Quantum speed limits are lower bounds on the evolution time for quantum systems. In this thesis, we consider closed quantum systems. We investigate how different principal bundles offers a geometrical method for obtaining generalizations of the Mandelstam-Tamm quantum speed limit for mixed states. We look at three different principal bundles from which we derive two already known quantum speed limits, the Uhlmann and Andersson QSLs, and one which is new, the Grassmann QSL. We also investigate the tightness of these quantum speed limits and how they compare with each other.