A superconducting circuit realization of combinatorial gauge symmetry

TL;DR

This paper introduces a superconducting circuit based on combinatorial gauge symmetry to emulate topologically-ordered quantum liquids, potentially enabling more observable topological qubits due to larger energy gaps.

Contribution

It presents a novel superconducting circuit design that realizes combinatorial gauge symmetry, leading to robust topological order with potential advantages over previous methods.

Findings

Classical ground state features two superimposed loop structures.

Quantum case exhibits ${\f Z}_2$ topological order with finite capacitances.

Amplitudes between loop states are controlled by dimensional confinement.

Abstract

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.