A pseudo-simulation of Shor's quantum factoring algorithm

TL;DR

This paper introduces a Maple-based pseudo-simulation tool that mimics the output of Shor's quantum factoring algorithm, enabling users to gain practical understanding of quantum factoring processes without requiring actual quantum hardware.

Contribution

It provides a novel, accessible simulation method that models key aspects of Shor's algorithm, facilitating educational and experimental exploration of quantum factoring.

Findings

Simulation successfully mimics quantum readout at the crucial step

Allows factoring of numbers up to 10 digits on classical computers

Identifies performance limitations of the simulation

Abstract

This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out by a quantum computer but does faithfully mimic its output at the crucial "readout" step of the order-finding process. The program reqires only two inputs from the user - the number to be factored (which can be up to 10 digits long) and the number of qubits to be used in the factoring (for which a helpful hint is given). The program then returns a detailed history of all its attempts at factoring the number, beginning with its various unsuccessful attempts and ending with the final successful attempt that leads to the correct factors. The structure of the simulation is described, a typical output produced by it is shown, and the factors limiting its performance are discussed. The purpose of this simulation is to provide the user with some "hands-on" experience of how quantum factoring works on integers somewhat larger than can be handled by today's quantum computers.