Dr. Paolo Meda

Classification of One-dimensional Single Fermionic Quantum Cellular Automata

Fermionic Quantum Cellular Automata (FQCA) define a local and causal discrete evolution of a grid of Fermionic modes located at each cell. The mathematical description of FQCA may be provided by assigning a graded quasi-local algebra of observables for each Fermionic mode, and thus homogeneous automorphisms modelling the evolution of the quantum cells. In this talk, I discuss some new developments in the study of FQCA and their properties of implementability as finite depth quantum circuits (FDQCs). In the first step, it is shown how to relate two FQCA through a FDQC without the addition of ancilla degrees of freedom, by employing the so-called method of ancilla removal. In the second step, I present a complete classification of nearest-neighbours FQCA over one-dimensional cubic lattices, consisting of a single local Fermionic mode per site. Among all possible cases, a novel class of automata called forking automata is discovered, which is unique to the Fermionic theory and has not ungraded counterparts. The talk is based on a joint work with A. Bisio, M. Lugli, P. Perinotti, A. Tosini, and L. Trezzini which is currently in preparation.