Non-Markovian decoherence in the adiabatic quantum search algorithm
Abstract
We consider an adiabatic quantum algorithm (Grover's search routine) weakly coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum algorithm. We find that, under appropriate conditions (such as low temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most important. Hence the scalability of the adiabatic quantum algorithm depends on the infra-red behavior of the environment: a reasonably small coupling to the three-dimensional electromagnetic field does not destroy the scaling behavior, whereas phonons or localized degrees of freedom can be problematic. PACS: 03.67.Pp, 03.67.Lx, 03.67.-a, 03.65.Yz.
Cite
@article{arxiv.quant-ph/0608123,
title = {Non-Markovian decoherence in the adiabatic quantum search algorithm},
author = {Markus Tiersch and Ralf Schützhold},
journal= {arXiv preprint arXiv:quant-ph/0608123},
year = {2011}
}