toric码与规范-希格斯模型中拓扑序和边界序的仅测量动力学相变

Self-dual random-plaquette gauge model and the quantum toric code

We study the four-dimensional Z_2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs) phase, and phase boundary between the ordered (Higgs) and disordered (confinement) phases gives the accuracy threshold of error correction. Using self-duality of the model in conjunction with the replica method, we show that this model has exactly the same mathematical structure as that of the two dimensional random-bond Ising model, which has been studied ve…

Toric Code 与规范-Higgs模型中由体测量诱导的边界相变

Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model

本文研究 toric code 在圆柱几何下由体投影测量诱导的边界相变，通过数值与非局域规范不变算子刻画 $Z_2$ 自发破缺及 Higgs 相临界性，并讨论体相变关联。

来自Hopf代数规范理论的具有通量附着的修正环面码模型

Modified toric code models with flux attachment from Hopf algebra gauge theory

本文研究在有限规范群上引入非平凡拟三角结构（R-矩阵）对环面码的推广，构造了保持拓扑类型但粒子种类按R-矩阵置换的哈密顿量模型，并证明在Z_N规范理论中该修正等价于通量附着。

Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory

We study the phase structure of the random-plaquette Z_2 lattice gauge model in three dimensions. In this model, the "gauge coupling" for each plaquette is a quenched random variable that takes the value βwith the probability 1-p and -βwith the probability p. This model is relevant for the recently proposed quantum memory of toric code. The parameter p is the concentration of the plaquettes with "wrong-sign" couplings -β, and interpreted as the error probability per qubit in quantum code. In the gauge system with p=0, i.e., with the uniform gauge couplings β, it is known that there exists a se…

$\mathbb{Z}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Kitaev's toric code is an exactly solvable model with $\mathbb{Z}_2$-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge. Here, we propose a building block for $\mathbb{Z}_2$ lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The prop…

From Doubled Chern-Simons-Maxwell Lattice Gauge Theory to Extensions of the Toric Code

We regularize compact and non-compact Abelian Chern-Simons-Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group $\mathbb{R}$, each local Hilbert space is analogous to the one of a charged "particle" moving in the link-pair group space $\mat…