Optimal Quantum Feedback Control via Quantum Dynamic Programming

We describe the quantum filtering dynamics for a diffusive non-demolition measurement on an open quantum system. This is then used to determine appropriate feedback controls for the system and the quantum Bellman equation for optimal quantum feedback control is derived. These equations are demonstrated on the fully solvable model of the multi-dimensional controllable quantum particle in a quadratic potential with a noisy environment. We observe a duality between the solutions of quantum filtering and optimal quantum control for this example and note many similarities to the corresponding classical problem.

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