Classification of Qubit Cellular Automata on Hypercubic Lattices

We classify quantum cellular automata whose cells are qubits, on hypercubic lattices Zs, 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.