This research explores the integration of the Quantum Approximate Optimization Algorithm (QAOA) into Hybrid Quantum-HPC systems for solving the Max-Cut problem, comparing its performance with classical algorithms like brute-force search and greedy heuristics. We develop a theoretical model to analyze the time complexity, scalability, and communication overhead in hybrid systems. Using simulations, we evaluate QAOA's performance on small-scale Max-Cut instances, benchmarking its runtime, solution accuracy, and resource utilization. The study also investigates the scalability of QAOA with increasing problem size, offering insights into its potential advantages over classical methods for large-scale combinatorial optimization problems, with implications for future Quantum computing applications in HPC environments.

翻译：本研究探讨了将量子近似优化算法（QAOA）集成到混合量子-高性能计算系统中以求解最大割问题，并将其性能与经典算法（如暴力搜索和贪心启发式算法）进行比较。我们建立了一个理论模型来分析混合系统中的时间复杂度、可扩展性和通信开销。通过仿真实验，我们评估了QAOA在小规模最大割实例上的性能，对其运行时间、求解精度和资源利用率进行了基准测试。本研究还考察了QAOA随问题规模增大的可扩展性，揭示了其在大规模组合优化问题上相较于经典方法的潜在优势，并对未来量子计算在高性能计算环境中的应用前景提出了见解。