  It is natural to measure the observables from the Hamiltonian-based quantum
dynamics, and its inverse process that Hamiltonians are estimated from the
measured data also is a vital topic. In this work, we propose a recurrent
neural network to learn the parameters of the target Hamiltonians from the
temporal records of single-qubit measurements. The method does not require the
assumption of ground states and only measures single-qubit observables. It is
applicable on both time-independent and time-dependent Hamiltonians and can
simultaneously capture the magnitude and sign of Hamiltonian parameters. Taking
quantum Ising Hamiltonians with the nearest-neighbor interactions as examples,
we trained our recurrent neural networks to learn the Hamiltonian parameters
with high accuracy, including the magnetic fields and coupling values. The
numerical study also shows that our method has good robustness against the
measurement noise and decoherence effect. Therefore, it has widespread
applications in estimating the parameters of quantum devices and characterizing
the Hamiltonian-based quantum dynamics.
