1:30 pm MCP 201
Quantum Cellular Automata, Invertible Phases, and Beyond.
Quantum cellular automata (QCA) are discrete time unitary dynamics with a light cone. A typical question is whether QCA time evolution can be expressed as Hamiltonian time evolution, in other words whether the discrete time can be extended to continuous time. A classic result of GNVW showed that 1d lattice translations are not expressible by a finite depth quantum circuit, and they fully classified 1d QCA up to circuits. Recently it has been appreciated that this problem is closely related to the classification of topological phases. A lot of rigorous progress on the classification of topological phases has come out of this observation, and I will try to give some highlights. Topics include the one-to-one correspondence between equivalence classes of QCAs and invertible topological phases, the bulk-boundary correspondence for invertible states and SPTs, the theory of 't Hooft anomalies on the lattice, continuum-lattice correspondence for 1+1d conformal field theories, and the Kitaev spectrum of invertible states.