  Following the recent theory of $f(Q)$ gravity, we continue to investigate the
possible existence of wormhole geometries, where $Q$ is the non-metricity
scalar. Recently, the non-metricity scalar and the corresponding field
equations have been studied for some spherically symmetric configurations in [
Phys. Lett. B 821, 136612 (2021) and Phys. Rev. D 103, 124001 (2021) ]. One can
note that field equations are different in these two studies. Following [Phys.
Rev. D 103, 124001 (2021)], we systematically study the field equations for
wormhole solutions and found the violation of null energy conditions in the
throat neighborhood. More specifically, considering specific choices for the
$f(Q)$ form and for constant redshift with different shape functions, we
present a class of solutions for static and spherically symmetric wormholes.
Our survey indicates that wormhole solutions could not exist for specific form
function $f(Q)= Q+ \alpha Q^2$. To summarize, exact wormhole models can be
constructed with violation of the null energy condition throughout the
spacetime while being $\rho \geq 0$ and vice versa.
