量子生成模型若输出抗集中分布则难训练，但稀疏分布可提升可训练性。
Limits of quantum generative models with classical sampling hardness
- 从输出分布角度分析量子生成模型，发现抗集中分布难以训练。
- 稀疏分布的模型可被有效训练，且可能被经典算法替代。
- 量子优势需来自非抗集中机制，适用于验证量子过程的场景。
采样任务在理论上和实验中均成功展示了量子优势，推动了利用量子计算机进行生成建模以生成符合数据集概率分布的样本。特别是，构建在经典困难分布上的生成模型能直接排除经典模拟的可能性，基于理论分离。本文从输出分布视角研究量子生成模型，表明具有抗集中特性的模型平均情况下无法训练，包括展示量子优势的模型。相反，输出稀疏分布的模型可被训练。我们考察了特殊情形以增强可训练性，观察到这为经典代理采样算法打开了路径。该权衡与量子过程验证相关。结论是：量子优势仍可在生成模型中存在，但其来源必须区别于抗集中现象。
原文摘要 · Abstract (English)
Sampling tasks have been successful in establishing quantum advantages both in theory and experiments. This has fueled the use of quantum computers for generative modeling to create samples following the probability distribution underlying a given dataset. In particular, the potential to build generative models on classically hard distributions would immediately preclude classical simulability, due to theoretical separations. In this work, we study quantum generative models from the perspective of output distributions, showing that models that anticoncentrate are not trainable on average, including those exhibiting quantum advantage. In contrast, models outputting data from sparse distributions can be trained. We consider special cases to enhance trainability, and observe that this opens the path for classical algorithms for surrogate sampling. This observed trade-off is linked to verification of quantum processes. We conclude that quantum advantage can still be found in generative models, although its source must be distinct from anticoncentration.
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