Hybrid Quantum Approximate Optimization Using Enhanced Ant Colony Optimization to Solve Large-Scale Combinatorial Optimization Problems

Abstract

Quantum computing is a promising technology that may provide breakthrough solutions to today’s difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. A class of algorithms referred to as Quantum Approximate Optimization Algorithm (QAOA) have been recently proposed. QAOA attempts to approximately solve hard problems using a protocol know as bang-bang. The technique is based on the unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. QAOA has been explored in the context of several optimization problems such as Max-Cut problem, variational Eigenvalue problem etc. Recently, attempts have been made to create QAOA for the Traveling Salesman Problem (TSP). Due to small node size and limited solution capability of the currently available Quantum computers and/or simulators, we develop a hybrid approach where subgraphs of a TSP tour are executed on a Quantum computer and the results from the quantum optimization are combined in further optimization of the whole tour. Since the local optimization of a subgraph is prone to getting stuck in a local minima, we overcome this problem by using a parallel Ant Colony Optimization Algorithm with periodic pheromone exchange between colonies. Our results are encouraging and yield optimum results for benchmarks with less than 50 nodes, and usually within 1% of the optimal solution for benchmarks with around 200 nodes.