Simpósio Brasileiro de Computação e Comunicação Quânticas (SBCCQ)
Applying the Quantum Approximate Optimization Algorithm to the UAV Collision Avoidance Problem
Kalleb C. Santos, Maria Eduarda W. M. Vianna, Mateus K. de Oliveira, Evandro C. R. Rosa, Alison Roberto Panisson, Luiz F. Bittencourt, Roberto Rodrigues Filho
The increasing availability of quantum hardware has stimulated interest in applying quantum algorithms to combinatorial optimization problems. Collision avoidance for unmanned aerial vehicles (UAVs) is one such challenge due to the computational complexity of coordinating multiple agents in shared airspace. In this paper, we formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model that captures route selection and collision constraints, enabling the use of the Quantum Approximate Optimization Algorithm (QAOA). To improve efficiency, we introduce a constrained QAOA Ansatz employing an XY-mixer that preserves one-hot route assignment constraints and restricts the search space to valid solutions. We evaluate the approach through noiseless simulations and device-based noise models, analyzing its behavior under realistic conditions and highlighting the opportunities and limitations of near-term quantum hardware for multi-agent routing problems.
The increasing availability of quantum hardware has stimulated interest in applying quantum algorithms to combinatorial optimization problems. Collision avoidance for unmanned aerial vehicles (UAVs) is one such challenge due to the computational complexity of coordinating multiple agents in shared airspace. In this paper, we formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model that captures route selection and collision constraints, enabling the use of the Quantum Approximate Optimization Algorithm (QAOA). To improve efficiency, we introduce a constrained QAOA Ansatz employing an XY-mixer that preserves one-hot route assignment constraints and restricts the search space to valid solutions. We evaluate the approach through noiseless simulations and device-based noise models, analyzing its behavior under realistic conditions and highlighting the opportunities and limitations of near-term quantum hardware for multi-agent routing problems.
Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the era of noisy intermediate-scale quantum (NISQ) devices, variational quantum algorithms (VQA) for optimizing parameterized quantum circuits with the help of classical optimizers are currently one of the most promising strategies to gain quantum advantage. In this paper, we propose a mathematical model for the UAV collision avoidance problem that maps the collision avoidance problem to a quadratic unconstrained binary optimization (QUBO) problem. The problem is formulated as an Ising Hamiltonian, then the ground state is solved using two kinds of VQAs: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We select conditional value-at-risk (CVaR) to further promote the performance of our model. Four examples are given to validate that with our method the probability of obtaining a feasible solution can exceed 90% based on appropriate parameters, and our method can enhance the efficiency of a UAVs' collision avoidance model.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it poses a major feasibility challenge for standard QAOA because feasible solutions occupy only a tiny fraction of the search space, and the conventional Pauli-X mixer can disrupt partial solution structures that satisfy key local constraints. To address this issue, we propose a constraint-aware QAOA framework with two complementary components. First, we design a lightweight initialization strategy that encodes a selected subset of simple yet informative local one-hot constraints into the initial state, thereby reducing the initial superposition space and increasing the probability mass on states with important local structure. Second, we introduce a hybrid XY-X mixer that preserves the constraint structure imposed at initialization while retaining exploratory flexibility over the remaining unconstrained degrees of freedom during QAOA evolution. We evaluate the proposed framework against standard QAOA under three progressively more realistic regimes: ideal statevector simulation, finite-shot sampling, and noisy finite-shot sampling. Across all regimes, the proposed method consistently achieves lower average energy and higher feasible-solution ratios than standard QAOA, indicating more effective guidance toward structurally valid, lower-cost VRP solutions. However, the performance gap narrows in the noisy regime. Because this setting adopts a hardware-inspired error model based on near-best-reported laboratory-level qubit gate and readout fidelities, the observed attenuation suggests that the practical advantage of the more structured mixer is likely to grow as quantum hardware improves and error rates decline.
Rapid advancement in Unmanned Aerial Vehicles (UAVs) and their increasing utility in different areas of human life raises a need for collision-free flying in airspace during operation. Especially when thousands of UAVs operates in specific airspace of few kilometres then it is difficult to manage collision free operations of these UAVs. However, each UAV can choose from many possible trajectories, speeds, or altitudes to avoid conflicts. As the number of UAVs increases, it becomes computationally infeasible to find an optimal and collision-free solution by examining all possible configurations. As a result, this is classified as NP-complete problem, meaning that there is no known conventional algorithm can provide a solution in feasible time. It means that the classical algorithms require exponential time to solve it for large problem instances. On the other hand quantum computing could provide potential speed up for solving such problem. Here, we present a quantum method for reduce the time complexity of solving the problem. Our contribution in this paper are to design a quantum algorithm for unmanned aerial vehicles conflict resolution (UAVs-CR) problem, to design an explicit oracle to solve this problem as well as encoding the problem information into basis states in order to use quantum search algorithm, known for its quadratic speed-up in unstructured database search. A series of experiments were carried out using the IBM Quantum computer and the AerSimulator running locally to examine the scalability, correctness, and runtime efficiency of the proposed quantum methodology.
