Optimal parametrizations of adiabatic paths
Quantum Physics
2013-05-29 v3 Mathematical Physics
math.MP
Abstract
The parametrization of adiabatic paths is optimal when tunneling is minimized. Hamiltonian evolutions do not have unique optimizers. However, dephasing Lindblad evolutions do. The optimizers are simply characterized by an Euler-Lagrange equation and have a constant tunneling rate along the path irrespective of the gap. Application to quantum search algorithms recovers the Grover result for appropriate scaling of the dephasing. Dephasing rates that beat Grover imply hidden resources in Lindblad operators.
Keywords
Cite
@article{arxiv.1003.2172,
title = {Optimal parametrizations of adiabatic paths},
author = {J. E. Avron and M. Fraas and G. M. Graf and P. Grech},
journal= {arXiv preprint arXiv:1003.2172},
year = {2013}
}
Comments
4 pages, 2 figures; To prevent from misunderstanding, we clarified the discussion of an apparent speedup in the Grover algorithm; figures improved + minor changes