发表机构
Global Technology Applied Research, JPMorganChase; Google Quantum AI（摩根大通全球技术应用研究; 谷歌量子人工智能）
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QAOA在混合稠密自旋玻璃上可近似解耦为独立自旋-玻色子系统，并利用张量网络实现高深度下的能量计算，发现高阶问题需更多层且角度优化更难。
AI 中文摘要
量子近似优化算法（QAOA）被视为近期在组合优化中实现量子优势的有前景的候选方案，然而我们在大规模下研究它的能力是有限的。已有精确递归公式被引入用于预测大规模自旋玻璃上的QAOA性能，但评估这些公式的计算成本随QAOA层数呈指数增长，阻碍了在有前景的高深度区域研究QAOA。在这项工作中，我们表明对于计算任何混合稠密自旋玻璃问题上的QAOA能量这一任务，自旋近似解耦为独立的自旋-玻色子系统。在无限大小极限下，解耦变得精确，从而确立了自旋-玻色映射作为QAOA多体物理的自然框架。这种广义的自旋-玻色映射给出了一种递归程序，用于计算QAOA能量，该程序可以使用张量网络以适度的成本执行。作为数值应用，我们在先前技术难以处理的深度上优化纯和混合自旋玻璃上的QAOA，观察到对于相当的近似比，更高阶的问题需要更多的层，而角度优化变得更加困难。虽然解耦使得在大规模和深度下评估QAOA能量成为可能，但它并不能实现QAOA的强模拟；需要量子计算机来采样对应于预测能量的比特串。
英文摘要
The Quantum Approximate Optimization Algorithm (QAOA) is regarded as a promising candidate for near-term quantum advantage in combinatorial optimization, yet our ability to study it at scale is limited. Exact recursive formulas have been introduced for predicting QAOA performance on large spin glasses, but the computational cost of evaluating them grows exponentially with the number of QAOA layers, preventing the study of QAOA in the promising high-depth regime. In this work, we show that for the task of computing QAOA energy on any mixed dense spin glass problem, spins approximately decouple into independent spin-boson systems. In the infinite-size limit, the decoupling becomes exact, establishing the spin-boson mapping as a natural framework for the many-body physics of QAOA. This generalized spin-boson mapping gives a recursive procedure for computing QAOA energies that can be executed at modest cost using tensor networks. As a numerical application, we optimize QAOA on pure and mixed spin glasses at depths intractable for prior techniques, observing that higher-degree problems require more layers for a comparable approximation ratio while angle optimization becomes more challenging. While decoupling enables the evaluations of QAOA energies at large size and depth, it does not enable strong simulation of QAOA; a quantum computer is required to sample the bitstring corresponding to the predicted energy.
Comments108 pages, 8 figures, 2 tables
