用深度学习动态生成适配量子电路深度的混合哈密顿量，提升变分量子优化性能。
MG-Net: Learn to Customize QAOA with Circuit Depth Awareness
- 基于深度学习构建混合哈密顿量生成网络，根据任务和电路深度自适应设计
- 在64比特伊辛模型与加权最大割问题上，逼近比与效率均优于传统方法
- 为当前量子设备限制下的优化算法提供可扩展的实用解决方案
变分量子算法（如QAOA）在解决组合优化问题上展现出巨大潜力，但其实际应用面临困境：达到理想性能所需的电路深度依赖于具体问题，且常超出当前量子设备的最大承载能力。本文首先分析了QAOA的收敛特性，揭示了该困境的根源，并阐明了所用混合哈密顿量、具体问题与允许最大电路深度之间的复杂关系。基于此理解，我们提出混合哈密顿量生成网络（MG-Net），一种统一的深度学习框架，可动态生成适配不同任务与电路深度的最优混合哈密顿量。系统仿真涵盖最多64个量子比特的伊辛模型与加权最大割实例，验证了理论发现，表明MG-Net在逼近比与计算效率方面均表现更优。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。