Semi-Classical limit and quantum corrections in noncoincidence power-law $f(Q)$-Cosmology

Within the framework of symmetric teleparallel $f\left( Q\right) $-gravity for a connection defined in the non-coincidence gauge we derive the Wheeler-DeWitt equation of quantum cosmology. Because the gravitational field equation in $f\left( Q\right) $-gravity admits a minisuperspace description the Wheeler-DeWitt equation is a single inhomogeneous partial differential equations. We assume the power-law $f\left( Q\right) =f_{0}Q^{\mu}$ model and with the application of linear quantum observables we calculate the wavefunction of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit.