  The Vehicle Routing Problem (VRP) is an example of a combinatorial
optimization problem that has attracted academic attention due to its potential
use in various contexts. VRP aims to arrange vehicle deliveries to several
sites in the most efficient and economical manner possible. Quantum machine
learning offers a new way to obtain solutions by harnessing the natural
speedups of quantum effects, although many solutions and methodologies are
modified using classical tools to provide excellent approximations of the VRP.
In this paper, we implement and test hybrid quantum machine learning methods
for solving VRP of 3 and 4-city scenarios, which use 6 and 12 qubit circuits,
respectively. The proposed method is based on quantum support vector machines
(QSVMs) with a variational quantum eigensolver on a fixed or variable ansatz.
Different encoding strategies are used in the experiment to transform the VRP
formulation into a QSVM and solve it. Multiple optimizers from the IBM Qiskit
framework are also evaluated and compared.
