  By reformulating the Wang tiles formalism with tensors, we propose a natural
generalization to the probabilistic and quantum setting. In this new framework,
we introduce notions of tilings and periodicity directly extending their
classical counterparts. In the one dimensional case, we recover the
decidability of the generalized domino problem by linking it to the trace
characterization of nilpotent matrices. In the two-dimensional case, we provide
extension of weak and strong aperiodicity respectively and show the equivalence
of those generalized notions, extending the well known equivalence in the
classical case. We also exhibit a quantum tile set being aperiodic while its
underlying classical tile set is not, proving that quantum interference can
suppress periodic patterns.
