Discrete-time semiclassical Szegedy quantum walks

• Published in: Physica A Vol. 625; p. 129021
• Main Authors: Ortega, Sergio A., Martin-Delgado, Miguel A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-09-2023
• Subjects: Quantum computing; Quantum walk; Random walk; Semiclassical walk; Szegedy quantum walk; Semiclassical walk; Quantum computing; Quantum walk; Szegedy quantum walk; Random walk
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2023.129021

Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical and quantum dynamics. Specifically, a semiclassical walk can be understood as a classical walk where the transition matrix encodes the quantum evolution. We have applied this algorithm to Szegedy’s quantum walk, which can be applied to any arbitrary weighted graph. We first have solved the problem analytically on regular 1D cycles to show the performance of the semiclassical walks. Next, we have simulated our algorithm in a general inhomogeneous symmetric graph, finding that the inhomogeneity drives a symmetry breaking on the graph. Moreover, we show that this phenomenon is useful for the problem of ranking nodes in symmetric graphs, where the classical PageRank fails. We have demonstrated experimentally that the semiclassical walks can be applied on real quantum computers using the platform IBM Quantum.
•Semiclassical walks combine classical and quantum dynamics.•Semiclassical Szegedy walks break the symmetry of classical inhomogeneous graphs.•Semiclassical Szegedy walks can be implemented in actual quantum computers.