论文标题
组合量规对称的超导电路实现
A superconducting circuit realization of combinatorial gauge symmetry
论文作者
论文摘要
我们提出了一个基于一般对称原理的超导量子电路 - 组合量规对称性 - 旨在模拟拓扑订购的量子液体，并作为建造拓扑量子的基础。拟议的电路表现出丰富的特征：在大型电容的经典限制下，其基态由两个叠加的环结构组成；一个是包含无序$ u（1）$自由度的小环形的水晶，另一个是与$ \ mathbb {z} _2 $拓扑顺序相关的各种尺寸的循环的气体。我们表明，这些经典的结果延续到了量子案例中，在量子情况下，相位波动是由于存在有限的电容而产生的，产生了$ {\ mathbb z} _2 $量子拓扑顺序。精确规格对称性的一个关键功能是连接不同$ {\ Mathbb z} _2 $循环状态的振幅来自零经典能源成本的路径。结果，这些幅度由维度限制而不是通过能量屏障进行隧穿控制。我们认为，这种影响可能会导致更大的能量差距，而这些提议受到此类障碍的限制，这可能使拓扑阶段更有可能在实验上观察到。最后，我们讨论了如何在实践中实现组合量规对称性的超导电路实现。
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.
