Quantum Walk based genetic algorithm for 0–1 quadratic knapsack problem

Abstract

This paper proposes a genetic quantum algorithm based on discrete time quantum walk (QWGA) to solve 0–1 quadratic knapsack problem. Genetic Quantum Algorithms makes use of the qubit representation and superposition phenomenon which are the counter-intuitive characteristics of quantum mechanics. Discrete Quantum Walk (DQW) on a hypercube is used in the place of genetic operators like mutation, crossover, etc. Achievement of rapid convergence and avoidance of local optima with the help of the quantum principles is explained in this paper. The possibilities of extending the proposed algorithm to various combinatorial optimization problems is discussed in detail. Superiority of the proposed algorithm over genetic quantum algorithm based on rotation operators is evident from the results.