Copula-based Risk Aggregation with Trapped Ion Quantum Computers

TL;DR

This paper demonstrates the application of quantum computers, specifically trapped ion quantum computers, to model copulas for risk aggregation, showing promising results and improved training strategies for multi-variable models.

Contribution

It introduces a quantum approach using QCBMs for copula modeling on trapped ion computers and proposes an annealing-inspired training strategy to enhance scalability.

Findings

Quantum models perform comparably or better than classical models in risk tasks.

Training efficacy decreases with model complexity, but can be improved with annealing strategies.

Successful modeling of 3- and 4-variable copulas on quantum hardware.

Abstract

Copulas are mathematical tools for modeling joint probability distributions. Since copulas enable one to conveniently treat the marginal distribution of each variable and the interdependencies among variables separately, in the past 60 years they have become an essential analysis tool on classical computers in various fields ranging from quantitative finance and civil engineering to signal processing and medicine. The recent finding that copulas can be expressed as maximally entangled quantum states has revealed a promising approach to practical quantum advantages: performing tasks faster, requiring less memory, or, as we show, yielding better predictions. Studying the scalability of this quantum approach as both the precision and the number of modeled variables increase is crucial for its adoption in real-world applications. In this paper, we successfully apply a Quantum Circuit Born Machine (QCBM) based approach to modeling 3- and 4-variable copulas on trapped ion quantum computers. We study the training of QCBMs with different levels of precision and circuit design on a simulator and a state-of-the-art trapped ion quantum computer. We observe decreased training efficacy due to the increased complexity in parameter optimization as the models scale up. To address this challenge, we introduce an annealing-inspired strategy that dramatically improves the training results. In our end-to-end tests, various configurations of the quantum models make a comparable or better prediction in risk aggregation tasks than the standard classical models. Our detailed study of the copula paradigm using quantum computing opens opportunities for its deployment in various industries.