Generative modeling focuses on learning a data distribution $p_{\text{data}}(x)$ and creating new samples $x \sim p_{\text{model}}(x)$ that resemble the original data. This chapter introduces quantum approaches to this task. Classical methods like Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) provide a foundation, but quantum circuits offer potentially different ways to represent and sample from complex probability distributions.

You will study two primary quantum generative models:

• Quantum Circuit Born Machines (QCBMs): Learn how parameterized quantum circuits can implicitly model probability distributions defined by their measurement outcomes, $p(x) = |\langle x | \psi(\theta) \rangle|^2$.
• Quantum Generative Adversarial Networks (QGANs): Understand the framework where quantum circuits serve as generators, competing against classical or quantum discriminators.

We will examine the operational principles, architectures, and specific training challenges associated with these models, such as balancing the adversarial components in QGANs. You will also learn about methods for evaluating the quality of generated samples and the techniques required to sample effectively from the trained quantum models. The chapter concludes with a practical exercise in implementing a basic QGAN.