Many successful families of generative models leverage a low-dimensional latent distribution that is mapped to a data distribution. Though simple latent distributions are often used, the choice of distribution has a strong impact on model performance. Recent experiments have suggested that the probability distributions produced by quantum processors, which are typically highly correlated and classically intractable, can lead to improved performance on some datasets. However, when and why latent distributions produced by quantum processors can improve performance, and whether these improvements are connected to quantum properties of these distributions, are open questions that we investigate in this work. We show in theory that, under certain conditions, these "quantum latent distributions" enable generative models to produce data distributions that classical latent distributions cannot efficiently produce. We provide intuition as to the underlying mechanisms that could explain a performance advantage on real datasets. Based on this, we perform extensive benchmarking on a synthetic quantum dataset and the QM9 molecular dataset, using both simulated and real photonic quantum processors. We find that the statistics arising from quantum interference lead to improved generative performance compared to classical baselines, suggesting that quantum processors can play a role in expanding the capabilities of deep generative models.

翻译：许多成功的生成模型系列利用低维潜在分布，该分布被映射到数据分布。尽管通常使用简单的潜在分布，但分布的选择对模型性能有显著影响。最近的实验表明，量子处理器产生的概率分布（通常具有高度相关性且经典计算难以处理）在某些数据集上能够带来性能提升。然而，量子处理器产生的潜在分布何时以及为何能够提升性能，以及这些提升是否与这些分布的量子特性相关，仍是本工作中探讨的开放性问题。我们在理论上证明，在特定条件下，这些“量子潜在分布”使得生成模型能够产生经典潜在分布无法高效生成的数据分布。我们提供了关于潜在机制的解释，以说明为何在真实数据集上可能产生性能优势。基于此，我们在合成量子数据集和QM9分子数据集上进行了广泛基准测试，使用了模拟和真实的光子量子处理器。研究发现，源于量子干涉的统计特性相比经典基线带来了生成性能的提升，这表明量子处理器能够在扩展深度生成模型能力方面发挥作用。