  Modeling joint probability distributions is an important task in a wide
variety of fields. One popular technique for this employs a family of
multivariate distributions with uniform marginals called copulas. While the
theory of modeling joint distributions via copulas is well understood, it gets
practically challenging to accurately model real data with many variables. In
this work, we design quantum machine learning algorithms to model copulas. We
show that any copula can be naturally mapped to a multipartite maximally
entangled state. A variational ansatz we christen as a `qopula' creates
arbitrary correlations between variables while maintaining the copula structure
starting from a set of Bell pairs for two variables, or GHZ states for multiple
variables. As an application, we train a Quantum Generative Adversarial Network
(QGAN) and a Quantum Circuit Born Machine (QCBM) using this variational ansatz
to generate samples from joint distributions of two variables for historical
data from the stock market. We demonstrate our generative learning algorithms
on trapped ion quantum computers from IonQ for up to 8 qubits and show that our
results outperform those obtained through equivalent classical generative
learning. Further, we present theoretical arguments for exponential advantage
in our model's expressivity over classical models based on communication and
computational complexity arguments.
