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arXiv · 2307.14314

SQUWALS: A Szegedy QUantum WALks Simulator

Sergio A. Ortega·Miguel A. Martin-Delgado
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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 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.

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Sergio A. Ortega, Miguel A. Martin-Delgado. 2023-07-26. SQUWALS: A Szegedy QUantum WALks Simulator. https://doi.org/10.1002/qute.202400022

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