Integer Factorization through Func-QAOA

TL;DR

This paper introduces Func-QAOA, a quantum algorithm designed to improve integer factorization on NISQ devices by overcoming limitations of previous quantum approaches and incorporating advanced techniques.

Contribution

The paper presents the Func-QAOA approach for integer factorization, addressing limitations of prior quantum methods and demonstrating its potential through illustrative examples.

Findings

Func-QAOA can incorporate advanced factorization techniques.

The approach shows promise in reducing search space and speeding up optimization.

Preliminary examples demonstrate its efficacy for quantum factorization.

Abstract

Integer factorization is a significant problem, with implications for the security of widely-used cryptographic schemes. No efficient classical algorithm for polynomial-time integer factorization has been found despite extensive research. Although Peter Shor's breakthrough quantum algorithm offers a viable solution, current limitations of noisy intermediate-scale quantum (NISQ) computers hinder its practical implementation. To address this, researchers have explored alternative methods for factorization suitable for NISQ devices. One such method is the Quantum Approximate Optimization Algorithm, which treats factoring as an optimization problem defined over binary bits, resulting in various problematic aspects. In this paper, we explore the Func-QAOA approach for factorization, which premises overcoming some of the limitations of previous approaches and allows the incorporation of more advanced factorization techniques. After reviewing the most promising quantum implementations for integer arithmetics, we present a few illustrative examples to demonstrate the efficacy of the Func-QAOA approach and discuss methods to reduce the search space to speed up the optimization process.