论文标题
用Majorana晶格编织：地面脱位和超对称性
Braiding with Majorana lattices: Groundstate degeneracy and supersymmetry
论文作者
论文摘要
预计基于主要的拓扑位量子位将利用拓扑超导体中Majorana模式的非亚伯编织统计数据，以实现容忍缺陷的拓扑量子量子计算。可扩展的Qubit设计需要在量子线网络上定位的几种Majorana模式，而编织操作依赖于拓扑上非平凡的超导阶段的地面变性的存在。然而，由于主要距离以有限距离定位的Majorana模式之间的杂交，因此取消了这种退化。在这里，我们描述了一个三式式的编织协议，每个分支由一个有限距离重叠的Majorana模式组成。我们发现，如果该系统处于拓扑不是平凡的状态，地下晶体和最低能量状态之间的能量分裂会随着Majorana模式的数量呈指数下降。该结果不依赖于特定的编织几何形状和编织方案的细节，而是有效的低能量汉密尔顿（Hamiltonian）的超对称性和非平凡拓扑的结果，描述了Majorana晶格。
Majorana-based topological qubits are expected to exploit the nonabelian braiding statistics of Majorana modes in topological superconductors to realize fault-tolerant topological quantum computation. Scalable qubit designs require several Majorana modes localized on quantum wires networks, with braiding operations relying on the presence of the groundstate degeneracy of the topologically nontrivial superconducting phase. However, this degeneracy is lifted due to the hybridization between Majorana modes localized at a finite distance. Here, we describe a braiding protocol in a trijunction where each branch consists of a lattice of Majorana modes overlapping at a finite distance. We find that the energy splitting between the groundstate and the lowest-energy state decreases exponentially with the number of Majorana modes if the system is in its topologically nontrivial regime. This result does not rely on the specific braiding geometry and on the details of the braiding scheme but is a consequence of the supersymmetry and nontrivial topology of the effective low-energy Hamiltonian describing the Majorana lattice.
