Hybrid-Computing for Finding Solutions to NP-Complete Problems in Graphs Using Ant Colony Optimization

Finding solutions to NP-Complete problems is colloquially related to finding a needle in a haystack because of its complexity, which, in consequence, yields exponential time algorithms. In particular, one strategy to find "good solutions" to these problems is to evaluate potential solutions generated at random and measure the quality of each in every attempt. However, true randomness cannot be implemented on classical computers. Hence it is emulated through algorithms that create pseudo-random numbers. This paper analyzes two NP-complete problems in graphs: the Traveling Salesman and the Hamiltonian path problems. The Ant Colony Optimization algorithm was used to find solutions to these with different random number generators: pseudo-random and quantum-random. The convergence time and overall cost of varying graph setups (different complexity levels, i.e. 50, 100, 150, and 200 nodes) were compared under both random number generators. The results indicate that, generally, when quantum random number generators are used, faster convergence is achieved and better results are obtained.