Towards non-quantum implementations of Shor’s factorization algorithm

Abstract

It has been established that Physarum polycephalum slime-mould organisms retain the time-period of a regular pulse of brief stimuli. We ask whether a period can equally well be imparted not via regular pulses, but via more general periodic functions-for example via stimulus intensity varying sinusoidally with time, or even varying with time as a function with unknown period (whence the organisms not merely retain the period, but in a sense compute it); we discuss this theoretically, and also outline, though defer to future work, an experimental investigation. As motivation, we note that the ability to determine a function’s period is computationally highly desirable, not least since from such ability follow methods of integer factorization. Specifically, the phenomena described herein afford a novel (albeit inefficient), non-quantum implementation of Shor’s algorithm; inefficiency aside, this offers interesting, alternative perspectives on approaches to factorization and on the computational uses of P. polycephalum.