We solve the group classification problem for the $2+1$ generalized quantum Zakharov-Kuznetsov equation. Particularly we consider the generalized equation $u_{t}+fleft( uright) u_{z}+u_{zzz}+u_{xxz}=0$, and the time-dependent Zakharov-Kuznetsov equation $u_{t}+delta left( tright) uu_{z}+lambda left( tright) u_{zzz}+varepsilon left( tright) u_{xxz}=0$% . Function $fleft( uright) $ and $delta left( tright) ,~lambda left( tright) $,~$varepsilon left( tright) $ 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.
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