  We solve the group classification problem for the $2+1$ generalized quantum
Zakharov-Kuznetsov equation. Particularly we consider the generalized equation
$u_{t}+f\left( u\right) u_{z}+u_{zzz}+u_{xxz}=0$, and the time-dependent
Zakharov-Kuznetsov equation $u_{t}+\delta \left( t\right) uu_{z}+\lambda \left(
t\right) u_{zzz}+\varepsilon \left( t\right) u_{xxz}=0$% . Function $f\left(
u\right) $ and $\delta \left( t\right) ,~\lambda \left( t\right)
$,~$\varepsilon \left( t\right) $ are determine in order the equations to admit
additional Lie symmetries.\ Finally, we apply the Lie invariants to find
similarity solutions for the generalized quantum Zakharov-Kuznetsov equation.
