This paper presents the minimum supports of states for stationary measures of the Grover walk on the d-dimensional lattice by solving the corresponding eigenvalue problem. The numbers of the minimum supports for moving and flip-flop shifts are 2^d (d ge 1) and 4 (d ge 2), respectively.
@article{arxiv.2001.10261,
title = {On the support of the Grover walk on higher-dimensional lattices},
author = {Norio Konno and Sarato Takahashi},
journal= {arXiv preprint arXiv:2001.10261},
year = {2021}
}