Qade: solving differential equations on quantum annealers. (1st January 2023)

• Record Type: Journal Article
• Authors: Criado, Juan Carlos; Spannowsky, Michael
• Is Part Of: Quantum science and technology. Volume 8:Number 1(2023)
• Publication Date: 2023-01-01
• Subjects: quantum annealing -- differential equations -- quantum adiabatic computation; Quantum theory -- Periodicals; Quantum theory; Periodicals; 530
• DOI: 10.1088/2058-9565/acaa51
• Languages: English
• ISSNs: 2058-9565

Abstract

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 .