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This paper presents a new algorithm for solving the travelling salesman problem (TSP). The TSP is one of the most known combinatorial optimisation problems. It is about finding the shortest Hamiltonian cycle relating N cities. The algorithm is inspired from both genetic algorithms and quantum computing fields. It extends the standard genetic algorithms by combining them to some concepts and principles provided from quantum computing field such as quantum bit, states superposition and interference. The obtained results from the application of the proposed algorithm on some instances of TSP are significantly better than those provided by standard genetic algorithms.