Abstracts
Poster Abstracts | Talk Abstracts
Quantum brachistochrone curves as geodesics
Presenting Author: Xiaoting Wang, Louisiana State University
Contributing Author(s): Michele Allegra,
Kurt Jacobs,
Seth Lloyd,
Cosmo Lupo,
Masoud Mohseni
Quantum control provides a useful tool to design the physical process of implementing a quantum logic gate. In this work, we will give a brief introduction to the quantum time-optimal control problem with energy constraints, and how the problem was studied historically. We will focus on our recent work on this problem, and how to utilize sub-Riemannian geometry to formulate the solution as a limit of geodesic curves that can be efficiently solved. Such a brachistochrone-geodesic connection turns out to be a useful tool to study gate complexity problems. We will also show that the controllability analysis combined with Pontryagin maximum principle gives a nice classification of all time-optimal problems, which is applicable to any QIP device characterized by a set of implementable Hamiltonians.
Read this article online: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.170501
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