  Quantum speed limits are the boundaries that define how quickly one quantum
state can transform into another. Instead of focusing on the transformation
between pairs of states, we provide bounds on the speed limit of quantum
evolution by unitary operators in arbitrary dimensions. These do not depend on
the initial and final state but depend only on the trace of the unitary
operator that is to be implemented and the gross characteristics (average and
variance) of the energy spectrum of the Hamiltonian which generates this
unitary evolution. The bounds that we find can be thought of as the
generalization of the Mandelstam-Tamm (TM) and the Margolus-Levitin (ML) bound
for state transformations to implementations of unitary operators. We will
discuss the application of these bounds in several classes of transformations
that are of interest in quantum information processing.
