Quantitative approach to Grover's quantum walk on graphs
Mathematical Physics
2022-07-06 v1 math.MP
Quantum Physics
Abstract
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding specific graph topologies convenient for the related quantum walk, we fix the graph topology and vary the underlying graph Laplacians. As a result, we search for the most appropriate analytical structure on graphs endowed with fixed topologies yielding better search outcomes. We discuss strategies to investigate the optimality of Grover's algorithm and provide an example with an easy tunable graph Laplacian to investigate our ideas.
Cite
@article{arxiv.2207.01686,
title = {Quantitative approach to Grover's quantum walk on graphs},
author = {Gamal Mograby and Radhakrishnan Balu and Kasso A. Okoudjou and Alexander Teplyaev},
journal= {arXiv preprint arXiv:2207.01686},
year = {2022}
}