SQUWALS: A Szegedy QUantum WALks Simulator
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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(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 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.
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