发表机构
Quantinuum（Quantinuum）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明，将量子生成模型的采样难度转移至未知数据分布需全局分布认证，导致高熵分布需指数级样本，区分了生成器级与源级难度。
AI 中文摘要
量子生成模型通常以输出分布被认为经典上难以采样的电路族为动机。然而，当此类模型在普通经典数据集上训练时，这种难度并不会自动转移到未知的数据生成分布。我们表明，通过总变差接近性将采样难度从量子模型转移到未知源，需要认证两个分布之间的全局关系，从而将问题简化为分布认证。将此简化与现有的认证下界相结合，对于与许多采样难度提议相关的高熵分布，得出指数级样本需求。因此，一般而言，多项式数量的样本无法证明将采样难度归因于未知的数据生成分布。此外，即使在经典上平凡的分布（如均匀分布和乘积分布）中，在缺乏结构假设的情况下，也需要指数级数量的样本来进行认证。我们的结果阐明了采样难度在量子生成建模中的作用，并在从普通数据集学习时区分了生成器级难度与源级难度。
英文摘要
Quantum generative models are often motivated by circuit families whose output distributions are believed to be classically hard to sample from. When such models are trained on ordinary classical datasets, however, this hardness does not automatically transfer to the unknown data-generating distribution. We show that transferring sampling hardness via total-variation closeness from a quantum model to an unknown source requires certifying a global relation between the two distributions, thereby reducing the problem to distribution certification. Combining this reduction with existing certification lower bounds yields an exponential sample requirement for the high-entropy distributions relevant to many sampling-hardness proposals. Consequently, polynomially many samples cannot, in general, justify attributing sampling hardness to an unknown data-generating distribution. Moreover, even classically trivial distributions, such as the uniform distribution and product distributions, require exponentially many samples to certify in the absence of structural assumptions. Our results clarify the role of sampling hardness in quantum generative modeling and distinguish generator-level hardness from source-level hardness when learning from ordinary datasets.
