论文标题
来自手性半表面拓扑秩序的三维量子细胞自动机
Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
论文作者
论文摘要
我们基于具有短距离纠缠和手性半边界拓扑顺序的系统，构建了一种新型的三维量子细胞自动机（QCA）。我们认为，QCA是非平凡的，即不是局部量子门的有限深度，或者存在二维通勤投影仪Hamiltonian意识到手性半拓扑秩序（以$ U（1）_2 $ CHERN-SIMONS理论为特征）。我们的QCA是通过首先构建四个订单的特定量张量类别的Walker-wang Hamiltonian获得的，然后在晶格操作员级别凝结拆卸的散装玻色子。我们表明，在边界存在的情况下，由此产生的哈密顿量托管了手性半拓扑顺序，可以在QCA上定义QCA上的非Pauli稳定器代码。然后将构造推广到由$ {2^n} $ - 尺寸qudits上的非Pauli稳定器代码定义的一类QCA，这些Qudits具有$ u（1）_ {2^n} $ CHERN-SIMONS理论所描述的表面。我们的结果支持以下猜想：非平凡的三维QCA群对非分类编织融合类别的WITT组是同构。
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 ${2^n}$-dimensional qudits that feature surface anyons described by $U(1)_{2^n}$ 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.
