On the structure of Clifford quantum cellular automata

Understand

We study reversible quantum cellular automata with the restriction that these are also Clifford operations.

• This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators.
• Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space.
• We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection invariant with respect to the origin.