A practical applicable quantum–classical hybrid ant colony algorithm for the NISQ era

Quantum ant colony optimization (QACO) has drew much attention since it combines the advantages of quantum computing and ant colony optimization (ACO) algorithm overcoming some limitations of the traditional ACO algorithm. However, due to the hardware resource limitations of currently available quantum computers, the practical application of the QACO is still not realized. In this paper, we developed a quantum–classical hybrid algorithm by combining the clustering algorithm with QACO algorithm. This extended QACO can handle large-scale optimization problems with currently available quantum computing resources. We have tested the effectiveness and performance of the extended QACO algorithm with the traveling salesman problem (TSP) as benchmarks and found the algorithm achieves better performance under multiple diverse datasets. In addition, we investigated the noise impact on the extended QACO and evaluated its operation possibility on current available noisy intermediate-scale quantum (NISQ) devices. Our work shows that the combination of the clustering algorithm with QACO effectively improved its problem-solving scale, which makes its practical application possible in the current NISQ era of quantum computing.