Quantum cellular automata and invertible phases of matter

Speaker: Nikita Sopenko (Harvard University)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

Quantum cellular automata (QCAs) describe discrete-time local dynamics of quantum lattice systems. It has long been known that their classification up to quantum circuits is closely related to the classification of invertible phases of matter, since applying a QCA to an unentangled state produces an invertible state. In the most studied setting of spin systems, however, this relation is not one-to-one. I will discuss it for lattice systems with infinite-dimensional on-site Hilbert spaces, and show that there the correspondence becomes exact. One consequence is the existence of local commuting Hamiltonians for all invertible phases, including chiral 2d phases such as the (p+ip) superconductor.