With the fast development of quantum technology, the sizes of both digital
and analog quantum systems increase drastically. In order to have better
control and understanding of the quantum hardware, an important task is to
characterize the interaction, i.e., to learn the Hamiltonian, which determines
both static and dynamic properties of the system. Conventional Hamiltonian
learning methods either require costly process tomography or adopt impractical
assumptions, such as prior information on the Hamiltonian structure and the
ground or thermal states of the system. In this work, we present a robust and
efficient Hamiltonian learning method that circumvents these limitations based
only on mild assumptions. The proposed method can efficiently learn any
Hamiltonian that is sparse on the Pauli basis using only short-time dynamics
and local operations without any information on the Hamiltonian or preparing
any eigenstates or thermal states. The method has a scalable complexity and a
vanishing failure probability regarding the qubit number. Meanwhile, it
performs robustly given the presence of state preparation and measurement
errors and resiliently against a certain amount of circuit and shot noise. We
numerically test the scaling and the estimation accuracy of the method for
transverse field Ising Hamiltonian with random interaction strengths and
molecular Hamiltonians, both with varying sizes and manually added noise. All
these results verify the robustness and efficacy of the method, paving the way
for a systematic understanding of the dynamics of large quantum systems.Comment: 41 pages, 6 figures, Open source implementation available at
https://github.com/zyHan2077/HamiltonianLearnin