# Szegedy Quantum Walks with Memory on Regular Graphs

## TL;DR

This paper introduces a general model of Szegedy quantum walks with memory on regular graphs, revealing their relation to coined quantum walks with memory and uncovering new results through transformation techniques.

## Contribution

It presents a unified framework for Szegedy quantum walks with memory and establishes their connection to coined quantum walks with memory, enabling new insights.

## Key findings

- Relation between Szegedy and coined QWM established
- Transformation method reveals new properties of QWM
- Enhanced understanding of quantum walk memory effects

## Abstract

Quantum walks with memory(QWM) are a type of modified quantum walks that record the walker's latest path. The general model of coined QWM is presented in Phys. Rev. A 93, 042323 (2016). In this paper, we present general model of Szegedy QWM. Importantly, the relation of coined QWM and Szegedy QWM is revealed. By transforming coined QWM to Szegedy QWM, some amazing results about QWM are founded.