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 with $x⩽\sqrt{N}⩽y$, 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. (paper)