Multi-Agent Path Finding (MAPF) remains a fundamental challenge in robotics, where classical centralized approaches exhibit exponential growth in joint-state complexity as the number of agents increases. This paper investigates Quadratic Unconstrained Binary Optimization (QUBO) as a structurally scalable alternative for simultaneous multi-robot path planning. This approach is a robotics-oriented QUBO formulation incorporating BFS-based logical pre-processing (achieving over 95% variable reduction), adaptive penalty design for collision and constraint enforcement, and a time-windowed decomposition strategy that enables execution within current hardware limitations. An experimental evaluation in grid environments with up to four robots demonstrated near-optimal solutions in dense scenarios and favorable scaling behavior compared to sequential classical planning. These results establish a practical and reproducible baseline for future quantum and quantum-inspired multi-robot coordinations.
Multi-Agent Path Finding (MAPF) remains a fundamental challenge in robotics, where classical centralized approaches exhibit exponential growth in joint-state complexity as the number of agents increases. This paper investigates Quadratic Unconstrained Binary Optimization (QUBO) as a structurally scalable alternative for simultaneous multi-robot path planning. This approach is a robotics-oriented QUBO formulation incorporating BFS-based logical pre-processing (achieving over 95% variable reduction), adaptive penalty design for collision and constraint enforcement, and a time-windowed decomposition strategy that enables execution within current hardware limitations. An experimental evaluation in grid environments with up to four robots demonstrated near-optimal solutions in dense scenarios and favorable scaling behavior compared to sequential classical planning. These results establish a practical and reproducible baseline for future quantum and quantum-inspired multi-robot coordinations.
Quadratic Unconstrained Binary Optimization (QUBO) is a central formulation for combinatorial optimization and has gained increasing attention due to its compatibility with quantum, hybrid quantum-classical, and quantum-inspired solvers. However, translating natural-language problem descriptions into correct QUBO formulations remains difficult, requiring the identification of binary variables, constraints, objective functions, penalty terms, and suitable penalty weights. This process is time-consuming and often demands substantial domain expertise. To address this challenge, we propose an end-to-end multi-agent framework that automatically generates QUBO formulations from natural-language problem descriptions, supported by structured or unstructured test cases. To evaluate its performance, We also introduce QUBOBench, a benchmark containing 100 combinatorial optimization problems across 12 application domains, curated from peer-reviewed literature, competitions, and canonical NP-hard problems. Experimental results show that our framework achieves 68% accuracy on QUBOBench, outperforming a direct single-call baseline by 22%. Further analysis identifies iterative self-repair as the most important component contributing to improved performance. The data and code are open-sourced at https://quitttcat.github.io/QuantumQUBOAgent.
Multi-Agent Route Planning considers selecting vehicles, each associated with a single predefined route, such that route-level coverage utility is maximized while redundant spatial overlaps are limited. This paper gives a formal problem definition, proves NP-hardness by reduction from the Weighted Set Packing problem, and derives a Quadratic Unconstrained Binary Optimization formulation whose coefficients directly encode route utility rewards and pairwise overlap penalties. A single penalty parameter λ controls the coverage--overlap trade-off. We distinguish between a soft regime, which supports multi-objective exploration, and a hard regime, in which the penalty is strong enough to effectively enforce near-disjoint routes. We describe a practical pipeline for generating city instances, constructing candidate routes, building the QUBO matrix, and solving it with a binary quadratic programming baseline (Gurobi), simulated annealing, and D-Wave hybrid quantum annealing. Experiments on Barcelona instances with up to 10,000 vehicles reveal a clear coverage--overlap knee and show that Pareto-optimal solutions are mainly obtained under the hard-penalty regime, while D-Wave hybrid solvers and Gurobi achieve very similar objective values on matching configurations with only minor runtime differences as problem size grows.
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.
Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling large numbers of agents, as frequently encountered in practical applications like coordinating autonomous vehicles. Quantum Computing (QC) is a promising candidate in overcoming such limits. However, current quantum hardware is still in its infancy and thus limited in terms of computing power and error robustness. In this work, we present the first optimal hybrid quantum-classical MAPF algorithms which are based on branch-andcut-and-price. QC is integrated by iteratively solving QUBO problems, based on conflict graphs. Experiments on actual quantum hardware and results on benchmark data suggest that our approach dominates previous QUBO formulationsand state-of-the-art MAPF solvers.
Combinatorial optimization problems are typically formulated using Quadratic Unconstrained Binary Optimization (QUBO), where constraints are enforced through penalty terms that introduce auxiliary variables and rapidly increase Hamiltonian complexity, limiting scalability on near term quantum devices. In this work, we systematically study Quadratic Unconstrained D-ary Optimization (QUDO) as an alternative formulation in which decision variables are encoded directly in higher dimensional Hilbert spaces. We demonstrate that QUDO naturally captures structural constraints across a range of problem classes, including the Traveling Salesman Problem, two variants of the Vehicle Routing Problem, graph coloring, job scheduling, and Max-K-Cut, without the need for extensive penalty constructions. Using a qudit-level implementation of the Quantum Approximate Optimization Algorithm (qudit QAOA), we benchmark these formulations against their binary QUBO counterparts and exact classical solutions. Our study show consistently improved approximation ratios and substantially reduced computational overhead at comparable circuit depths, highlighting QUDO as a scalable and expressive representation for quantum combinatorial optimization.
Quantum Optimization (QO) is emerging as a promising approach to tackle hard combinatorial optimization problems by leveraging the unique computational properties of quantum hardware. In recent years, QO has gained traction in Machine Learning (ML), where problems such as clustering and vector quantization can be naturally expressed as Quadratic Unconstrained Binary Optimization (QUBO) problems. These ML applications often involve complex, high-dimensional data, which directly influences both the structure and scale of the resulting QUBO formulations. However, current quantum devices fall under the category of Noisy Intermediate-Scale Quantum (NISQ) hardware, which imposes significant limitations on qubit counts and small error rates. This dissertation investigates the impact of data complexity and data scale—as encountered in ML settings—on the effectiveness and feasibility of QO on NISQ devices. We propose novel, hardware-aware methods to overcome these challenges. The first part of this thesis focuses on the effect of data complexity for QO. We analyze how problem structure—particularly when QUBO formulations are derived from ML tasks—affects quantum solvability. We identify the spectral gap as a key factor in the success of adiabatic quantum algorithms and provide a theoretical and empirical analysis linking data-induced complexity to optimization performance.To address noise sensitivity and limited precision, we introduce a preprocessing framework based on a principled Branch-and-Bound algorithm that reduces dynamic range while preserving global optima. This improves robustness on both quantum annealers and classical solvers. In the second part, the thesis addresses challenges introduced by data scale. First, we propose a recursive Divide-and-Conquer strategy that breaks down large QUBO problems into tractable subproblems, demonstrated through an application to Bundle Adjustment in 3D scene reconstruction. Second, we introduce a variable and constraint generation method inspired by column generation for Integer Linear Programming, enabling dynamic QUBO size growth. This technique is successfully applied to Multi-Agent Pathfinding, where it scales well on NISQ devices while maintaining compatibility with classical solvers. Finally, we explore QUBO reformulations that reduce problem size through compact encodings and cyclic expansion, enabling the use of quantum hardware for tasks such as FPGA placement in chip design. Across all contributions, the developed algorithms are evaluated both theoretically and empirically, with experiments conducted on real quantum and quantum-inspired hardware. These methods significantly improve solution quality, scalability, and hardware compatibility, paving the way for more effective use of QO in practical settings. While tailored for NISQ era constraints, the results remain relevant for fault-tolerant quantum computing, offering insights into the long-term viability of QO across hardware generations.