Learning quantum Hamiltonians from single-qubit measurements

In the Hamiltonian-based quantum dynamics, to estimate Hamiltonians from the measured data is a vital topic. In this work, we propose a recurrent neural network to learn the target Hamiltonians from the temporal records of single-qubit measurements, which does not require the 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 the Hamiltonians with the nearest-neighbor interactions as numerical examples, we trained our recurrent neural networks to learn different types of Hamiltonians with high accuracy. The 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.