  Digital quantum simulators provide a diversified tool for solving the
evolution of quantum systems with complicated Hamiltonians and hold great
potential for a wide range of applications. Although much attention is paid to
the unitary evolution of closed quantum systems, dissipation and noise are
vital in understanding the dynamics of practical quantum systems. In this work,
we experimentally demonstrate a digital simulation of an open quantum system in
a controllable Markovian environment with the assistance of a single ancillary
qubit. By Trotterizing the quantum Liouvillians, the continuous evolution of an
open quantum system is effectively realized, and its application in error
mitigation is demonstrated by adjusting the simulated noise intensities.
High-order Trotter for open quantum dynamics is also experimentally
investigated and shows higher accuracy. Our results represent a significant
step towards hardware-efficient simulation of open quantum systems and error
mitigation in quantum algorithms in noisy intermediate-scale quantum systems.
