  This report is concerned with the efficiency of numerical methods for
simulating quantum spin systems, with the aim to implement an improved method
for simulation of a time-dependent Hamiltonian that displays chirped pulses at
a high frequency.
  Working in the density matrix formulation of quantum systems, we study
evolution under the Liouville-von Neumann equation, presenting analysis of and
benchmarking current numerical methods. The accuracy of existing techniques is
assessed in the presence of chirped pulses.
  We also discuss the Magnus expansion and detail how a truncation of it is
used to solve differential equations. The results of this work are implemented
in the Python package MagPy to provide a better error-to-cost ratio than
current approaches allow for time-dependent Hamiltonians.
