Compressed simulation of evolutions of the XY model

We extend the notion of compressed quantum simulation to the XY model. We derive a quantum circuit processing log(n) qubits which simulates the one-dimensional 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.