Continuous-Time Quantum Search on Balanced Trees
Quantum Physics
2016-03-09 v1
Abstract
We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use analytical and numerical arguments to show that the exponent of the asymptotic running time changes uniformly from to as the searched-for site is moved from the root of the tree towards the leaves. These results imply that the time complexity of the quantum search algorithm on a balanced tree is closely correlated with certain path-based centrality measures of the searched-for site.
Cite
@article{arxiv.1601.01154,
title = {Continuous-Time Quantum Search on Balanced Trees},
author = {Pascal Philipp and Luís Tarrataca and Stefan Boettcher},
journal= {arXiv preprint arXiv:1601.01154},
year = {2016}
}