Speaker: Sahand Seifnashri (IAS)
Title: Non-invertible Quantum Cellular Automata
Abstract: We propose a general definition of non-invertible symmetries on the lattice based on their action on local operators, leading to a natural notion of non-invertible Quantum Cellular Automata (QCAs). We formulate them as locality-preserving, unital completely positive (UCP) maps that satisfy additional conditions of dualizability and purity. We motivate these conditions and conjecture that they guarantee the existence of topological defects, or equivalently, sequential circuit presentations. Finally, we discuss an index theory that classifies the blend-equivalence classes of these non-invertible QCAs in 1+1d.