发表机构
College of Computer Science, and ZJU-Ningbo Global Innovation Center, Zhejiang University; School of Physics, South China Normal University; Center on Frontiers of Computing Studies, School of Computer Science, Peking University（浙江大学计算机科学与技术学院及ZJU-宁波全球创新中心; 华南师范大学物理学院; 北京大学计算机科学与技术学院前沿计算研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出结构感知量子数据编码框架，将问题结构编译为高效状态制备电路，在计入编码成本后仍能恢复并扩展量子加速优势，确立问题结构为量子计算资源。
AI 中文摘要
量子算法可以提供可观的计算加速，然而一旦考虑与结构无关的经典数据编码成本，这些优势可能会消失。然而，现实世界的问题实例通常具有丰富的内部结构。这引出了一个基本问题：能否利用这种结构使量子加速在端到端成本核算中得以保留？在此，我们证明这是可行的。我们引入了一个用于结构感知量子数据编码的通用框架，该框架将问题结构的紧凑递归描述编译为高效的状态制备电路，直接将结构信息转化为降低的编码复杂度。对于无容量限制的设施选址问题，与结构无关的编码允许经典的去量子化，从而消除二次量子加速，而利用潜在的问题结构则可以在计入状态制备成本的情况下恢复这一优势。更广泛地，同一框架为组合优化制备结构化量子态，这些量子态捕获约束之间的非平凡关系，包括组平衡、冲突和协同奖励，将先前报道的超多项式量子优势扩展到更广泛的目标类别。这些结果确立了可利用的问题结构作为量子算法的计算资源，并为在数据密集型问题中实现量子优势提供了一条系统化路径。
英文摘要
Quantum algorithms can offer substantial computational speed-ups, yet these advantages may disappear once the cost of structure-agnostic classical data encoding is taken into account. Real-world problem instances, however, often possess rich internal structure. This raises a fundamental question: can such structure be harnessed to make quantum speed-ups survive end-to-end cost accounting? Here we show that it can. We introduce a general framework for structure-aware quantum data encoding that compiles compact recursive descriptions of problem structure into efficient state-preparation circuits, translating structural information directly into reduced encoding complexity. For the uncapacitated facility-location problem, structure-agnostic encoding admits a classical dequantization that eliminates the quadratic quantum speed-up, whereas exploiting the underlying problem structure restores this advantage even when state-preparation costs are included. More broadly, the same framework prepares structured quantum states for combinatorial optimization that capture non-trivial relations among constraints, including group balance, conflicts and synergistic rewards, extending previously reported super-polynomial quantum advantages to broader classes of objectives. These results establish exploitable problem structure as a computational resource for quantum algorithms and provide a systematic route towards realizing quantum advantage in data-intensive problems.
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