Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the inception score. In this paper, we propose the quantum inception score, which relates the quality to the Holevo information of the quantum channel that classifies a given dataset. We prove that, under this proposed measure, the quantum generative models provide better quality than their classical counterparts because of the presence of quantum coherence, characterized by the resource theory of asymmetry, and entanglement. Furthermore, we harness the quantum fluctuation theorem to characterize the physical limitation of the quality of quantum generative models. Finally, we apply the quantum inception score to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics.

翻译：受经典生成模型在机器学习中巨大成功的启发，其量子版本的探索最近已开始活跃开展。为了开启这一研究，开发评估量子生成模型质量的相关指标至关重要；在经典情形中，Inception分数便是一个典型例子。本文提出量子Inception分数，该指标通过将质量与对给定数据集进行分类的量子信道的Holevo信息相关联。我们证明，在该拟议度量下，由于量子相干性（由不对称资源理论刻画）和纠缠的存在，量子生成模型的质量优于经典对应模型。此外，我们利用量子涨落定理来刻画量子生成模型质量的物理极限。最后，我们将量子Inception分数应用于评估一维自旋链模型作为量子生成模型的质量，其中以量子卷积神经网络作为量子分类器，用于量子多体物理中的相分类问题。