Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling combinatorial optimization challenges. However, their practical realization confronts a dilemma: the requisite circuit depth for satisfactory performance is problem-specific and often exceeds the maximum capability of current quantum devices. To address this dilemma, here we first analyze the convergence behavior of QAOA, uncovering the origins of this dilemma and elucidating the intricate relationship between the employed mixer Hamiltonian, the specific problem at hand, and the permissible maximum circuit depth. Harnessing this understanding, we introduce the Mixer Generator Network (MG-Net), a unified deep learning framework adept at dynamically formulating optimal mixer Hamiltonians tailored to distinct tasks and circuit depths. Systematic simulations, encompassing Ising models and weighted Max-Cut instances with up to 64 qubits, substantiate our theoretical findings, highlighting MG-Net's superior performance in terms of both approximation ratio and efficiency.

翻译：量子近似优化算法（Quantum Approximate Optimization Algorithm, QAOA）及其变体在解决组合优化问题方面展现出巨大潜力。然而，其实际应用面临一个困境：获得满意性能所需的电路深度具有问题依赖性，且通常超出当前量子设备的极限能力。为应对此困境，本文首先分析了QAOA的收敛行为，揭示了该困境的根源，并阐明了所采用的混合器哈密顿量、待解决的具体问题以及允许的最大电路深度三者之间复杂的相互作用关系。基于这一理解，我们提出了混合器生成网络（Mixer Generator Network, MG-Net），这是一个统一的深度学习框架，能够针对不同任务和电路深度动态构建最优的混合器哈密顿量。涵盖伊辛模型和高达64量子比特的加权最大割问题的系统仿真验证了我们的理论发现，突显了MG-Net在近似比和效率方面的卓越性能。