



01959nas a2200217   4500008004100000245010400041210006900145260001400214520119900228653002701427653003501454653003101489653005201520100002001572700001601592700001501608700002301623700003001646700002801676856003701704       2022                        eng d00aThree-dimensional quantum cellular automata from chiral semion surface topological order and beyond0 aThreedimensional quantum cellular automata from chiral semion su  c2/10/20223 a<p>We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by U(1)2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2n-dimensional qudits that feature surface anyons described by U(1)2n Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.</p>10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aShirley, Wilbur1 aChen, Yu-An1 aDua, Arpit1 aEllison, Tyler, D.1 aTantivasadakarn, Nathanan1 aWilliamson, Dominic, J.  uhttps://arxiv.org/abs/2202.05442