Efficient Hamiltonian learning from Gibbs states

We describe a novel algorithm that learns a Hamiltonian from local expectations of its Gibbs state using the free energy variational principle. The algorithm avoids the need to compute the free energy directly, instead using efficient estimates of the derivatives of the free energy with respect to perturbations of the state. These estimates are based on a new entropy bound for Lindblad evolutions, which is of independent interest. We benchmark the algorithm by performing black-box learning of a nearest-neighbour Hamiltonian on a 100-qubit spin chain. A implementation of the algorithm with a Python front-end is made available for use.