  Quantum ant colony optimization (QACO) has drew much attention since it
combines the advantages of quantum computing and ant colony optimization (ACO)
algorithms and overcomes some limitations of the traditional ACO algorithm.
However, due to the hardware resource limitations of currently available
quantum computers, such as the limited number of qubits, lack of high-fidelity
gating operation, and low noisy tolerance, the practical application of the
QACO is quite challenging. In this paper, we introduce a hybrid
quantum-classical algorithm by combining the clustering algorithm with QACO
algorithm, so that this extended QACO can handle large-scale optimization
problems, which makes the practical application of QACO based on available
quantum computation resource possible. To verify the effectiveness and
performance of the algorithm, we tested the developed QACO algorithm with the
Travelling Salesman Problem (TSP) as benchmarks. The developed QACO algorithm
shows better performance under multiple data set. In addition, the developed
QACO algorithm also manifests the robustness to noise of calculation process,
which is typically a major barrier for practical application of quantum
computers. Our work shows that the combination of the clustering algorithm with
QACO has effectively extended the application scenario of QACO in current NISQ
era of quantum computing.
