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arXiv · 1409.3204

Solution to the quantum Zermelo navigation problem

Dorje C. Brody·David Meier
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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'.

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Dorje C. Brody, David Meier. 2014-09-10. Solution to the quantum Zermelo navigation problem. https://doi.org/10.1103/physrevlett.114.100502

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