# Partition of graphs and quantum walk based search algorithms

## TL;DR

This paper introduces a graph partitioning technique called equitable partition to optimize quantum walk-based search algorithms by reducing problem size through effective subspace determination.

## Contribution

It extends equitable partition concepts to quantum walk algorithms, enabling more efficient search by reducing the problem's effective subspace.

## Key findings

- Effective subspace can be determined using equitable partition
- Reduced operators improve search efficiency
- Method applicable to various graph structures

## Abstract

In this paper, we show reduction methods for search algorithms on graphs using quantum walks. By using a graph partitioning method called equitable partition for the the given graph, we determine "effective subspace" for the search algorithm to reduce the size of the problem. We introduce the equitable partition for quantum walk based search algorithms and show how to determine "effective subspace" and reduced operator.