We prove quantum ergodicity for a family of periodic Schr\”odinger operators
$H$ on periodic graphs. This means that most eigenfunctions of $H$ on large
finite periodic graphs are equidistributed in some sense, hence delocalized.
Our results cover the adjacency matrix on $\mathbb{Z}^d$, the triangular
lattice, the honeycomb lattice, Cartesian products and periodic Schr\”odinger
operators on $\mathbb{Z}^d$. The theorem applies more generally to any periodic
Schr\”odinger operator satisfying an assumption on the Floquet eigenvalues.
