论文标题
哈密顿人的绝热途径，拓扑顺序的对称性和自动形态代码
Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes
论文作者
论文摘要
最近的“蜂窝状代码”是一种易于故障的量子存储器，该记忆由一系列检查序列定义，该检查实现了曲折代码的非平凡自动形态。我们认为，理解此代码的一般框架是考虑张开的哈密顿量的连续绝热路径，我们在两个空间维度中对该空间的基本组和第二和第三均匀组进行了猜想的描述。这样的路径的单个周期可以实现该哈密顿式拓扑顺序的某些自动形态。我们为二维双拓扑顺序的任意自态构建了这样的路径。然后，在复曲面代码的情况下意识到这一点，我们将此路径转换为一系列检查，构建与蜂窝代码密切相关的自动形态代码。
The recent "honeycomb code" is a fault-tolerant quantum memory defined by a sequence of checks which implements a nontrivial automorphism of the toric code. We argue that a general framework to understand this code is to consider continuous adiabatic paths of gapped Hamiltonians and we give a conjectured description of the fundamental group and second and third homotopy groups of this space in two spatial dimensions. A single cycle of such a path can implement some automorphism of the topological order of that Hamiltonian. We construct such paths for arbitrary automorphisms of two-dimensional doubled topological order. Then, realizing this in the case of the toric code, we turn this path back into a sequence of checks, constructing an automorphism code closely related to the honeycomb code.
