Scalar fermionic cellular automata on finite Cayley graphs

Understand

A map on finitely many fermionic modes represents a unitary evolution if and only if it preserves canonical anti-commutation relations.

• We use this condition for the classification of fermionic cellu- lar automata (FCA) on Cayley graphs of finite groups in two simple but paradigmatic case studies.
• The physical properties of the solutions are discussed.
• Finally, features of the solutions that can be extended to the case of cellular automata on infinite graphs are analyzed.