Given an initial quantum state and a final quantum state in a Hilbert space, there exist Hamiltonians H that transform one into the other. Subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time? For Hermitian Hamiltonians this time has a nonzero lower bound. However, among complex PT-symmetric Hamiltonians satisfying the same energy constraint, this time can be made arbitrarily small without violating the time-energy uncertainty principle. The talk will discuss the possible implications of this result.