  We present an algorithmic method for the digital quantum simulation of
many-body locally indivisible non-Markovian open quantum systems. It consists
of two parts: firstly, a Suzuki-Lie-Trotter decomposition of the global system
propagator into the product of subsystem propagators, which may not be quantum
channels, and secondly, an algorithmic procedure for the implementation of the
subsystem propagators through unitary operations and measurements on a dilated
space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter
decomposition, we are able to analyze the efficiency of the method, and connect
it with an appropriate measure of the local indivisibility of the system. In
light of our analysis, the proposed method is expected to be experimentally
achievable for a variety of interesting cases.
