Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
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DOI：
10.22331/q-2020-02-10-228
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发表时间：
2019-07
期刊：
影响因子：
6.4
通讯作者：
Austin K. Daniel;R. N. Alexander;A. Miyake
中科院分区：
文献类型：
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作者：
Austin K. Daniel;R. N. Alexander;A. Miyake
什么样的受保护拓扑有序（SPTO）基态可以以类似于2D团簇态的方式用于基于测量的通用量子计算？2D SPTO状态不仅通过全局现场对称性，而且通过子系统对称性进行分类，子系统对称性是依赖于晶格几何形状的细粒度对称性。最近，基于量子元胞自动机的子系统对称性和相关结构的存在，在正方形和六边形晶格上的所谓SPTO簇相内的所有状态都被证明是普适的。出于这一观察，我们分析了所有顶点平移二维阿基米德晶格上的SPTO簇相位的计算能力。这里有四个子系统对称性，称为带状对称性、锥对称性、分形对称性和1-形式对称性，前三种对称性基本上与三类Clifford量子细胞自动机一一对应。我们的结论是，九出11阿基米德晶格支持普遍的集群阶段的前三个对称性之一的保护，而其余的晶格具有1-形式的对称性，并有不同的能力有关的纠错。
What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by this observation, we analyze the computational capability of SPTO cluster phases on all vertex-translative 2D Archimedean lattices. There are four subsystem symmetries here called ribbon, cone, fractal, and 1-form symmetries, and the former three are fundamentally in one-to-one correspondence with three classes of Clifford quantum cellular automata. We conclude that nine out of the eleven Archimedean lattices support universal cluster phases protected by one of the former three symmetries, while the remaining lattices possess 1-form symmetries and have a different capability related to error correction.