Mission planning often involves optimising the use of ISR (Intelligence, Surveillance and Reconnaissance) assets in order to achieve a set of mission objectives within allowed parameters subject to constraints. The missions of interest here, involve routing multiple UAVs visiting multiple targets, utilising sensors to capture data relating to each target. Finding such solutions is often an NP-Hard problem and cannot be solved efficiently on classical computers. Furthermore, during the mission new constraints and objectives may arise, requiring a new solution to be computed within a short time period. To achieve this we investigate near term quantum algorithms that have the potential to offer speed-ups against current classical methods. We demonstrate how a large family of these problems can be formulated as a Mixed Integer Linear Program (MILP) and then converted to a Quadratic Unconstrained Binary Optimisation (QUBO). The formulation provided is versatile and can be adapted for many different constraints with clear qubit scaling provided. We discuss the results of solving the QUBO formulation using commercial quantum annealers and compare the solutions to current edge classical solvers. We also analyse the results from solving the QUBO using Quantum Approximate Optimisation Algorithms (QAOA) and discuss their results. Finally, we also provide efficient methods to encode to the problem into the Variational Quantum Eigensolver (VQE) formalism, where we have tailored the ansatz to the problem making efficient use of the qubits available.
The quantum approximate optimization algorithm (QAOA) is designed to determine optimum and near optimum solutions of quadratic (and higher order) unconstrained binary optimization (QUBO or HUBO) problems, which in turn accurately model unconstrained combinatorial optimization problems. While the solution space of an unconstrained combinatorial optimization problem consists of all possible combinations of the objective function's decision variables, for a constrained combinatorial optimization problem, the solution space consists only of solutions that satisfy the problem constraints. While solving such a QUBO problem optimally results in an optimal solution to the underlying constrained problem, setting the right penalty parameters is crucial. Moreover, finding suitable penalties that ensure near-optimal solutions is also challenging. In this article, we introduce our innovative profit-relaxation framework to solve constrained combinatorial optimization problems. Our effective hybrid approach transforms a selected constrained combinatorial optimization problem into an unconstrained profit problem, such that the solution spaces of the two problems are interrelated with respect to their solution qualities. This allows us to determine optimal and near-optimal solutions for the constrained problem. We use three NP-hard problems -- Minimum Vertex Cover, Maximum Independent Set, and Maximum Clique -- to demonstrate the feasibility and effectiveness of our approach. We conducted a detailed performance evaluation of our profit-relaxation framework on two different platforms: Xanadu PennyLane and Argonne QTensor Quantum Circuit Simulator.
Transportation routing problems such as the Traveling Salesperson Problem (TSP) and the Vehicle Routing Problem (VRP) are characterized by strict feasibility requirements involving customer assignment and visit rules, route sequencing, and depot-return logic alongside cost minimization. Most quantum routing formulations adopt Quadratic Unconstrained Binary Optimization (QUBO) encodings, where feasibility is incorporated indirectly via penalty terms in the cost Hamiltonian. While convenient for standard implementations of the Quantum Approximate Optimization Algorithm (QAOA), QUBO encodings allow the quantum search dynamics to allocate substantial probability to infeasible route configurations. This study develops a transportation-grounded constraint-aware Quantum Alternating Operator Ansatz (QAOA+) framework that embeds feasibility-preserving logic directly into the search operator. We introduce a custom mixer that functions as a quantum analogue of feasibility-preserving routing neighborhoods, using column-wise swap moves, it restricts evolution to feasible configurations while enabling structured exploration of valid routes. We compare three constraint-handling architectures: penalty-based QUBO QAOA, penalty free QAOA+ with the feasibility-preserving mixer, and a Hybrid QAOA+ combining mixer based feasibility with and penalty guidance. Results on small TSP and VRP instances show that constraint-handling architecture strongly influences feasible-route sampling, convergence behavior, and probability concentration over low-cost feasible routes. These findings position constraint-aware quantum search as a methodological extension of transportation routing search approaches, where feasibility is enforced through admissible quantum transitions rather than post-hoc penalties.