Factorization of numbers with Gauss sums: III. Algorithms with entanglement
S Wölk, W P Schleich · New Journal of Physics · 2012
We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of Gauss sums in the probability amplitudes of two entangled states. These schemes are rather efficient provided that there exists a fast algorithm that can detect a period of a function hidden in its zeros.