In three dimensions, there is a nontrivial quantum cellular automaton (QCA), which disentangles [Haah, Fidkowski, and Hastings, Commun. Math. Phys. 398, 469 (2023)] the three-fermion Walker-Wang model, a model whose action depends on Stiefel-Whitney classes of the spacetime manifold. Here we present a conjectured generalization to higher dimensions. For an arbitrary symmetry protected topological phase of time reversal whose action depends on Stiefel-Whitney classes, we construct a corresponding QCA that we conjecture disentangles that phase. Some of our QCA are Clifford, and we relate these to a classification theorem of Clifford QCA. We also identify Clifford QCA in $4m+1$ dimensions, for which we find a low-depth circuit description using non-Clifford gates but not with Clifford gates.

Close

PrevNext

View figure in article

• Quantum circuits
• Symmetry protected topological states
• Cellular automata