Risk aggregation by quantum generative modeling of copulas

The copula is a type of multivariate distribution with uniform marginals, which has been widely used in various fields to study the dependence between random variables. A recent study [1] demonstrated a technique that leverages the expressive power of quantum computers to model copulas for two variables. In particular, the structure of a copula is naturally mapped to a variational ansatz that creates a multipartite maximally entangled state. Here we extend the technique to model the joint distribution of three variables using IonQ quantum computers, specifically, The Dow Jones Total Stock Market Index, The Market Volatility Index, and the Japan Nikkei Market Index. We present numerical and experimental results comparing our approach to state-of-the-art classical methods. We also present and characterize methods that improve the initialization and training of the variational ansatz. Such improvements address vanishing gradients (barren plateaus), which are crucial for real applications which may involve several variables.

[1] arXiv:2109.06315