A Data Driven Approach to Learning The Hamiltonian Matrix in Quantum Mechanics
This work addresses the challenge of extracting Hamiltonian matrices in quantum mechanics, which is incremental as it builds on existing data-driven approaches but introduces a novel cost function and validation.
The authors tackled the problem of learning a Hamiltonian matrix from experimental data in quantum mechanics, presenting a new machine learning technique with a novel cost function proven to have the correct Hamiltonian as a global minimum, and demonstrated results using simulated data and IBM's quantum computer.
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.