Giuseppe Corrente^1,2,*, Carlo Vincenzo Stanzione^3,4, Vittoria Stanzione⁵

Journal of Quantum Computing, Vol.5, pp. 55-70, 2023, DOI:10.32604/jqc.2023.044786

Abstract 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,… More >

Giuseppe Corrente^*

Journal of Quantum Computing, Vol.2, No.3, pp. 137-145, 2020, DOI:10.32604/jqc.2020.014586

Abstract We want in this article to show the usefulness of Quantum Turing Machine (QTM) in a high-level didactic context as well as in theoretical studies. We use QTM to show its equivalence with quantum circuit model for Deutsch and Deutsch-Jozsa algorithms. Further we introduce a strategy of translation from Quantum Circuit to Quantum Turing models by these examples. Moreover we illustrate some features of Quantum Computing such as superposition from a QTM point of view and starting with few simple examples very known in Quantum Circuit form. More >