# An adiabatic quantum algorithm for the Frobenius problem

## TL;DR

This paper introduces an adiabatic quantum algorithm tailored for the NP-hard Frobenius problem, translating it into a QUBO formulation to leverage D-Wave quantum hardware.

## Contribution

It presents a novel quantum algorithm for the Frobenius problem that utilizes the Apéry set and is optimized for D-Wave quantum annealers.

## Key findings

- Algorithm successfully encodes the Frobenius problem as a QUBO.
- Designed specifically for the D-Wave 2X quantum annealer.
- Provides a new approach to solving a classical NP-hard problem using quantum computing.

## Abstract

The (Diophantine) Frobenius problem is a well-known NP-hard problem (also called the stamp problem or the chicken nugget problem) whose origins lie in the realm of combinatorial number theory. In this paper we present an adiabatic quantum algorithm which solves it, using the so-called Ap\'ery set of a numerical semigroup, via a translation into a QUBO problem. The algorithm has been specifically designed to run in a D-Wave 2X machine.