Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed

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.

13 pages, 4 figures

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• Deterministic generation of Gaussian pure state in quasi-local dissipative system
• Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups
• Exact stabilization of entangled states in finite time by dissipative quantum circuits
• Control landscape for ultrafast manipulation by a qubit
• Switching Quantum Dynamics for Fast Stabilization
• Zeroth law of thermodynamics for thermalized open quantum systems having integrals of motion
• Information flow and error scaling for fully-quantum control
• Ground-state Stabilization of Open Quantum Systems by Dissipation
• Noisy Coherent Population Trapping: Applications to Noise Estimation and Qubit State Preparation
• A proposal of adaptive parameter tuning for robust stabilizing control of $N$--level quantum angular momentum systems
• Eigenvalue Attraction
• Improving robustness of quantum feedback control with reinforcement learning
• Modelling and Control of Quantum Measurement Induced Backaction in Double Quantum Dots
• Reachability, Coolability, and Stabilizability of Open Markovian Quantum Systems with Fast Unitary Control
• Subspace Stabilization Analysis for Non-Markovian Open Quantum Systems
• Alternating Projections Methods for Discrete-time Stabilization of Quantum States
• Model-Free Quantum Stabilization via Finite-Difference Lyapunov Control