发表机构
Yau Mathematical Sciences Center, Tsinghua University; Qiuzhen College, Tsinghua University; Beijing International Center for Mathematical Research, Peking University; Institute for Applied Mathematics, Tsinghua University; Beijing Institute of Mathematical Sciences and Applications（清华大学丘成桐数学科学中心; 清华大学求真学院; 北京大学北京国际数学研究中心; 清华大学应用数学中心; 北京数学与应用科学研究所以）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对传统QAOA忽视问题层次结构的问题，提出学习投影子QAOA（LP-QAOA），通过冻结电路并利用输出状态定义投影子混合器，在BCST实例上实现更优采样概率、更低资源需求和更好可训练性，并扩展到软层次结构问题。
AI 中文摘要
许多优化问题在需要昂贵的最终评估之前，会揭示出廉价的结构信息，而传统的量子近似优化算法（QAOA）在整个过程中应用单一的聚合目标。我们引入了学习投影子量子交替算子拟设（LP-QAOA），这是一种多阶段协议，它冻结已优化的电路，并利用其输出状态来定义后续的投影子混合器。我们证明了LP-QAOA的一个稳定性定理，该定理限制了近似误差在连续冻结阶段中的传播。我们的分析还表明，学习投影子混合避免了局部混合器的高阶隧穿抑制。我们在块约束自旋平铺（BCST）实例上进行了态矢量模拟，其中LP-QAOA在采样最优解的概率、估计的逻辑资源需求以及可训练性方面均优于测试的基线。一个辅助的随机块模型实验将LP-QAOA扩展到具有软层次结构的优化问题。我们的结果凸显了LP-QAOA通过利用层次问题结构来改进变分量子优化的潜力。
英文摘要
Many optimization problems reveal inexpensive structural information before requiring costly final evaluation, whereas the conventional quantum approximate optimization algorithm (QAOA) applies a single aggregate objective throughout. We introduce the learned-projector quantum alternating operator ansatz (LP-QAOA), a multistage protocol that freezes optimized circuits and uses their output states to define later projector mixers. We prove a stability theorem for LP-QAOA that bounds the propagation of approximation errors through successive frozen stages. Our analysis also shows how learned-projector mixing avoids the high-order tunnelling suppression of local mixers. We conduct state-vector simulations on block-constrained spin tiling (BCST) instances, where LP-QAOA achieves higher probabilities of sampling the optimum, lower estimated logical-resource requirements, and better trainability than the tested baselines. A supporting stochastic block model experiment extends LP-QAOA to optimization problems with soft hierarchical structure. Our results highlight the potential of LP-QAOA to improve variational quantum optimization by exploiting hierarchical problem structure.
Comments51 pages, 9 figures
