Optimal control, geometry, and quantum computing
Quantum Physics
2009-11-13 v2
Abstract
We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, subriemannian, and Finslerian manifolds. These results generalize the results of Nielsen, Dowling, Gu, and Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity can be related to distances on a Riemannian manifold
Cite
@article{arxiv.quant-ph/0603160,
title = {Optimal control, geometry, and quantum computing},
author = {Michael A. Nielsen and Mark R. Dowling and Mile Gu and Andrew C. Doherty},
journal= {arXiv preprint arXiv:quant-ph/0603160},
year = {2009}
}
Comments
7 Pages Added Full Names to Authors