Projecte Final de Màster Oficial fet en col.laboració amb el Departament de Física Fonamental, Facultat de Física,Universitat de Barcelona

We present the numerical results obtained using quantum annealing (QA) in a hard combinatorial problem: the coloring problem (q-COL) of an Erd˝os-R´enyi graph. We first propose a quantum coloring Hamiltonian, natural extension of q-COL, based on the quantum Ising model in a transverse field. We then test several QA schemes and find the one that solves the highest number of graphs in the smallest number of iterations. Our results suggest that the computation time of QA scales exponentially in the size and it does not improve the results obtained by thermal annealing (TA) for q-COL.