English

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 Nβ\sim N^{\beta} changes uniformly from β=0.5\beta=0.5 to β=1\beta=1 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.

Keywords

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}
}
R2 v1 2026-06-22T12:23:58.333Z