发表机构
University of Alicante（阿利坎特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过转录级可容许关系审计量子加速的接口依赖性，区分三种接口机制，并证明在特定条件下经典算法可实现端到端多项式复杂度。
AI 中文摘要
原始量子加速是接口相对的：它们依赖于运行原始算法所用的输入访问方式以及消耗其状态或样本的输出契约。本文引入了一个转录级别的可容许关系 \\(A_M\preceq_{\mathrm{int}}A_Q\\)，该关系相对于量子接口的声明实现包来定义。它识别了同一包所许可的自适应经典访问转录，并计入了所有设置、转录生成和精度开销。主要应用是对团复形TDA中归一化贝蒂估计的操作性审计，区分了三种声明接口机制。可逆索引单纯形接口通过评估其在单个计算分支上的可逆例程，证明了匹配的经典单纯形采样和局部拉普拉斯行访问。基于成员资格的制备引发了一个开销为 \\(\binom{n}{k+1}/|S_k|\\) 的拒绝路径。抽象谱或块编码接口需要附带的实现包、转录缩减或共享表示。在索引证书和接口封闭性下，端到端成本由导入估计器对间隙 \\(\gamma\\) 的谱依赖性决定；具体实现的有限树宽族已经允许通过 \\(\mathbb{Q}\\) 上的秩进行精确的 \\(\mathrm{poly}(n)\\) 经典贝蒂计算。低秩分离支持了访问和输出契约的作用。
英文摘要
Primitive quantum speedups are interface-relative: they depend on the input access used to run the primitive and on the output contract used to consume its state or samples. This paper introduces a transcript-level admissibility relation \(A_M\preceq_{\mathrm{int}}A_Q\), defined relative to the declared implementation package of the quantum interface. It identifies which adaptive classical access transcripts that same package licenses, with all setup, transcript-generation, and precision overheads charged. The main application is an operational audit for normalized-Betti estimation in clique-complex TDA, separating three declared-interface regimes. Reversible indexed simplex interfaces certify matched classical simplex sampling and local Laplacian row access by evaluating their reversible routines on single computational branches. Membership-based preparations induce a rejection route of overhead \(\binom{n}{k+1}/|S_k|\). Abstract spectral or block-encoding interfaces require an accompanying implementation package, transcript reduction, or shared representation. Under the indexed certificate and interface closure, the end-to-end cost is fixed by the imported estimator's spectral dependence on the gap \(γ\); the concretely realized bounded-treewidth family already admits exact \(\mathrm{poly}(n)\) classical Betti computation by rank over \(\mathbb{Q}\). A low-rank separation supports the role of access and output contracts.
