论文标题
美元
$\mathbb{Z}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
论文作者
论文摘要
Kitaev的曲线代码是一个可解决的模型，具有$ \ mathbb {z} _2 $ - topological Order，它在量子计算和误差校正中具有潜在的应用程序。但是，直接实现的实现仍然是一个开放的挑战。在这里，我们为$ \ mathbb {z} _2 $晶格规定的理论提出了一个构建块，并展示了它如何允许实现圆环代码基态及其拓扑激励。这是通过对单个plaquettes引入单独的物质激发来实现的，该纸张的运动诱发了所需的纸条术语。拟议的构建块在二阶耦合方案中实现，非常适合具有超导量子台的实施。此外，我们提出了一条准备拓扑非平凡的初始状态的途径，在此期间，存在基础耦合强度的顺序存在很大的差距。分析论证和数值研究都证实了这一点。此外，我们概述了地面波函数的实验签名，并引入了最少的编织方案。在该协议中发现Ramsey Fringes之间的$π$ - 相移，这揭示了在只有三个三角形盖子的系统中，曲奇代码汉密尔顿的任何兴奋。我们的工作为在模拟量子模拟器中实现非亚伯式的人铺平了道路。
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 proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically non-trivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wavefunction and introduce a minimal braiding protocol. Detecting a $π$-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.
