Analogue factoring algorithm based on polychromatic interference

Abstract

We present a novel factorization algorithm which can be computed using an analogue computer based on a polychromatic source with a given wavelength bandwidth, a multi-path interferometer and a spectrometer. The core of this algorithm stands on the measurement of the periodicity of a "factoring" function given by an exponential sum at continuous argument by recording a sequence of interferograms associated with suitable units of displacement in the inteferometer. A remarking rescaling property of such interferograms allows, in principle, the prime number decomposition of several large integers. The information about factors is encoded in the location of the inteferogram maxima.