量子近似优化算法可加速特定优化问题求解，适合当前量子计算机使用。
Quantum Optimization Algorithms
- 基于量子门的变分算法，结合哈密顿量模拟与参数梯度训练
- 在最大割问题上实现有效求解，支持约束条件直接编码进算法
- 适用于当前噪声中等量子设备，对初学者友好且代码开源
量子优化可在特定、可能具有工业应用价值的问题上实现指数级加速。作为该领域的核心算法，本文阐述了量子近似优化算法（QAOA），其可视为适用于门模型量子计算机的广义量子退火方法。文章深入探讨了QAOA的量子电路实现，包括高阶伊辛模型的哈密顿量模拟技术，以及利用参数移位法则进行参数训练的方法。通过Pennylane源码示例，展示了最大割问题的实际应用。此外，我们还介绍了利用格罗弗混态（Grover mixers）将约束融入QAOA，从而将搜索空间限制在严格可行解内。最后，将变分量子本征值求解器（VQE）作为QAOA的通用化扩展，强调其在含噪中等规模量子（NISQ）时代的优势，并讨论了平庸梯度（barren plateaus）和电路结构设计等挑战。
原文摘要 · Abstract (English)
Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA), which can be understood as a slightly generalized version of Quantum Annealing for gate-based quantum computers. We delve into the quantum circuit implementation of the QAOA, including Hamiltonian simulation techniques for higher-order Ising models, and discuss parameter training using the parameter shift rule. An example implementation with Pennylane source code demonstrates practical application for the Maximum Cut problem. Further, we show how constraints can be incorporated into the QAOA using Grover mixers, allowing to restrict the search space to strictly valid solutions for specific problems. Finally, we outline the Variational Quantum Eigensolver (VQE) as a generalization of the QAOA, highlighting its potential in the NISQ era and addressing challenges such as barren plateaus and ansatz design.
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