  We investigate the non-Markovian dynamics of an open Ising model simulated by
a superconducting circuit. The quantum many-body system is weakly coupled to a
white, pink- or blue-colored environment. The relaxation of the system in the
strong inter-qubit interaction regime shows a metastable behaviour. In
comparison with the dissipative system in the Markovian limit, the negative
memory of the blue-colored noise weakens the system's relaxation. However, for
the pink-colored noise the relaxation rate of the system is enhanced due to the
positive memory effect. The understanding of quantum many-body systems
responding to different colored noise fields is necessary for designing the
environment of superconducting qubits in a large scale quantum processor.
