  A wide class of exact master equations for a multiple qubit system can be
explicitly constructed by using the corresponding exact non-Markovian quantum
state diffusion equations. These exact master equations arise naturally from
the quantum decoherence dynamics of qubit system as a quantum memory coupled to
a collective colored noisy source. The exact master equations are also
important in optimal quantum control, quantum dissipation and quantum
thermodynamics. In this paper, we show that the exact non-Markovian master
equation for a dissipative N-qubit system can be derived explicitly from the
statistical average of the corresponding non-Markovian quantum trajectories. We
illustrated our general formulation by an explicit construction of a
three-qubit system coupled to a non-Markovian bosonic environment. This
multiple qubit master equation offers an accurate time evolution of quantum
systems in various domains, and paves a way to investigate the memory effect of
an open system in a non-Markovian regime without any approximation.
