Corey Jones: Symmetric quantum cellular automata in 1D

Abstract: Quantum cellular automata (QCA) are models of discrete-time unitary dynamics on quantum spin systems on a lattice. They can be formulated as a certain group of automorphisms on the quasi-local C*-algebra of a spin system. A problem of interest is to understand the group of QCA modulo the normal subgroup of finite depth circuits. Recent developments in the theory of 2+1D topologically ordered spin systems have spurred significant interest in a version of this problem for 1D QCA defined only on operators invariant under a (weak)-Hopf algebra symmetry. We will give a gentle introduction to all of the ingredients of this problem mentioned above, and discuss recent progress