Quantum-Inspired Computing: Shor's Algorithm and Euler's Totient Function

In this paper, an attempt is made to apply the Euler's Totient function and Euler's theorem to organizing calculations of the period of the modular exponentiation function inspired by Shor's quantum algorithm. A particular method for determining the period by a classical computer is described and a general method for its determination is proposed. For the first 10,000 prime numbers, semiprime numbers are compiled and the distribution of periods of exponentiation functions modulo a semiprime number is studied. The relationship between the Euler's Totient function and the period of the modular exponentiation function is established.

I. Introduction

The development of quantum computers aroused interest in trying to implement quantum algorithms on classical computers, which gave impetus to the development of quantum-inspired computing [1].