Work

Fermionic cellular automata in one dimension

Year: 2026

Type: article

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.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0267907

Authors: Lorenzo S. Trezzini, Matteo Lugli, Paolo Meda, Alessandro Bisio, Paolo Perinotti, Alessandro Tosini

Institutions: Istituto Nazionale di Fisica Nucleare, University of Pavia, Istituto Nazionale di Fisica Nucleare, Sezione di Pavia

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green