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arXiv 2006.10060quant-phcond-mat.supr-con
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组合规范对称性的超导电路实现

A superconducting circuit realization of combinatorial gauge symmetry

Claudio Chamon, Dmitry Green, Andrew J. Kerman

备注：
Joined by new author. Added section on experimental realization. Added analytical results
发表信息：
PRX Quantum 2, 030341 (2021)
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摘要：

我们提出了一个超导量子线路的基础上的一般对称性原则-组合规范对称性-旨在模拟拓扑有序的量子液体，并作为基础的拓扑量子比特的建设。该电路具有丰富的功能：在经典的限制大电容的基态由两个叠加的回路结构，一个是晶体的小回路包含无序$U(1)$自由度，另一个是气体的回路的所有大小相关的$\mathbb{Z}_2$拓扑顺序。我们表明，这些经典的结果结转到量子的情况下，相位波动产生的有限电容的存在下，产生${\mathbb Z}_2$量子拓扑秩序。精确规范对称性的一个关键特征是，连接不同${\mathbb Z}_2$环态的振幅来自于具有零经典能量成本的路径。因此，这些振幅是由尺寸限制控制的，而不是通过能量势垒的隧穿。我们认为，这种效应可能会导致更大的能隙比以前的建议，这是有限的，这样的障碍，可能使它更有可能的拓扑相是实验观察。最后，我们讨论了我们的超导电路实现的组合规范对称性可以在实践中实现。

英文摘要：

We propose a superconducting quantum circuit based on a general symmetry principle -- combinatorial gauge symmetry -- designed to emulate topologically-ordered quantum liquids and serve as a foundation for the construction of topological qubits. The proposed circuit exhibits rich features: in the classical limit of large capacitances its ground state consists of two superimposed loop structures; one is a crystal of small loops containing disordered $U(1)$ degrees of freedom, and the other is a gas of loops of all sizes associated to $\mathbb{Z}_2$ topological order. We show that these classical results carry over to the quantum case, where phase fluctuations arise from the presence of finite capacitances, yielding ${\mathbb Z}_2$ quantum topological order. A key feature of the exact gauge symmetry is that amplitudes connecting different ${\mathbb Z}_2$ loop states arise from paths having zero classical energy cost. As a result, these amplitudes are controlled by dimensional confinement rather than tunneling through energy barriers. We argue that this effect may lead to larger energy gaps than previous proposals which are limited by such barriers, potentially making it more likely for a topological phase to be experimentally observable. Finally, we discuss how our superconducting circuit realization of combinatorial gauge symmetry can be implemented in practice.

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