  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.
