Qade: Solving Differential Equations on Quantum Annealers
This addresses the problem of leveraging quantum annealers for computational tasks in physics and engineering, though it is incremental as it builds on existing quantum annealing approaches.
The authors tackled solving differential equations on quantum annealers by introducing Qade, a method that expresses solutions as linear combinations of basis functions, and found it accurately solves certain systems on current devices when the basis is small.
We present a general method, called Qade, for solving differential equations using a quantum annealer. The solution is obtained as a linear combination of a set of basis functions. 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 the method with several examples and find that state-of-the-art quantum annealers can find the solution accurately for problems requiring a small enough function basis. We provide a Python package implementing the method at gitlab.com/jccriado/qade.