  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.
