Quantum algorithm for credit valuation adjustments

TL;DR

This paper explores the potential of quantum algorithms to accelerate credit valuation adjustment calculations in finance, proposing methods to improve quantum circuit efficiency and analyzing prospects for quantum speedup over classical methods.

Contribution

It introduces a quantum algorithm framework for CVA, utilizing Bayesian quantum amplitude estimation and heuristics to reduce resource requirements and enhance practical quantum advantage.

Findings

Numerical analysis shows potential quantum speedup over classical Monte Carlo methods.

Heuristics improve quantum circuit depths for CVA calculations.

Quantum advantage depends on noise levels and problem size.

Abstract

Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases, credit valuation adjustment (CVA), and identify opportunities and challenges towards quantum advantage for practical instances. To improve the depths of quantum circuits for solving such problem, we draw on various heuristics that indicate the potential for significant improvement over well-known techniques such as reversible logical circuit synthesis. In minimizing the resource requirements for amplitude amplification while maximizing the speedup gained from the quantum coherence of a noisy device, we adopt a recently developed Bayesian variant of quantum amplitude estimation using engineered likelihood functions (ELF). We perform numerical analyses to characterize the prospect of quantum speedup in concrete CVA instances over classical Monte Carlo simulations.