  Predicting properties across system parameters is an important task in
quantum physics, with applications ranging from molecular dynamics to
variational quantum algorithms. Recently, provably efficient algorithms to
solve this task for ground states within a gapped phase were developed. Here we
dramatically improve the efficiency of these algorithms by showing how to learn
properties of all ground states for systems with periodic boundary conditions
from a single ground state sample. We prove that the prediction error tends to
zero in the thermodynamic limit and numerically verify the results.
