  We prove that the orthogonal free quantum group factors
$\mathcal{L}(\mathbb{F}O_N)$ are strongly $1$-bounded in the sense of Jung. In
particular, they are not isomorphic to free group factors. This result is
obtained by establishing a spectral regularity result for the edge reversing
operator on the quantum Cayley tree associated to $\mathbb{F}O_N$, and
combining this result with a recent free entropy dimension rank theorem of Jung
and Shlyakhtenko.
