Fermionic cellular automata in one dimension

Abstract

We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the addition of ancillary systems. We strengthen this result removing the ancilla degrees of freedom in defining the equivalence classes. A complete characterization of nearest-neighbours automata is given. A class of Fermionic automata is found which cannot be expressed in terms of single mode and controlled-phase gates composed with shifts, as is the case for qubit cellular automata.