  A long-standing open problem in non-Markovian quantum state diffusion (QSD)
approach to open quantum systems is to establish the non-Markovian QSD
equations for multiple qubit systems. In this paper, we settle this important
question by explicitly constructing a set of exact time-local QSD equations for
$N$-qubit systems. Our exact time-local (convolutionless) QSD equations have
paved the way towards simulating quantum dynamics of many-body open systems
interacting with a common bosonic environment. The applicability of this
multiple-qubit stochastic equation is exemplified by numerically solving
several quantum open many-body systems concerning quantum coherence dynamics
and dynamical control.
