Special Quantum Matter Seminar

We will show how quantum cellular automata (QCA), which originated in quantum information theory, appear naturally in the study of symmetry protected topological (SPT) phases of matter. Specifically, they appear when one studies these phases in the "condensed matter" or "many-qubit model" context, i.e. in a Hamiltonian formalism with a tensor product Hilbert space of finite dimensional site Hilbert spaces. We will make connections between QCA and the field theoretic methods for classifying these phases. We will also give a very simple explicit form for a non-trivial three dimensional QCA which was found previously via a computer assisted method, and relate this form to discrete Chern Simons theory.