We propose a new hybrid quantum algorithm based on the classical Ant Colony
Optimization algorithm to produce approximate solutions for NP-hard problems,
in particular optimization problems. First, we discuss some previously proposed
Quantum Ant Colony Optimization algorithms, and based on them, we develop an
improved algorithm that can be truly implemented on near-term quantum
computers. Our iterative algorithm codifies only the information about the
pheromones and the exploration parameter in the quantum state, while
subrogating the calculation of the numerical result to a classical computer. A
new guided exploration strategy is used in order to take advantage of the
quantum computation power and generate new possible solutions as a
superposition of states. This approach is specially useful to solve constrained
optimization problems, where we can implement efficiently the exploration of
new paths without having to check the correspondence of a path to a solution
before the measurement of the state. As an example of a NP-hard problem, we
choose to solve the Quadratic Assignment Problem. The benchmarks made by
simulating the noiseless quantum circuit and the experiments made on IBM
quantum computers show the validity of the algorithm.Comment: 19 pages, 6 figures, submitted to Quantum Machine Intelligenc
