I will outline a classification framework for quantum phases within the setting of stabilizer states and quantum cellular automata (QCA). Both admit a precise algebraic formulation—stabilizer codes as modules over Laurent polynomial rings, and QCA as locality-preserving automorphisms of operator algebras—through which topological invariants such as Witt classes and boundary charge modules arise. I will review my recent work classifying Clifford QCA and Pauli stabilizer codes, which fit naturally into the same mathematical framework.
A Case Study in the Classification of Quantum Phase Sponsored by the Meyer Fund
A Case Study in the Classification of Quantum Phase