Simulating the non-Hermitian dynamics of financial option pricing with quantum computers

Kumar, S and Wilmott, CM ORCID: https://orcid.org/0000-0003-4738-4227, 2025. Simulating the non-Hermitian dynamics of financial option pricing with quantum computers. Nature Scientific Reports, 15 (1): 13268. ISSN 2045-2322

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Abstract

The Schrödinger equation describes how quantum states evolve according to the Hamiltonian of the system. For physical systems, we have it that the Hamiltonian must be a Hermitian operator to ensure unitary dynamics. For anti-Hermitian Hamiltonians, the Schrödinger equation instead models the evolution of quantum states in imaginary time. This process of imaginary time evolution has been used successfully to calculate the ground state of a quantum system. Although imaginary time evolution is non-unitary, the normalised dynamics of this evolution can be simulated on a quantum computer using the quantum imaginary time evolution (QITE) algorithm. In this paper, we broaden the scope of QITE by removing its restriction to anti-Hermitian Hamiltonians, which allows us to solve any partial differential equation (PDE) that is equivalent to the Schrödinger equation with an arbitrary, non-Hermitian Hamiltonian. An example of such a PDE is the famous Black-Scholes equation that models the price of financial derivatives. We will demonstrate how our generalised QITE methodology offers a feasible approach for real-world applications by using it to price various European option contracts modelled according to the Black-Scholes equation.

Item Type:	Journal article
Publication Title:	Nature Scientific Reports
Creators:	Kumar, S. and Wilmott, C.M.
Publisher:	Springer Science and Business Media LLC
Date:	April 2025
Volume:	15
Number:	1
ISSN:	2045-2322
Identifiers:	Number Type 10.1038/s41598-025-97245-3 DOI 2430553 Other
Rights:	© The Author(s) 2025 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Divisions:	Schools > School of Science and Technology
Record created by:	Jeremy Silvester
Date Added:	20 Jun 2025 12:45
Last Modified:	20 Jun 2025 12:45
URI:	https://irep.ntu.ac.uk/id/eprint/53776

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