论文标题
拓扑阶段和逻辑门的费米子缺陷
Fermionic defects of topological phases and logical gates
论文作者
论文摘要
我们讨论了（2+1）d骨拓扑阶段的Codimension-1缺陷，其中缺陷可以支持典型的自由度。我们将这些缺陷称为费米子缺陷，并引入了可逆的费米子缺陷的某些子类，称为“测量的Gu-wen spt缺陷”，这些缺陷可以改变Anyons的自我统计。我们从融合的GU-WEN SPT缺陷和波斯尼克可逆缺陷中得出了一般的费米尼可逆缺陷的规范形式，与缺陷上的费米子解耦。然后，我们得出通用可逆的费米子缺陷的融合规则。在存在其他附属费用的情况下，测量的Gu-Wen SPT缺陷导致了稳定器代码的有趣逻辑大门。例如，我们在（2+1）d $ \ mathbb {z} _2 $ to cont堆叠的（2+1）d ancilla trivial原子绝缘子（由有限深度电路实现）上找到了CZ逻辑门的实现。我们还研究了在（3+1）D Walker-Wang模型边界上实现的（2+1）D骨拓扑阶段（2+1）D的纤维化界面。在这种情况下，间隙界面可以移动（2+1）d相的手性中心电荷。在这些费米子界面中，我们研究了一个有趣的例子，其中（3+1）d相具有空间反射对称性，并且在反射平面上支持Fermionic界面，该反射平面将A（2+1）D表面拓扑顺序及其方向反向 - 反向 - 反向 - 反向。我们构造了一个（3+1）d可以解决此设置的可溶解性哈密顿量，并发现该模型生成了（3+1）d可逆阶段的$ \ Mathbb {Z} _8 $分类，并具有空间反射对称性对称性和Fermion Parity和Fermion Parity。我们与有效的田间理论接触，在文献中被称为具有时尚的可逆阶段，具有时空高层对称性。
We discuss the codimension-1 defects of (2+1)D bosonic topological phases, where the defects can support fermionic degrees of freedom. We refer to such defects as fermionic defects, and introduce a certain subclass of invertible fermionic defects called "gauged Gu-Wen SPT defects" that can shift self-statistics of anyons. We derive a canonical form of a general fermionic invertible defect, in terms of the fusion of a gauged Gu-Wen SPT defect and a bosonic invertible defect decoupled from fermions on the defect. We then derive the fusion rule of generic invertible fermionic defects. The gauged Gu-Wen SPT defects give rise to interesting logical gates of stabilizer codes in the presence of additional ancilla fermions. For example, we find a realization of the CZ logical gate on the (2+1)D $\mathbb{Z}_2$ toric code stacked with a (2+1)D ancilla trivial atomic insulator, which is implemented by a finite depth circuit. We also investigate a gapped fermionic interface between (2+1)D bosonic topological phases realized on the boundary of the (3+1)D Walker-Wang model. In that case, the gapped interface can shift the chiral central charge of the (2+1)D phase. Among these fermionic interfaces, we study an interesting example where the (3+1)D phase has a spatial reflection symmetry, and the fermionic interface is supported on a reflection plane that interpolates a (2+1)D surface topological order and its orientation-reversal. We construct a (3+1)D exactly solvable Hamiltonian realizing this setup, and find that the model generates the $\mathbb{Z}_8$ classification of the (3+1)D invertible phase with spatial reflection symmetry and fermion parity on the reflection plane. We make contact with an effective field theory, known in literature as the exotic invertible phase with spacetime higher-group symmetry.
