量子生成对抗网络在图像生成中泛化能力差，仅能学习数据平均特征。
On the Generalization Limits of Quantum Generative Adversarial Networks with Pure State Generators
- 纯态生成器输出与目标分布的保真度决定判别器下限
- 现有模型训练后仅学得数据平均表示，无法泛化到新数据
- 对量子生成模型的泛化瓶颈提供理论解释，适合量子机器学习研究者
我们研究了量子生成对抗网络（QGAN）在图像生成任务中的能力。分析聚焦于生成器和判别器均为全量子实现的情况。通过对当前主流架构进行大量数值测试，发现QGAN在跨数据集泛化方面表现不佳，收敛结果仅为训练数据的平均表示。当生成器输出为纯态时，我们通过分析推导出判别器性能的理论下界，该下界由生成器输出纯态与目标数据分布之间的保真度决定，从而为现有模型的局限性提供了理论解释。研究揭示了现有量子生成模型在泛化能力上的根本挑战。尽管分析集中于QGAN，但结论对相关量子生成模型具有普遍意义。
原文摘要 · Abstract (English)
We investigate the capabilities of Quantum Generative Adversarial Networks (QGANs) in image generations tasks. Our analysis centers on fully quantum implementations of both the generator and discriminator. Through extensive numerical testing of current main architectures, we find that QGANs struggle to generalize across datasets, converging on merely the average representation of the training data. When the output of the generator is a pure-state, we analytically derive a lower bound for the discriminator quality given by the fidelity between the pure-state output of the generator and the target data distribution, thereby providing a theoretical explanation for the limitations observed in current models. Our findings reveal fundamental challenges in the generalization capabilities of existing quantum generative models. While our analysis focuses on QGANs, the results carry broader implications for the performance of related quantum generative models.
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