Hamiltonian Reconstruction Research Articles

Hamiltonian reconstruction: The correlation matrix and incomplete operator bases

Hamiltonian reconstruction: The correlation matrix and incomplete operator bases

Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates

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.

Reconstruction of Hamiltonians from given time evolutions

In this paper, we propose a systematic method to solve the inverse dynamical problem for a finite-level quantum system governed by the von Neumann equation: to find a class of Hamiltonians reproducing a prescribed time evolution of a pure or mixed state of the system. Our approach exploits the equivalence between the action of the group of evolution operators over the state space and the adjoint action of the unitary group over Hermitian matrices. The method is illustrated by two examples involving a pure and a mixed state.