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Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle Problem

Giuseppe Corrente1,2,*, Carlo Vincenzo Stanzione3,4, Vittoria Stanzione5

1 Computer Science Department, Università di Torino, Torino, Italy
2 Computer Science Department, ITIS Avogadro Serale, Torino, Italy
3 Computer Engineering Department (DII), Università Degli Studi di Pisa, Pisa, 56122, Italy
4 Justonearth SRL, Roma, 00168, Italy
5 Physics Deparment E.Fermi, Università Degli Studi di Pisa, Pisa, 56127, Italy

* Corresponding Author: Giuseppe Corrente. Email: email

Journal of Quantum Computing 2023, 5, 55-70.


The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with 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 This Article

G. Corrente, C. V. Stanzione and V. Stanzione, "Comparison among classical, probabilistic and quantum algorithms for hamiltonian cycle problem," Journal of Quantum Computing, vol. 5, pp. 55–70, 2023.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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