  We present an exact solution for an itinerant hole added into the oxygen
orbitals of a CuO$_{3}$-like ferromagnetic chain. Using the Green's function
method, the quantum polarons obtained for the Heisenberg SU(2) interaction
between localized Cu spins are compared with the polarons in the Ising chain.
We find that magnons with large energy are favorable towards quasiparticle
existence, even in the case of relatively modest electron-magnon coupling. We
observe two quasiparticle states with dispersion $\sim 2t$ each, which emerge
from the incoherent continuum when the exchange coupling $J$ increases. Quantum
fluctuations in the spin system modify the incoherent part of the spectrum and
change the spectral function qualitatively, beyond the bands derived from the
perturbation theory.
