A statistical mechanics approach to the factorization problem

(Dated: February 8, 2011)We map the problem of finding the prime factors of an integer to the statistical physics problemof finding the ground state of a long-range Ising-like model. As in the strongly disordered Newman-Stein (NS) spin-glass model, the bond distribution is exponentially wide and grows with system size,but unlike the NS model we find that it is not wide enough for a greedy algorithm to be applicable.On the other hand, we also find that the frustration and exponential width of the bond distributionrenders classical and quantum annealing and tempering methods no faster than a random searchfor this challenging model.