Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed

TL;DR

This paper explores how Hamiltonian control can stabilize quantum states and enhance convergence speed in finite-dimensional open quantum systems, providing a framework for designing effective control strategies.

Contribution

It introduces a dissipation-induced decomposition method for analyzing and synthesizing controls to stabilize states and optimize convergence in Markovian quantum systems.

Findings

Dissipation-induced decomposition aids stability analysis.

Control strategies can be designed for rapid convergence.

Applications demonstrated in quantum optics and NV centers.

Abstract

We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-independent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed. For a generic Lindblad master equation, we introduce a dissipation-induced decomposition of the associated Hilbert space, and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence. The resulting design principles are illustrated in realistic Markovian control settings motivated by quantum information processing, including quantum-optical systems and nitrogen-vacancy centers in diamond.