Quantitative approach to Grover's quantum walk on graphs

TL;DR

This paper explores a novel optimization method for Grover's quantum search algorithm on graphs by fixing graph topology and varying Laplacians, aiming to improve search efficiency through analytical structure tuning.

Contribution

It introduces an alternative approach to optimize Grover's algorithm on graphs by fixing topology and adjusting Laplacians, diverging from traditional topology-based optimization.

Findings

Proposes fixing graph topology and tuning Laplacians for better search outcomes

Provides an example with a tunable graph Laplacian to demonstrate the approach

Discusses strategies for assessing the optimality of the quantum walk algorithm

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.