  Quantum state tomography is an essential tool for the characterization and
verification of quantum states. However, as it cannot be directly applied to
systems with more than a few qubits, efficient tomography of larger states on
mid-sized quantum devices remains an important challenge in quantum computing.
We develop a tomography approach that requires moderate computational and
quantum resources for the tomography of states that can be approximated by
Gibbs states of local Hamiltonians. The proposed method, Hamiltonian Learning
Tomography, uses a Hamiltonian learning algorithm to get a parametrized ansatz
for the Gibbs Hamiltonian, and optimizes it with respect to the results of
local measurements. We demonstrate the utility of this method with a high
fidelity reconstruction of the density matrix of 4 to 10 qubits in a Gibbs
state of the transverse-field Ising model, in numerical simulations as well as
in experiments on IBM Quantum superconducting devices accessed via the cloud.
Code implementation of the our method is freely available as an open source
software in Python.
