  The resolution of dynamics in out of equilibrium quantum spin systems lies at
the heart of fundamental questions among Quantum Information Processing,
Statistical Mechanics and Nano-Technologies. Efficient computational
simulations of interacting many-spin systems are extremely valuable tools for
tackling such questions. Here, we use the Trotter-Suzuki (TS) algorithm, a
well-known strategy that provides the evolution of quantum systems, to address
the spin dynamics. We present a GPU implementation of a particular TS version,
which has been previously implemented on single cores in CPUs. We develop a
massive parallel version of this algorithm and compare the efficiency between
CPU and GPU implementations. This method reduces the execution time
considerably and is capable of dealing with systems of up to 27 spins (only
limited by GPU memory).
