Faithful Simulation and Detection of Quantum Spin Hall Effect on Superconducting Circuits

TL;DR

This paper demonstrates a faithful quantum simulation of the quantum spin Hall effect using superconducting circuits, enabling better understanding of topological states with high controllability and stability.

Contribution

It introduces a novel superconducting circuit system that faithfully simulates a $ ext{Z}_2$ topological insulator exhibiting the quantum spin Hall effect, with experimental verification of topological edge states.

Findings

Successful realization of a $ ext{Z}_2$ topological insulator in superconducting circuits

Experimental detection of topological edge states at the boundary

Enhanced controllability and stability over previous simulation methods

Abstract

Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum simulation of topological matter is very important in deepening our understanding of these states. This requirement puts the quantum superconducting circuits system as a good option for mimicking topological materials, owing to their flexible tunability and fine controllability. As a typical example herein, we realize a $\mathbb{Z}_2$-type topological insulator featuring the quantum spin Hall effect state, using a coupled system of transmission-line resonators and transmons. The single-excitation eigenstates of each unit cell are used as a pseudo-spin 1/2 system. The boundary of the topological phase transition is fixed in the phase diagram. Topological edge states are shown, which can be experimentally verified by detecting the population at the boundary of the plane. Compared to the previous simulations, this compositional system is fairly controllable, stable and less limited. Therefore, our scheme provides a reliable platform for faithful quantum simulations of topological matter.