  We report an experimental quantum simulation of unitary dynamics of an XY
spin chain with pre-engineered couplings. Using this simulation, we demonstrate
the mirror inversion of quantum states, proposed by Albanese et al. [Phys. Rev.
Lett. 93, 230502 (2004)]. The experiment is performed with a 5-qubit dipolar
coupled spin system using nuclear magnetic resonance techniques. To perform
quantum simulation we make use of the recently proposed unitary operator
decomposition algorithm of Ajoy et al. [Phys. Rev. A 85, 030303 (2012)] along
with numerical pulse optimization techniques. Further, using mirror inversion,
we demonstrate that entangled states can be transferred from one end of the
chain to the other end. The simulations are implemented with high experimental
fidelity, which implies that these kind of simulations may be possible in
larger systems.
