  We present a new machine learning technique which calculates a real-valued,
time independent, finite dimensional Hamiltonian matrix from only experimental
data. A novel cost function is given along with a proof that the cost function
has the theoretically correct Hamiltonian as a global minimum. We present
results based on data simulated on a classical computer and results based on
simulations of quantum systems on IBM's ibmqx2 quantum computer. We conclude
with a discussion on the limitations of this data driven framework, as well as
several possible extensions of this work. We also note that algorithm presented
in this article not only serves as an example of using domain knowledge to
design a machine learning framework, but also as an example of using domain
knowledge to improve the speed of such algorithm.
