  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 $\mathcal{O}(N^2)$
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 $\mathcal{O}(N^2)$ 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.
