Factorization of numbers with Gauss sums: III. Algorithms with Entanglement

TL;DR

This paper introduces two quantum algorithms leveraging Gauss sums and entanglement for number factorization, aiming to improve efficiency by detecting periods in functions through quantum superpositions and entanglement.

Contribution

The paper presents novel quantum algorithms that encode Gauss sums in entangled states for efficient number factorization, extending previous methods with new entanglement-based techniques.

Findings

Algorithms are efficient if a fast period detection method exists.

Encoding Gauss sums in entangled states enhances factorization.

Potential for improved quantum factoring methods.

Abstract

We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard Gauss sum in one of two entangled states and (ii) in an interference algorithm we create a superposition of Gauss sums in the probability amplitudes of two entangled states.These schemes are rather efficient provided that there exists a fast algorithm that can detect a period of a function hidden in its zeros.