Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates. (11th November 2020)

• Record Type: Journal Article
• Authors: Cao, Chenfeng; Hou, Shi-Yao; Cao, Ningping; Zeng, Bei
• Is Part Of: Journal of physics. Volume 33:Number 6(2021)
• Publication Date: 2020-11-11
• Subjects: Hamiltonian learning -- inverse problem -- neural network; Condensed matter -- Periodicals; Matière condensée -- Périodiques; Vaste stoffen; Vloeistoffen; Natuurkunde; Electronic journals; Computer network resources; 530.4105
• DOI: 10.1088/1361-648X/abc4cf
• Languages: English
• ISSNs: 0953-8984

Abstract

Abstract: 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 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.