Quantum Inception Score

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.