Graph coloring using the reduced quantum genetic algorithm

Abstract

Genetic algorithms (GA) are computational methods for solving optimization problems inspired by natural selection. Because we can simulate the quantum circuitsthat implement GA in different highly configurable noise models and even run GAon actual quantum computers, we can analyze this class of heuristic methods inthe quantum context for NP-hard problems. This paper proposes an instantiation ofthe Reduced Quantum Genetic Algorithm (RQGA) that solves the NP-hard graphcoloring problem in O(N1/2). The proposed implementation solves both vertex andedge coloring and can also determine the chromatic number (i.e., the minimumnumber of colors required to color the graph). We examine the results, analyze thealgorithm convergence, and measure the algorithm's performance using the Qiskitsimulation environment. Our Reduced Quantum Genetic Algorithm (RQGA) circuitimplementation and the graph coloring results show that quantum heuristics cantackle complex computational problems more efficiently than their conventionalcounterparts