Implementable Hybrid Quantum Ant Colony Optimization Algorithm

TL;DR

This paper introduces a hybrid quantum-classical ant colony optimization algorithm designed for near-term quantum computers, effectively solving NP-hard problems like the Quadratic Assignment Problem through quantum superposition and guided exploration.

Contribution

It presents an improved, implementable quantum ant colony optimization algorithm that leverages quantum superposition and exploration strategies for constrained NP-hard problems.

Findings

Simulated noiseless quantum circuit validates the algorithm.

Experiments on IBM quantum computers demonstrate practical feasibility.

The approach efficiently explores solution spaces without pre-checking solutions.

Abstract

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.