Logistics is a promising industry that has proliferated over the years. With growing operation sizes, the challenges in the supply chain have become more complex. Even minor improvements over the existing delivery routes can help companies significantly cut expenses. Current classical computers cannot optimally solve today's real-world applications, which created a commercial interest in quantum computing technologies that are potentially more capable than classical methods for these challenges. This Master's Thesis studies whether this interest is justified by solving Capacitated Vehicle Routing Problem (CVRP) with Quantum Approximate Optimization Algorithm (QAOA), a quantum computing algorithm designed to solve combinatorial optimization problems. The aim is to optimize the Hamiltonian formulation of CVRP, whose ground state encodes the optimal solution. This paper finds QAOA with its Ansatz variant in a column generation setting as a viable solution that scales well with increasing problem sizes. To this end, our Hamiltonian formulations are classically simulated in a problem with 12 customers and a single depot, which found near-optimal results. As far as we are aware, this problem is also currently the biggest CVRP instance that was solved by QAOA.