  In principle a quantum system could be used to simulate another quantum
system. The purpose of such a simulation would be to obtain information about
problems which cannot be simulated with a classical computer due to the
exponential increase of the Hilbert space with the size of the system and which
cannot be measured or controlled in an actual experiment. The system will
interact with the surrounding environment, with the other particles in the
system and be implemented using imperfect controls making it subject to noise.
It has been suggested that noise does not need to be controlled to the same
extent as it must be for general quantum computing. However the effects of
noise in quantum simulations and how to treat them are not completely
understood. In this paper we study an existing quantum algorithm for the
one-dimensional Fano-Anderson model to be simulated using a liquid-state NMR
device. We calculate the evolution of different initial states in the original
model, and then we add interacting spins to simulate a more realistic
situation. We find that states which are entangled with their environment, and
sometimes correlated but not necessarily entangled have an evolution which is
described by maps which are not completely positive. We discuss the conditions
for this to occur and also the implications.
