Quantum Computing represents the most promising technology towards speed boost in computation, opening the possibility of major breakthroughs in several disciplines including Artificial Intelligence. This paper investigates the performance of a novel Ant Colony Optimization (ACO) algorithm for the realization (compilation) of nearest-neighbor compliant quantum circuits of minimum duration. In fact, current technological limitations (e.g., decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized, and therefore the production of minimum-makespan compiled circuits for present and future quantum machines is of paramount importance. In our ACO algorithm (QCC-ACO), we introduce a novel pheromone model, and we leverage a heuristic-based Priority Rule to control the iterative selection of the quantum gates to be inserted in the solution.

The proposed QCC-ACO algorithm has been tested on a set of quantum circuit benchmark instances of increasing sizes available from the recent literature. We demonstrate that the QCC-ACO obtains results that outperform the current best solutions in the literature against the same benchmark, succeeding in significantly improving the makespan values for a great number of instances and demonstrating the scalability of the approach.