  We extend the notion of compressed quantum simulation to the XY-model. We
derive a quantum circuit processing log(n) qubits which simulates the 1D
XY-model describing n qubits. In particular, we demonstrate how the adiabatic
evolution can be realized on this exponentially smaller system and how the
magnetization, which witnesses a quantum phase transition can be observed.
Furthermore, we analyze several dynamical processes, like quantum quenching and
finite time evolution and derive the corresponding compressed quantum circuit.
