Qade: solving differential equations on quantum annealers

Criado, Juan Carlos; Spannowsky, Michael

Abstract

We present a general method, called Qade, for solving differential equations using a quantum annealer. One of the main advantages of this method is its flexibility and reliability. On current devices, Qade can solve systems of coupled partial differential equations that depend linearly on the solution and its derivatives, with non-linear variable coefficients and arbitrary inhomogeneous terms. We test this through several examples that we implement in state-of-the-art quantum annealers. The examples include a partial differential equation and a system of coupled equations. This is the first time that equations of these types have been solved in such devices. We find that the solution can be obtained accurately for problems requiring a small enough function basis. We provide a Python package implementing the method at gitlab.com/jccriado/qade.

Citation

Criado, J. C., & Spannowsky, M. (2023). Qade: solving differential equations on quantum annealers. Quantum Science and Technology, 8(1), Article 015021. https://doi.org/10.1088/2058-9565/acaa51

• Journal Article Type: Article
• Acceptance Date: Dec 9, 2022
• Online Publication Date: Dec 21, 2022
• Publication Date: 2023
• Deposit Date: May 9, 2023
• Publicly Available Date: May 10, 2023
• Journal: Quantum Science and Technology
• Electronic ISSN: 2058-9565
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Issue: 1
• Article Number: 015021
• DOI: https://doi.org/10.1088/2058-9565/acaa51
• Public URL: https://durham-repository.worktribe.com/output/1173253