This paper tackles the multi-vehicle Coverage Path Planning (CPP) problem, crucial for applications like search and rescue or environmental monitoring. Due to its NP-hard nature, finding optimal solutions becomes infeasible with larger problem sizes. This motivates the development of heuristic approaches that enhance efficiency even marginally. We propose a novel approach for exploring paths in a 2D grid, specifically designed for easy integration with the Quantum Alternating Operator Ansatz (QAOA), a powerful quantum heuristic. Our contribution includes: 1) An objective function tailored to solve the multi-vehicle CPP using QAOA. 2) Theoretical proofs guaranteeing the validity of the proposed approach. 3) Efficient construction of QAOA operators for practical implementation. 4) Resource estimation to assess the feasibility of QAOA execution. 5) Performance comparison against established algorithms like the Depth First Search. This work paves the way for leveraging quantum computing in optimizing multi-vehicle path planning, potentially leading to real-world advancements in various applications.

翻译：本文研究了多车辆覆盖路径规划问题，该问题在搜救或环境监测等应用中至关重要。由于其NP难特性，随着问题规模增大，寻找最优解变得不可行。这促使我们开发启发式方法，即使效率提升有限。我们提出了一种在二维网格中探索路径的新方法，该方法专为与量子交替算子拟设这一强大的量子启发式算法轻松集成而设计。我们的贡献包括：1) 专为使用QAOA解决多车辆CPP问题而设计的目标函数；2) 保证所提方法有效性的理论证明；3) 面向实际应用的高效QAOA算子构建；4) 用于评估QAOA执行可行性的资源估算；5) 与深度优先搜索等现有算法的性能比较。这项工作为利用量子计算优化多车辆路径规划铺平了道路，有望推动各类实际应用的进步。