Shor's algorithm without partial fractions

TL;DR

This paper presents a simplified proof that Shor's algorithm for period finding operates in polynomial time, relying solely on the standard quantum Fourier transform and basic trigonometry.

Contribution

It offers a new proof of Shor's algorithm's polynomial complexity without using partial fractions, simplifying the understanding of its efficiency.

Findings

Shor's algorithm is polynomial-time using standard quantum Fourier transform.

The proof avoids complex partial fraction decomposition.

The approach clarifies the mathematical basis of Shor's algorithm.

Abstract

The purpose of this note was to give a proof that Shor's algorithm for period search is polynomial using only the standard $2^{n}$ quantum Fourier thansform and some simple trigonometry. There is an error that was pointed out to the author by Pavel Wocjan.