Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates

作     者：Cao, Chenfeng Hou, Shi-Yao Cao, Ningping Zeng, Bei 

作者机构：Department Of Physics The Hong Kong University Of Science And Technology Clear Water Bay Kowloon Hong Kong College Of Physics And Electronic Engineering Center For Computational Sciences Sichuan Normal University Chengdu610068 China Department Of Mathematics & Statistics University Of Guelph GuelphON Canada Institute For Quantum Computing University Of Waterloo WaterlooON Canada 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2020年

核心收录：

主　　题：Hamiltonians 

摘      要：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. Copyright © 2020, The Authors. All rights reserved.