A Continuous Variable Shor Algorithm

Abstract

In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R from the reals R to the reals R, where F belongs to a very general class of functions, called the class of admissible functions. One objective in creating this continuous variable quantum algorithm was to make the structure of Shor's factoring algorithm more mathematically transparent, and thereby give some insight into the inner workings of Shor's original algorithm. This continuous quantum algorithm also gives some insight into the inner workings of Hallgren's Pell's equation algorithm. Two key questions remain unanswered. Is this quantum algorithm more efficient than its classical continuous variable counterpart? Is this quantum algorithm or some approximation of it implementable?