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Japanese Journal of Applied Physics

An Optical Parallel System for Prime Factorization

Kouichi Nitta, Nobuto Katsuta, Osamu Matoba

Published Sep 24, 2009• 4 citations
Publisher

Abstract

A system for prime factorization with optical modulo operations is developed and demonstrated. In the system, two-dimensional parallel processing is employed to achieve large-scale information processing for modulo multiplication, which is one of the important elements in an algorithm for prime factorization. This optical component is implemented on a Michelson interferometer. Electronic signal processing for pre-processing, postprocessing, and control of optical hardware is prepared as graphic user interface (GUI) software. With the constructed system, effective results can be obtained using the proposed method.

DOI
10.1143/jjap.48.09la02

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A system for prime factorization with optical modulo operations is developed and demonstrated. In the system, two-dimensional parallel processing is employed to achieve large-scale information processing for modulo multiplication, which is one of the important elements in an algorithm for prime factorization. This optical component is implemented on a Michelson interferometer. Electronic signal processing for pre-processing, postprocessing, and control of optical hardware is prepared as graphic user interface (GUI) software. With the constructed system, effective results can be obtained using the proposed method.
We introduce a new factorization algorithm based on the optical computation by multi-path interference of the periodicity of a "factoring" function given by exponential sums at continuous arguments. We demonstrate that this algorithm allows, in principle, the prime number decomposition of several large numbers by exploiting a remarking rescaling property of this periodic function. Such a function is recorded by measuring optical interferograms with a multi-path Michelson interferometer, a polychromatic light source and a spectrometer. The information about factors is encoded in the location of the inteferogram maxima.
We present a user-friendly software for photonic analog quantum computing with a graphical user interface (GUI) that allows for convenient operation without requiring programming skills. Hamiltonians can be flexibly set by either importing the waveguide position files or manually plotting the configuration on the interactive board of the GUI. Our software provides a powerful approach to theoretical studies of two-dimensional quantum walks, quantum stochastic walks, multiparticle quantum walks, and boson sampling, which may all be feasibly implemented in the physical experimental system on photonic chips, and it will inspire a rich diversity of applications for photonic quantum computing and quantum simulation. We have improved algorithms to ensure the efficiency of permanent calculation and provided case studies on educational uses, which bring users easier access to the studies of photonic quantum simulation.
The triumph of the graphical user interface has been one of the most impressive developments in software during the past three decades.1 Today the concept is so familiar as to need no description. Although from the beginning, windows, icons, menus, and pointing have been intuitive and easy to grasp for users, they remain a challenge for programmers. The internal GUI architecture baffles many newcomers, who often find it strange, backwards, mind-boggling, or weird. GUI programming is different because unlike traditional data processing, it is entirely event-driven. Events can occur at any time in any order. The application always must be prepared to handle them. GUI is an example of a complex reactive system.