  Pairing of composite fermions provides a possible mechanism for fractional
quantum Hall effect at even denominator fractions and is believed to serve as a
platform for realizing quasiparticles with non-Abelian braiding statistics. We
present results from fixed-phase diffusion Monte Carlo calculations which
predict that substantial Landau level mixing can induce a pairing of composite
fermions at filling factors $\nu=1/2$ and $\nu=1/4$ in the $l=-3$ relative
angular momentum channel, thereby destabilizing the composite-fermion Fermi
seas to produce non-Abelian fractional quantum Hall states.
