QBoost for regression problems: solving partial differential equations

Abstract: A hybrid algorithm based on machine learning and quantum ensemble learning is proposed that is capable of finding a solution to a partial differential equation with good precision and favorable scaling in the required number of qubits. The classical part is composed by training several regressors (weak-learners), capable of solving a partial differential equation using machine learning. The quantum part consists of adapting the QBoost algorithm to solve regression problems. We have successfully applied our framework to solve the 1D Burgers' equation with viscosity, showing that the quantum ensemble method really improves the solutions produced by weak-learners. We also implemented the algorithm on the D-Wave Systems, confirming the best performance of the quantum solution compared to the simulated annealing and exact solver methods, given the memory limitations of our classical computer used in the comparison.