  Vehicle routing problem (VRP) is an NP-hard optimization problem that has
been an interest of research for decades in science and industry. The objective
is to plan routes of vehicles to deliver a fixed number of customers with
optimal efficiency. Classical tools and methods provide good approximations to
reach the optimal global solution. Quantum computing and quantum machine
learning provide a new approach to solving combinatorial optimization of
problems faster due to inherent speedups of quantum effects. Many solutions of
VRP are offered across different quantum computing platforms using hybrid
algorithms such as quantum approximate optimization algorithm and quadratic
unconstrained binary optimization. Quantum computers such as IBM-Q experience
along with Qiskit framework offer tools to solve combinatorial optimization
problems. This work proposed here builds a basic VRP solution for 3 and 4
cities using variational quantum eigensolver on a variable ANSATZ. The work is
further extended to evaluate the robustness of the solution in noisy channels
available within the ambit of Qiskit framework.
