Year: 2015
Type: article
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."
Source: Physical Review Letters
Authors: Dorje C. Brody, David M. Meier
Institutions: ITMO University, Brunel University of London
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2161035167