Analogue factoring algorithm based on polychromatic interference
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Tamma, Vincenzo, Augusto Garuccio, and Yanhua Shih. “Analogue Factoring Algorithm Based on Polychromatic Interference.” Quantum Communications and Quantum Imaging VIII 7815 (August 2010): 145–50. https://doi.org/10.1117/12.877427.
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©2010 Society of Photo-Optical Instrumentation Engineers (SPIE). One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
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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.