[论文解读] A Review on Quantum Approximate Optimization Algorithm and its Variants

Kostas Blekos, Dean Brand+5 more|arXiv (Cornell University)|Jun 15, 2023

Quantum Computing Algorithms and Architecture参考文献 261被引用 12

一句话总结

本论文综述量子近似优化算法（QAOA）及其变体，分析性能、硬件挑战以及在 NISQ 设备上的实际使用指南。

ABSTRACT

The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios, its applicability across various problem instances, and considerations of hardware-specific challenges such as error susceptibility and noise resilience. Additionally, we conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm. We aim to provide insights into key questions about the algorithm, such as whether it can outperform classical algorithms and under what circumstances it should be used. Towards this goal, we offer specific practical points in a form of a short guide. Keywords: Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Algorithms (VQAs), Quantum Optimization, Combinatorial Optimization Problems, NISQ Algorithms

研究动机与目标

• 评估QAOA在不同问题实例和硬件条件下的现状。
• 比较选定的QAOA扩展和变体。
• 分析影响性能、错误鲁棒性和资源需求的因素。
• 提供在组合优化中何时以及如何使用QAOA的实际指南。

提出的方法

• 进行对QAOA及其变体的广泛文献综述。
• 对选定的QAOA扩展在MaxCut问题上进行对比研究。
• 分析参数优化、噪声效应和硬件因素。
• 综合实验结果与实际建议。
• 讨论QAOA的未解问题和未来方向。

Figure 1: Left: A problem graph with 6 vertices and 11 equal-weight edges. Right: The solution to the MaxCut problem, where the vertices are partitioned into two groups (red and blue) such that the number of edges crossed by the cut (black curve) is maximized, which is 8.

实验结果

研究问题

• RQ1 在何种情况下QAOA能够在组合优化中超越经典算法？
• RQ2 对于给定的问题类别（例如 MaxCut）和问题规模，哪些QAOA变体或 Ansatz 结构最有效？
• RQ3 噪声、硬件约束和 barren plateaus 如何影响QAOA的潜在量子优势？
• RQ4 哪些实用指南可以优化参数选择和在 NISQ 设备上的实现？

主要发现

• 存在通过自适应 Ansatz 和优化策略来改进性能的 QAOA 变体。
• 该算法的优势取决于问题实例特征和硬件质量，证据受噪声和限制影响。
• 参数优化、barren plateaus 以及参数的可复用性是跨变体的核心挑战。
• 针对硬件的具体方法和噪声抑制技术对于实现任何实用的量子优势都是必不可少的。
• 本文提供一个实用指南，回答在 MaxCut 及相关问题中应使用哪个变体以及如何优化参数。

Figure 2: Implementation of the elements of mixer (left) and cost (right) layers based on the cost and mixer Hamiltonians, $\hat{H}_{C}$ and $\hat{H}_{M}$ . By $\big{(}e^{-i\beta_{k}\hat{H}_{M}}\big{)}_{v_{i}}\eqqcolon\big{(}\hat{U}_{M}(\beta_{k})\big{)}_{v_{i}}$ we mean the element of $\hat{U}_{M}(