  We propose a new diagnostic for quantum chaos. We show that time evolution of
complexity for a particular type of target state can provide equivalent
information about the classical Lyapunov exponent and scrambling time as
out-of-time-order correlators. Moreover, for systems that can be switched from
a regular to unstable (chaotic) regime by a tuning of the coupling constant of
the interaction Hamiltonian, we find that the complexity defines a new time
scale. We interpret this time scale as recording when the system makes the
transition from regular to chaotic behaviour.
