J Gough et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S237 doi:10.1088/1464-4266/7/10/006
Hamilton–Jacobi–Bellman equations for quantum optimal feedback control
J Gough1, V P Belavkin2 and O G Smolyanov3
Show affiliationsWe exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton–Jacobi–Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton–Pontryagin set-up. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback. A controlled qubit with a feedback is considered as example.
- PACS
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42.50.Ar Photon statistics and coherence theory
03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Yz Decoherence; open systems; quantum statistical methods
- Subjects
- Dates
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Issue 10 (October 2005)
Received 14 March 2005, accepted for publication 27 June 2005
Published 14 September 2005
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Hamilton–Jacobi–Bellman equations for quantum optimal feedback control
J Gough et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 S237
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