2020/06/30 by Claudio Chamon, Dmitry Green, Andrew J. Kerman · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.supr-con
paper · pdf · doi:10.1103/prxquantum.2.030341
published as PRX Quantum 2, 030341 (2021) · Joined by new author. Added section on experimental realization. Added analytical results
arxiv created 2021/06/08 · arxiv updated 2021/09/14
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 ℤ2 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 Z2 quantum topological order. A key feature of the exact gauge symmetry is that amplitudes connecting different \mathbb Z2 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.