  This paper examines wormhole geometries in the context of $f(Q,T)$ gravity
under the background of non-commutative distributions. We discuss the
analytical solutions assuming spherical symmetry and the presence of conformal
Killing vectors, which provides a systematic approach for seeking exact
wormhole solutions. Specifically, the imposition of conformal symmetry places
noteworthy constraints on the model, shaping the analytical outcomes more
precisely. We studied the properties of traversable wormholes under both
Gaussian and Lorentzian distributions and noticed that NEC and SEC are violated
in the neighborhood of the wormhole throat. We also observed the influence of
model parameters as well as non-commutative parameters for these violations.
Employing the "volume integral quantifier," it is established that conformally
symmetric wormhole geometries may, in principle, be constructed with
infinitesimally small amounts of matter, violating the averaged null energy
condition. Further, equilibrium forces and the complexity factor of the
non-commutative distributed wormholes have also been explored.
