Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly enhanced. However, it is still an open question how to realize the digital quantum simulation of topological phases of matter. Here, using common single- and two-qubit elementary quantum gates, we propose and demonstrate an approach to design topologically protected quantum circuits on the current generation of noisy quantum processors where spin-orbital coupling and related topological matter can be digitally simulated. In particular, a low-depth topological quantum circuit is performed on both the IBM and Rigetti quantum processors. In the experiments, we not only observe but also distinguish the 0 and $\pi$ energy topological edge states by measuring the qubit excitation distribution at the output of the circuits.

中文翻译：

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可编程量子处理器上拓扑问题的数字仿真

在合成量子模拟器中模拟物质的拓扑阶段是一个令人关注的话题。鉴于数字量子模拟器的普遍性，极大地增强了数字模拟奇异拓扑相位的前景。然而，如何实现物质拓扑相的数字量子模拟仍然是一个悬而未决的问题。在这里，我们使用普通的单量子位和二量子位基本量子门，提出并演示了一种在当前一代的噪声量子处理器上设计受拓扑保护的量子电路的方法，在该电路中可以对自旋轨道耦合和相关的拓扑物质进行数字模拟。特别是，在IBM和Rigetti量子处理器上都执行了低深度拓扑量子电路。在实验中，我们不仅观察而且还区分了0和$\pi$ 通过测量电路输出处的量子位激励分布来获得能量拓扑边缘状态。