Quantum Optimization Pipeline for the Capacitated Vehicle Routing Problem (CVRP) This repository presents a research-oriented implementation of classical and quantum optimization techniques for solving the Capacitated Vehicle Routing Problem (CVRP). The project serves as an educational and experimental framework for studying hybrid quantum-classical optimization methods and benchmarking their performance on combinatorial optimization problems. The implementation includes: Classical CVRP optimization using Google OR-Tools Mathematical formulation of the routing problem Transformation of the optimization problem into a Quadratic Unconstrained Binary Optimization (QUBO) model Conversion of the QUBO formulation into an Ising Hamiltonian Implementation of the Quantum Approximate Optimization Algorithm (QAOA) using Qiskit Classical versus quantum performance comparison Route visualization and benchmarking Modular Python code designed for experimentation and future extensions The project is intended as a foundation for exploring applications of Quantum Computing, Operations Research, and Hybrid Quantum-Classical Optimization in real-world routing and logistics problems. It provides a reproducible environment for understanding optimization workflows, evaluating quantum algorithms, and extending the framework toward more complex scenarios such as dynamic vehicle routing and emergency ambulance dispatch. Keywords: Quantum Computing, Quantum Optimization, QAOA, QUBO, Ising Model, Capacitated Vehicle Routing Problem (CVRP), Operations Research, OR-Tools, Qiskit, Combinatorial Optimization, Hybrid Quantum-Classical Algorithms. This software was developed as part of a research internship focused on quantum optimization and serves as a learning and experimentation platform for future research.
The aim of a ranking aggregation problem is to combine several rankings into a single one that best represents them. A common method for solving this problem is due to Kemeny and selects as the aggregated ranking the one that minimizes the sum of the Kendall distances to the rankings to be aggregated. Unfortunately, the identification of the said ranking—called the Kemeny ranking—is known to be a computationally expensive task. In this paper, we study different ways of computing the Kemeny ranking with quantum optimization algorithms, and in particular, we provide some alternative formulations for the search for the Kemeny ranking as an optimization problem. To the best of our knowledge, this is the first time that this problem is addressed with quantum techniques. We propose four different ways of formulating the problem, one novel to this work. Two different quantum optimization algorithms—Quantum Approximate Optimization Algorithm and Quantum Adiabatic Computing—are used to evaluate each of the different formulations. The experimental results show that the choice of the formulation plays a big role on the performance of the quantum optimization algorithms.
Quantum computing has demonstrated its potential to solve various optimization problems, including drone scheduling, which is important not only for drone delivery but also for logistics in general. However, one of the main obstacles is that practical drone scheduling settings typically require quantum resources that current hardware cannot provide. Therefore, in this work, we introduce a new Quantum Optimization via Coordinate Descent (QUACOD) approach to address this problem under the constraint of a limited number of available qubits. By leveraging coordinate descent, QUACOD decomposes the original high-complexity problem into multiple subproblems, which are then solved using quantum optimization. In our experiments, QUACOD outperforms the state-of-the-art (SOTA) quantum-based drone scheduling method not only in optimized drone completion times but also in scalability, handling up to 5 times more drones and 35 times more routes. In addition, QUACOD demonstrates that hardware-efficient circuits are effective for optimization problems. Together, these contributions advance quantum computing toward practical applications in the noisy intermediate-scale quantum (NISQ) era.
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor’s algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world problems. It is likely that quantum methods can efficiently solve certain (NP-) hard optimization problems where classical approaches fail. In our perspective, we examine the field of quantum optimization, that is, solving optimization problems using quantum computers. We provide an entry point to quantum optimization for researchers from each topic, optimization or quantum computing, by demonstrating advances and obstacles with a suitable use case. We give an overview on problem formulation, available algorithms, and benchmarking. Although we show a proof-of-concept rather than a full benchmark between classical and quantum methods, this gives an idea of the current quality and capabilities of quantum computers for optimization problems. All observations are incorporated in a discussion on some recent quantum optimization breakthroughs, current status, and future directions.