Scalably learning quantum many-body Hamiltonians from dynamical data
This addresses the challenge of Hamiltonian estimation in quantum systems for physicists and engineers, offering a practical and scalable method that is incremental in its integration of machine learning and quantum techniques.
The paper tackles the problem of learning quantum many-body Hamiltonians from dynamical data by introducing a scalable, data-driven approach that combines gradient-based optimization with tensor network representations, achieving an error constant in system size and scaling as the inverse square root of data set size for the one-dimensional Heisenberg model.
The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system. In this work, we introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data, by bringing together techniques from gradient-based optimization from machine learning with efficient quantum state representations in terms of tensor networks. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins. In particular, we demonstrate on synthetic data that the algorithm works even if one is restricted to one simple initial state, a small number of single-qubit observables, and time evolution up to relatively short times. For the concrete example of the one-dimensional Heisenberg model our algorithm exhibits an error constant in the system size and scaling as the inverse square root of the size of the data set.