A factorisation algorithm in Adiabatic Quantum Computation

The problem of factorising positive integer N into two integer factors x and y is first reformulated as an optimisation problem over the positive integer domain of either of the Diophantine polynomials Q(N)(x, y) = N-2(N- xy)(2) + x(x - y)(2) or R-N(x, y) = N-2(N-xy)(2) + (x - y)(2) + x, of each of which the optimal solution is unique x <= root N <= y, and x = 1 if and only if N is prime. An algorithm in the context of Adiabatic Quantum Computation is then proposed for the general factorisation problem.