



02246nas a2200205   4500008004100000245006600041210006600107260001400173520157400187653002701761653003101788653005201819100002301871700001601894700001501910700002001925700003001945700002801975856003702003       2022                        eng d00aPauli topological subsystem codes from Abelian anyon theories0 aPauli topological subsystem codes from Abelian anyon theories  c11/7/20223 a<p>We construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the classification of two-dimensional Pauli topological subsystem codes to systems of composite-dimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories. We exemplify the construction with topological subsystem codes defined on four-dimensional qudits based on the Z(1)4 anyon theory with degenerate braiding relations and the chiral semion theory--both of which cannot be captured by topological stabilizer codes. The construction proceeds by &quot;gauging out&quot; certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory containing a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higher-form symmetries.</p>10aFOS: Physical sciences10aQuantum Physics (quant-ph)10aStrongly Correlated Electrons (cond-mat.str-el)1 aEllison, Tyler, D.1 aChen, Yu-An1 aDua, Arpit1 aShirley, Wilbur1 aTantivasadakarn, Nathanan1 aWilliamson, Dominic, J.  uhttps://arxiv.org/abs/2211.0379801959nas 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