发表机构
Institute for Frontier Materials on Earth and in Space, German Aerospace Center; Institute for Theoretical Physics, University of Cologne; Institute of Software Technology, German Aerospace Center（地球与太空前沿材料研究所; 科隆大学理论物理研究所; 德国航空航天中心软件技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明量子启发经典算法MF-AOA受重叠间隙性质限制，而QAOA能超越该障碍，在Max-4-XORSAT实例上表现更优，并发现参数从绝热到非绝热的转变。
AI 中文摘要
在本文中，我们证明了平均场近似优化算法（MF-AOA），一种量子近似优化算法（QAOA）的量子启发经典算法，无法为表现出重叠间隙性质（OGP）的问题提供任意接近最优的解。我们通过将MF-AOA与有限记忆近似消息传递（AMP）算法相关联来展示这一点，已知这些算法的性能受到OGP的限制。因此，我们的论文认为，表现出OGP的问题是QAOA能够普遍优于MF-AOA和AMP算法的一个实例。我们通过数值模拟QAOA在表现出OGP的Max-$4$-XORSAT实例上的性能来补充这一点，并发现QAOA能够超越这一障碍，而我们的有限尺寸缩放分析倾向于超多项式而非多项式深度依赖。此外，我们观察到QAOA在OGP障碍附近的性能存在一个不可微点，其中最优QAOA参数从绝热调度变为非绝热调度。
英文摘要
In this paper, we prove that the Mean-Field Approximate Optimization Algorithm (MF-AOA), a quantum-inspired classical algorithm of the Quantum Approximate Optimization Algorithm (QAOA), is unable to give arbitrary near optimal solution for problems exhibiting the Overlap Gap Property (OGP). We show this by relating the MF-AOA to finite-memory Approximate Message Passing (AMP) algorithms, which are known to be limited in performance by the OGP. Thus, our paper argues that problems exhibiting the OGP are one such instance where the QAOA can outperform the MF-AOA and AMP algorithms in general. We supplement this by numerically simulating the performance of the QAOA on instances of Max-$4$-XORSAT that exhibit the OGP and find that the QAOA is able to surpass the barrier, while our finite-size scaling analysis favors a super-polynomial over a polynomial depth dependence. In addition, we observe a non-differentiable point in the performance of the QAOA near by the OGP barrier, where the optimal QAOA parameters change from an adiabatic to a non-adiabatic schedule.
