  Recently, the tunable Weyl-semimetal bands and the associate topological
phase transition have been successfully simulated in superconducting quantum
circuits [X. Tan, \textit{et al.} Phys. Rev. Lett. {\bf 122}, 010501 (2019)].
Since the superconducting quantum circuits inevitably couple to the
environment, we here focus on the steady state and decoherence process by
taking the reservoir into consideration via quantum master equation. Our
results show that the purity of the steady state can be used to indicate the
topological phase transition and Weyl points. Furthermore, the coherence will
exponentially decay to zero at the Weyl points, and decay to a nonzero value
with oscillation at other points in the momentum space. Our work may have
significant impact on the study of quantum open topological system.
