  We consider the extent to which a noisy quantum computer is able to simulate
the time evolution of a quantum spin system in a faithful manner. Given a
specific set of assumptions regarding the manner in which noise acting on such
a device can be modelled at the circuit level, we show how the effects of noise
can be reinterpreted as a modification to the dynamics of the original system
being simulated. In particular, we find that this modification corresponds to
the introduction of static Lindblad noise terms, which act in addition to the
original unitary dynamics. The form of these noise terms depends not only on
the underlying noise processes occurring on the device, but also on the
original unitary dynamics, as well as the manner in which these dynamics are
simulated on the device, i.e., the choice of quantum algorithm. We call this
effectively simulated open quantum system the noisy algorithm model. Our
results are confirmed through numerical analysis.
