Factorization algorithm based on the periodicity measurement of a CTES

Abstract

We introduce a new factorization algorithm based on the measurement of the periodicity of a determined function, similar to Shor's algorithm. In particular, such a function is given by a generalized continuous truncated exponential sum (CTES). The CTES interference pattern satisfies a remarkable scaling property, which allows one to plot the interferogram as a function of a suitable continuous variable depending on the number to factorize. This allows one, in principle, to factorize arbitrary numbers with a single interferogram. In particular, information about the factors is encoded in the location of the interference maxima, which repeat periodically in the interferogram. A possible analogue computer for the implementation of such an algorithm can be realized using multi-path optical interferometers, with polychromatic light sources and a high-resolution spectrometer. The experimental accuracy in the realization of the CTES interferogram and the bandwidth of the polychromatic sources determine the largest number Nmax factorable. Once the CTES interferogram is recorded, all the numbers with value up to Nmax can be factorable, without performing any further measurement.