  We investigate the circuit complexity and Loschmidt echo for the (inverted)
harmonic oscillators. Focusing on the chaotic behaviors under the perturbation,
we analytically derive the Lyapunov exponent and scrambling time of the
inverted harmonic oscillators. We show that the circuit complexity and
Loschmidt echo exhibit qualitatively similar behaviors, particularly the
consistent Lyapunov exponent.
