# SQUWALS: A Szegedy QUantum WALks Simulator

arXiv: https://arxiv.org/abs/2307.14314 · HTML: https://mlsanity.com/paper/2307.14314/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [VQIL: Visible Quantum Interference Learning for Perturbation Response Ranking on Graphs](https://mlsanity.com/paper/2610.13689/) (2026)

## Abstract (arXiv)

Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a classical simulator. However, the current simulation algorithms require a great deal of memory due to the particular formulation of this quantum walk. In this paper we propose a memory-saving algorithm that scales as O(N2) with the size N of the graph. We provide additional procedures for simulating Szegedy's quantum walk over mixed states and also the Semiclassical Szegedy walk. With these techniques we have built a classical simulator in Python called SQUWALS. We show that our simulator scales as O(N2) in both time and memory resources. This package provides some high-level applications for algorithms based on Szegedy's quantum walk, as for example the quantum PageRank.