Mixer Hamiltonian with QAOA for Max k-coloring : numerical evaluations

TL;DR

This paper explores the use of Mixer Hamiltonians within the QAOA framework for solving Max k-coloring problems, providing numerical evaluations and highlighting the functional analogy with classical OR practices.

Contribution

It offers a clear presentation of Mixer Hamiltonians for Max k-coloring, connecting quantum heuristics with classical routing and scheduling methods.

Findings

Numerical evaluations demonstrate the effectiveness of Mixer Hamiltonians in QAOA.

The approach reveals functional analogies between quantum and classical optimization techniques.

Experiments validate the theoretical considerations using IBM's Qiskit library.

Abstract

This paper concerns quantum heuristics based on Mixer Hamiltonians that allow to restrict investigation on a specific subspace. Mixer Hamiltonian based approaches can be included in QAOA algorithm and we can state that Mixer Hamiltonians are mapping functions from the set of qubit-strings to the set of solutions. Mixer Hamiltonian offers an approach very similar to indirect representations commonly used in routing or in scheduling community for decades. After the initial publication of Cheng et al. in 1996 (Cheng et al., 1996), numerous propositions in OR lies on 1-to-n mapping functions, including the split algorithm that transform one TSP solution into a VRP solution. The objective is at first to give a compact and readable presentation of these Mixer Hamiltonians considering the functional analogies that exist between the OR community practices and the quantum field. Our experiments encompass numerical evaluations of circuit using the Qiskit library of IBM meeting the theoretical considerations.