  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.
