Pretending to factor large numbers on a quantum computer

TL;DR

This paper demonstrates a simplified implementation of Shor's quantum factoring algorithm that can factor large prime products using only two qubits, challenging traditional complexity assumptions.

Contribution

It introduces a method to factor large prime products with only two qubits, showing the difficulty depends on period length rather than number size.

Findings

Factors all prime products with p,q > 2 in constant time

Requires only two coherent qubits

Highlights period length as the key difficulty

Abstract

Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled version of Shor's quantum factoring algorithm. Our technique can factor all products of $p,q$ such that $p,q$ are unequal primes greater than two, runs in constant time, and requires only two coherent qubits. This illustrates that the correct measure of difficulty when implementing Shor's algorithm is not the size of number factored, but the length of the period found.