  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.
