QBoost for regression problems: solving partial differential equations

A hybrid algorithm based on machine learning and quantum ensemble learning is proposed to find an approximate solution to a partial differential equation with good precision and favorable scaling in the required number of qubits. The classical component consists in training several regressors (weak-learners), capable of solving a partial differential equation approximately using machine learning. The quantum component consists in adapting the QBoost algorithm to solve regression problems to build an ensemble of classical learners. 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 classical weak-learners. We also implemented the algorithm on the D-Wave Systems, confirming the good performance of the quantum solution compared to the simulated annealing and exact solver methods.