Parameterized Quantum Query Algorithms for Graph Problems

TL;DR

This paper develops and analyzes parameterized quantum query algorithms for graph problems like vertex cover and matching, establishing their optimality and providing lower bounds on their complexity.

Contribution

It introduces new parameterized quantum query algorithms for specific graph problems and proves their near-optimality with lower bounds.

Findings

Algorithms are optimal up to a constant factor for small parameters.

Lower bounds on the quantum query complexity are established.

The work advances understanding of quantum query efficiency for graph problems.

Abstract

In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum query complexity. Then, we show that our quantum query algorithms are optimal up to a constant factor when the parameters are small.