Based on the combination of the quantum theory and ant colony optimization,a novel algorithm,the quantum ant colony algorithm,was proposed.Ants’s positions were represented by a group of quantum bits and the quantum rotation gates were designed to update the ants’ positions for enabling the ants’ movements.The classical TSP was successfully solved by using the quantum ant colony algorithm,taking series of typical instances as the examples.The computational results show the effectiveness and robustness of the algorithm in numerical simulations.The algorithm can find the satisfactory solutions with a small size of populations and minimal relative error.