Quantum Generative Model with Variable-depth Circuit

In recent years, an increasing number of studies about quantum machine learning not only provide powerful tools for quantum chemistry and quantum physics but also improve the classical learning algorithm. The hybrid quantum-classical framework, which is constructed by a variational quantum circuit (VQC) and an optimizer, plays a key role in the latest quantum machine learning studies. Nevertheless, in these hybridframework-based quantum machine learning models, the VQC is mainly constructed with a fixed structure and this structure causes inflexibility problems. There are also few studies focused on comparing the performance of quantum generative models with different loss functions. In this study, we address the inflexibility problem by adopting the variable-depth VQC model to automatically change the structure of the quantum circuit according to the qBAS score. The basic idea behind the variable-depth VQC is to consider the depth of the quantum circuit as a parameter during the training. Meanwhile, we compared the performance of the variable-depth VQC model based on four widely used statistical distances set as the loss functions, including Kullback-Leibler divergence (KL-divergence), Jensen-Shannon divergence (JS-divergence), total variation distance, and maximum mean discrepancy. Our numerical experiment shows a promising result that the variable-depth VQC model works better than the original VQC in the generative learning tasks.