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Title: Solution to the quantum Zermelo navigation problem
Authors: Brody, DC
Meier, DM
Keywords: Time-optimal control Hamiltonian;Unitary gate;Uncontrollable ambient Hamiltonian;Zermelo navigation problem
Issue Date: 2015
Publisher: American Physical Society
Citation: Physical Review Letters, 2015, Forthcoming, 114
Abstract: The solution to the problem of finding a time-optimal control Hamiltonian to generate a given unitary gate, in an environment in which there exists an uncontrollable ambient Hamiltonian (e.g., a background field), is obtained. In the classical context, finding the time-optimal way to steer a ship in the presence of a background wind or current is known as the Zermelo navigation problem, whose solution can be obtained by working out geodesic curves on a space equipped with a Randers metric. The solution to the quantum Zermelo problem, which is shown here to take a remarkably simple form, is likewise obtained by finding explicit solutions to the geodesic equations of motion associated with a Randers metric on the space of unitary operators. The result reveals that the optimal control in a sense `goes along with the wind'.
ISSN: 1079-7114
Appears in Collections:Dept of Mathematics Research Papers

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