SQUWALS: A Szegedy QUantum WALks Simulator

Abstract

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, a memory‐saving algorithm is proposed that scales as with the size of the graph. Additional procedures are provided for simulating Szegedy's quantum walk over mixed states and also the Semiclassical Szegedy walk. With these techniques, a classical simulator in Python called SQUWALS (Szegedy QUantum WALks Simulator) has been built. It is shown that the simulator scales as 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.