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 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.

RevTex 4.2, 16 pages, 9 color figures

References in corpus (2)

• Array Programming with NumPy
• Exponential algorithmic speedup by quantum walk

Cited by in corpus (3)

• Implementing Semiclassical Szegedy Walks in Classical-Quantum Circuits for Homomorphic Encryption
• Randomized SearchRank: A Semiclassical Approach to a Quantum Search Engine
• Complex-Phase Extensions of Szegedy Quantum Walk on Graphs