

Findings

Established a dynamic programming principle in Hilbert-Schmidt space.

Proved quantum state reduction and exponential convergence in mean-field limit.

Demonstrated stabilization of monitored qubit systems using feedback laws.

Abstract

Working within the quantum filtering framework, we establish a dynamic programming principle in an infinite-dimensional setting by embedding the state space into the Hilbert-Schmidt space. We then study a stabilization problem for continuously monitored Ising-coupled qubits and, in the mean-field limit, demonstrate quantum state reduction together with exponential convergence toward prescribed eigenstates under suitable feedback laws.