Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle problem
Abstract
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a Hamiltonian cycle problem, using different models of computations and especially the probabilistic and quantum ones. Starting from the classical probabilistic approach of random walks, we take a step to the quantum direction by involving an ad hoc designed Quantum Turing Machine (QTM), which can be a useful conceptual project tool for quantum algorithms. Introducing several constraints to the graphs, our analysis leads to not-exponential speedup improvements to the best-known algorithms. In particular, the results are based on bounded degree graphs (graphs with nodes having a maximum number of edges) and graphs with the right limited number of nodes and edges to allow them to outperform the other algorithms.
Cite
@article{arxiv.2311.10941,
title = {Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle problem},
author = {Giuseppe Corrente and Carlo Vincenzo Stanzione and Vittoria Stanzione},
journal= {arXiv preprint arXiv:2311.10941},
year = {2023}
}
Comments
18 pages, 3 figures. It will appear in Journal of Quantum Computing, Tech Science Press