  For a quantum system with energy E, there is a limitation in quantum
computation which is identified by the minimum time needed for the state to
evolve to an orthogonal state. In this paper, we will compute the minimum time
of orthogonalization (i.e. quantum speed limit) for a simple anharmonic
oscillator and find an upper bound on the rate of computations. We will also
investigate the growth rate of complexity for the anharmonic oscillator by
treating the anharmonic terms perturbatively. More precisely, we will compute
the maximum rate of change of complexity and show that for even order
perturbations, the rate of complexity increases while for the odd order terms
it has a decreasing behavior.
