Quantum Hamiltonian Learning for the Fermi-Hubbard Model

This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve $ϵ$ $\epsilon $ -accurate estimation for all parameters, only $\tilde{\mathcal{O}}({ϵ}^{-1})$ $\tilde{\mathcal{O}}(\epsilon ^{-1})$ total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation.