Classification of qubit cellular automata on hypercubic lattices

Abstract

We classify quantum cellular automata whose cells are qubits, on hypercubic lattices ${\mathbb{Z}}^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of such automata and use its characterisation to simulate a few steps of evolution and evaluate the rate of entanglement production between one cell and its surroundings.

6+6 pages, 5+4 figures; v2 minor revisions