Bellman equations for optimal feedback control of qubit states

Abstract

Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser's amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of diffusive and counting measurements for vacuum field states. A full exact solution of the optimal control problem is given for a system with simpler, linear, dynamics. These linear dynamics can be obtained physically by considering a two-level atom in a strongly driven, heavily damped, optical cavity.

10 pages, no figures, replaced the simpler model in section 5

References in corpus (9)

• Quantum feedback control and classical control theory
• Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
• Feedback control of quantum state reduction
• Adaptive homodyne measurement of optical phase
• Quantum Computation with Vibrationally Excited Molecules
• Quantum Continual Measurements and a Posteriori Collapse on CCR
• Spin squeezing via quantum feedback
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Stochastic Schrodinger equations

Cited by in corpus (24)

• Quantum games: a review of the history, current state, and interpretation
• A discrete invitation to quantum filtering and feedback control
• Optimal Quantum Filtering and Quantum Feedback Control
• Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control
• A Quantum Langevin Formulation of Risk-Sensitive Optimal Control
• Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols
• On the separation principle of quantum control
• Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem
• Dynamical programming of continuously observed quantum systems
• Quantum filtering: a reference probability approach
• Weak measurement and rapid state reduction in bipartite quantum systems
• An introduction to quantum filtering
• Poisson and Diffusion Approximation of Stochastic Schrodinger equations with Control
• Ultracold Rydberg Atoms in a Ioffe-Pritchard Trap
• Eventum Mechanics of Quantum Trajectories: Continual Measurements, Quantum Predictions and Feedback Control
• Belavkin Filtering with Squeezed Light Sources
• Global versus local optimality in feedback-controlled qubit purification: new insights from minimizing Rényi entropies
• Applications of Feedback Control in Quantum Systems
• Quantum Trajectories for Squeezed Input Processes: Explicit Solutions
• Synthesis of stabilizing switched controllers for N-dimensional quantum angular momentum systems
• Optimal rotation control for a qubit subject to continuous measurement
• Control of Quantum Systems Despite Feedback Delay
• Discrete Quantum Control - State Preparation
• Performance Bounds for Quantum Feedback Control