Qade: Solving Differential Equations on Quantum Annealers

Abstract

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.

QFitter -- A Quantum Fitting Framework Applied to Effective Field Theories

“…To turn this into a QUBO, we need to re-formulate it as a quadratic polynomial in binary variables. Binarization can be achieved by means of a binary encoding [15,29]:…”