A Data Driven Approach to Learning The Hamiltonian Matrix in Quantum Mechanics

TL;DR

This paper introduces a machine learning method to determine the Hamiltonian matrix in quantum mechanics from experimental data, validated through classical and quantum computer simulations, highlighting its potential and limitations.

Contribution

It proposes a novel cost function and proof for learning the Hamiltonian matrix directly from data, integrating domain knowledge to enhance learning efficiency.

Findings

Successfully learned Hamiltonian matrices from simulated data

Validated approach on IBM quantum hardware

Discussed limitations and potential extensions

Abstract

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.