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Qade: solving differential equations on quantum annealers

Criado, Juan Carlos; Spannowsky, Michael

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Juan Carlos Criado


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


Criado, J. C., & Spannowsky, M. (2023). Qade: solving differential equations on quantum annealers. Quantum Science and Technology, 8(1), Article 015021.

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
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 8
Issue 1
Article Number 015021


Published Journal Article (1.1 Mb)

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Copyright Statement
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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