Three-Dimensional Quantum Cellular Automata from Chiral Semion Surface Topological Order and beyond

We construct a novel three-dimensional quantum cellular automaton (QCA) based on system with short-range entangled bulk and chiral semion boundary topological order. argue that either the QCA is nontrivial, i.e. not finite-depth circuit of local gates, or there exists two-dimensional commuting projector Hamiltonian realizing order (characterized by $U(1)_2$ Chern-Simons theory). Our obtained first constructing Walker-Wang certain premodular tensor category four, then condensing deconfined boson at level lattice operators. show resulting hosts surface in presence can be realized as non-Pauli stabilizer code qubits, from which defined. The construction generalized to class QCAs defined codes ${2^n}$-dimensional qudits feature anyons described $U(1)_{2^n}$ theory. results support conjecture group nontrivial isomorphic Witt non-degenerate braided fusion categories.