Success criteria for quantum search on graphs

TL;DR

This paper investigates the conditions under which quantum search algorithms succeed on graphs, providing a definitive criterion that distinguishes graphs suitable for efficient quantum search from those that are not.

Contribution

The authors establish a new criterion that determines the success of quantum search on graphs, resolving an open question in the field.

Findings

Identified a specific criterion for successful quantum search on graphs

Showed that properties like connectivity and symmetry are not reliable indicators

Provided a definitive condition for quantum search success

Abstract

We consider quantum search on graphs. Recently, it has been shown that the graph properties like connectivity, global symmetry, or regularity cannot serve as a reliable criteria that must be satisfied by a graph to allow a successful quantum search. It is an open question whether it is possible to find such a criteria. We solve this question by giving an affirmative answer.