The optimal search on graph by continuous-time quantum walks

TL;DR

This paper develops a method to construct graphs that enable optimal quantum search for any state, analyzing how adding edges can enhance search performance.

Contribution

It introduces a new approach for designing optimal graphs for quantum search and examines how graph modifications affect search efficiency.

Findings

Certain states cannot be searched optimally on some graphs

Adding edges can improve quantum search performance

A method for constructing optimal graphs for arbitrary states

Abstract

Chakraborty and Leonardo have shown that a spatial search by quantum walk is optimal for almost all graphs. However, we observed that on some graphs, certain states cannot be searched optimally. We present a method for constructing an optimal graph that searches an arbitrary state and provides the optimal condition. We also analyze the monotonicity of the search performance and conclude that the search performance can be improved by adding edges.