Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum variational autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relations and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

Quantum neural networks (QNNs) are gaining attention for their potential, but their lack of interpretability remains a barrier to wider adoption. In this paper, we adapt and extend explainability techniques commonly used in classical neural networks to the quantum domain, making QNNs more transparent and interpretable. By applying both feature-based and example-based methods, we provide a comprehensive analysis of how QNNs generate predictions. Our results demonstrate that these adapted techniques offer valuable insights into the internal mechanisms of QNNs, paving the way for more reliable and trustworthy quantum machine learning models. This work contributes to improving the explainability of QNNs, enhancing their applicability in complex, real-world scenarios.

We introduce the concept-driven quantum neural network (CD-QNN), an innovative architecture designed to enhance the interpretability of quantum neural networks (QNNs). CD-QNN merges the representational capabilities of QNNs with the transparency of self-explanatory models by mapping input data into a human-understandable concept space and making decisions based on these concepts. The algorithmic design of CD-QNN is comprehensively analyzed, detailing the roles of the concept generator, feature extractor, and feature integrator in improving and balancing model expressivity and interpretability. Experimental results demonstrate that CD-QNN maintains high predictive accuracy while offering clear and meaningful explanations of its decision-making process. This paradigm shift in QNN design underscores the growing importance of interpretability in quantum artificial intelligence, positioning CD-QNN and its derivative technologies as pivotal in advancing reliable and interpretable quantum intelligent systems for future research and applications.

Quantum generative models have shown promise in fields such as quantum chemistry, materials science, and optimization. However, their practical utility is hindered by a significant challenge: the lack of interpretability. In this work, we introduce model inversion to enhance both the interpretability and controllability of quantum generative models. Model inversion allows for tracing generated quantum states back to their latent variables, revealing the relationship between input parameters and generated outputs. We apply this method to models generating ground states for Hamiltonians, such as the transverse-field Ising model (TFIM) and generalized cluster Hamiltonians, achieving interpretability control without retraining the model. Experimental results demonstrate that our approach can accurately guide the generated quantum states across different quantum phases. This framework bridges the gap between theoretical models and practical applications by providing transparency and fine-tuning capabilities, particularly in high-stakes environments like drug discovery and material design.

Kernels play a crucial role in Gaussian process regression. Analyzing kernels from their spectral domain has attracted extensive attention in recent years. Gaussian mixture models (GMM) are used to model the spectrum of kernels. However, the number of components in a GMM is fixed. Thus, this model suffers from overfitting or underfitting. In this paper, we try to combine the spectral domain of kernels with nonparametric Bayesian models. Dirichlet processes mixture models are used to resolve this problem by changing the number of components according to the data size. Multiple experiments have been conducted on this model and it shows competitive performance.