Stabilizing Quantum States by Constructive Design of Open Quantum Dynamics

Abstract

Based on recent work on the asymptotic behavior of controlled quantum Markovian dynamics, we show that any generic quantum state can be stabilized by devising constructively a simple Lindblad-GKS generator that can achieve global asymptotic stability at the desired state. The applications of such result is demonstrated by designing a direct feedback strategy that achieves global stabilization of a qubit state encoded in a noise-protected subspace.

Revised version with stronger proofs showing uniqueness can be achieved in all cases by using the freedom to the choose diagonal elements of both the Hamiltonian and Lindblad operator, and exploiting the fact that the non-existence of two orthogonal eigenvectors of the Lindblad operator is sufficient but not necessary for global asymptotic stability of the target state

References in corpus (2)

• Stabilizing Open Quantum Systems by Markovian Reservoir Engineering
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems

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• Alternating Projections Methods for Discrete-time Stabilization of Quantum States
• Model-Free Quantum Stabilization via Finite-Difference Lyapunov Control