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Bulletin of the American Physical Society

Optimal control in presence of decoherence and measurement imperfections: Pure state preparation problem

Alireza Shabani

Published Mar 20, 2013• 0 citations
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In this article we analyze the optimal control strategy for rotating a monitored qubit from an initial pure state to an orthogonal state in minimum time. This strategy is described for two different cost functions of interest which do not have the usual regularity properties. Hence, as classically smooth cost functions may not exist, we interpret these functions as viscosity solutions to the optimal control problem. Specifically we prove their existence and uniqueness in this weak-solution setting. In addition, we also give bounds on the time optimal control to prepare any pure state from a mixed state.
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