A Quantum algorithm for linear PDEs arising in Finance

TL;DR

This paper introduces a hybrid quantum-classical algorithm leveraging quantum computing to efficiently price European and Asian options in finance by approximating the related PDE with shallow quantum circuits.

Contribution

It presents a novel quantum algorithm based on the equivalence between PDEs in finance and the Schrödinger equation, requiring only few qubits and suitable for noisy quantum devices.

Findings

Developed a shallow quantum circuit approximation for option pricing PDEs.

Demonstrated potential for quantum computing in practical financial applications.

Bridged quantum chemistry techniques with quantitative finance methods.

Abstract

We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation and the Schrodinger equation in imaginary time. We devise a strategy to build a shallow quantum circuit approximation to this equation, only requiring few qubits. This constitutes a promising candidate for the application of Quantum Computing techniques (with large number of qubits affected by noise) in Quantitative Finance.