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Prediction of Toric Code Topological Order from Rydberg Blockade
Physical Review X ( IF 12.5 ) Pub Date : 2021-07-08 , DOI: 10.1103/physrevx.11.031005
Ruben Verresen , Mikhail D. Lukin , Ashvin Vishwanath

The physical realization of Z2 topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius. First, we show that the blockade model—also known as a “PXP” model—realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term. This model can be interpreted as a Z2 gauge theory whose dynamics is generated by monomer fluctuations. We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap. Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions V(r)1/r6 for a choice of lattice parameters. Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter. We show how these can be measured experimentally using a dynamic protocol, providing a “smoking gun” experimental signature of the TQL phase. Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.

中文翻译:

从里德堡封锁预测环面码拓扑序

物理实现 Z2在范式复曲面代码中遇到的拓扑顺序已被证明是一个难以实现的目标。我们预测,物质的这一阶段可以在放置在红宝石晶格上的二维里德堡原子阵列中实现,在里德堡封锁半径的特定值下。首先,我们展示了封锁模型——也称为“X”模型——用单点动力学项在 Kagome 晶格上实现单体-二聚体模型。这个模型可以解释为Z2其动力学由单体波动产生的规范理论。我们使用数值密度矩阵重整化群方法获得了它的相图,并找到了一种拓扑量子液体 (TQL),这可以通过多种措施来证明,包括 (i) 两个无特征相之间的连续转变,(ii) 的拓扑纠缠熵输入2如在各种几何结构中测量的,(iii)退化拓扑基态,以及(iv)来自基态重叠的预期模矩阵。接下来,我们证明 TQL 在包含现实的、代数衰减的范德瓦尔斯相互作用时仍然存在(r)1/r6用于晶格参数的选择。此外,我们可以直接访问拓扑循环运算符,包括 Fredenhagen-Marcu 阶参数。我们展示了如何使用动态协议通过实验测量这些,提供 TQL 阶段的“确凿证据”实验特征。最后,我们展示了如何捕获出现的任意子并实现不同的拓扑边界条件,并讨论对探索容错量子存储器的影响。
更新日期:2021-07-08
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