Dynamical programming of continuously observed quantum systems
arXiv:0805.4741 · doi:10.1103/PhysRevA.79.022123
Abstract
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes, which correspond respectively to deterministic and stochastic Master Equation dynamics. For the quantum feedback control scheme with continuous non-demolition observations we exploit the separation theorem of filtering and control aspects for quantum stochastic dynamics to derive a generalized Hamilton-Jacobi-Bellman equation. If the control is restricted to only Hamiltonian terms this is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term. In this work, we consider, in particular, the case when control is restricted to only observation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure state from a mixed state of a quantum two-level system.
11 pages, no figures, published version
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- Errors in quantum optimal control and strategy for the search of easily implementable control pulses
- Global versus local optimality in feedback-controlled qubit purification: new insights from minimizing Rényi entropies
- Optimal rotation control for a qubit subject to continuous measurement
- Quantum measurements as a control resource
- Performance Bounds for Quantum Feedback Control