Proper Agnostic Learning of Matrix Product States and Tree Tensor Networks

We establish proper agnostic learning of matrix product states and tree tensor networks. Given copies of an arbitrary quantum state $ρ$, our algorithms return a state $|ψ\rangle$ of chosen bond dimension such that $\langleψ| ρ|ψ\rangle$ is within $\varepsilon$ of the optimum over the model class, wi