Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates

• Main Authors: Cao, Chenfeng, Hou, Shi-Yao, Cao, Ningping, Zeng, Bei
• Format: Journal Article
• Language: English
• Published: 11-02-2022
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.2007.05962

Journal of Physics: Condensed Matter 33 (6), 064002 (2020) Reconstructing a system Hamiltonian through measurements on its eigenstates
is an important inverse problem in quantum physics. Recently, it was shown that
generic many-body local Hamiltonians can be recovered by local measurements
without knowing the values of the correlation functions. In this work, we
discuss this problem in more depth for different systems and apply the
supervised learning method via neural networks to solve it. For low-lying
eigenstates, the inverse problem is well-posed, neural networks turn out to be
efficient and scalable even with a shallow network and a small data set. For
middle-lying eigenstates, the problem is ill-posed, we present a modified
method based on transfer learning accordingly. Neural networks can also
efficiently generate appropriate initial points for numerical optimization
based on the BFGS method.