Quantum ant colony algorithm (QACA) is an efficient biological evolutionary algorithm. It combines quantum theory with traditional ant colony optimization algorithm (ACO). It is mainly applied to the solving of fault diagnosis,path planning,image segmentation. Based on the process of ACO,this paper introduces the quantum theory foundation of QACA and how it is applied to QACA. The advantages of QACA over ACO are analyzed by applying them to several examples of traveling salesman problem. Current research often uses discrete indexes to evaluate different algorithms,and it is difficult to intuitively display the differences of algorithms. In view of that,a comprehensive evaluation method for algorithm search efficiency is proposed. It is successfully applied to the comparison between QACA and ACO.