论文标题
Rydberg Blockade的复合代码拓扑顺序的预测
Prediction of Toric Code Topological Order from Rydberg Blockade
论文作者
论文摘要
范式复合代码中遇到的$ \ Mathbb Z_2 $拓扑顺序的物理实现已被证明是一个难以捉摸的目标。我们预测，在Rydberg封锁半径的特定值下，可以在二维的Rydberg原子的二维阵列中实现这一阶段。首先，我们表明封锁模型（也称为“ PXP”模型）在具有单位点动力学项的Kagome晶格上实现了单体二聚体模型。这可以解释为$ \ Mathbb Z_2 $量规理论，其动力学是由单体波动产生的。 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 $\ln 2$ as measured in various geometries, (iii) degenerate topological ground states and (iv) the expected modular matrix from ground state 重叠。接下来，我们表明TQL持续存在，包括逼真的，代数销售的范德华交互，$ v（r）\ sim 1/r^6 $，用于选择晶格参数。此外，我们可以直接访问拓扑循环操作员，包括Fredenhagen-Marcu订单参数。我们展示了如何使用动态方案实验测量这些，从而提供了``吸烟枪''的实验签名。最后，我们展示了如何捕获新兴的人并实现不同的拓扑边界条件，并讨论了探索容忍断层量子记忆的含义。
The physical realization of $\mathbb Z_2$ 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 can be interpreted as a $\mathbb Z_2$ 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 $\ln 2$ 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 $V(r) \sim 1/r^6$ 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.
