CMSA Special Seminar: Quantum Cellular Automata

A discrete time evolution on lattice systems that has a notion of lightcone is called a quantum cellular automaton. Lattice translation in 1D is a well-known example of QCA that is nontrivial in the sense that it is not a local Hamiltonian evolution. In higher dimensions, more subtle QCA are found in relation to certain topological phases of matter, but the scope of all QCA is far from being fully determined. I will report the status of our understanding on this subject, emphasizing the role of locally generated simple subalgebras.