  Krylov complexity is a novel observable for detecting quantum chaos, and an
indicator of a possible gravity dual. In this paper, we compute the Krylov
complexity and the associated Lanczos coefficients in the SU(2) Yang-Mills
theory, which can be reduced to a nonlinearly coupled harmonic oscillators
(CHO) model. We show that there exists a chaotic transition in the growth of
Krylov complexity. The Krylov complexity shows a quadratic growth in the early
time stage and then grows linearly. The corresponding Lanczos coefficient
satisfies the universal operator growth hypothesis, i.e., grows linearly first
and then enters the saturation plateau. By the linear growth of Lanczos
coefficients, we obtain an upper bound of the quantum Lyapunov exponent.
Finally, we investigate the effect of different energy sectors on the
K-complexity and Lanczos coefficients.
