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Q is not considered a state function because it is path dependent. Enthalpy is determined by the internal energy, pressure, and volume, which are all state functions. Q, however, is a process state that depends on specific transitions between equilibriums.
The above discussion is excellent! A small analogy, if you set the amount of gas needed to travel on the shortest way to go from UCLA to Hollywood is Qp, then it equals to enthalpy and it will always be the same because the distance between them does not change (do not take into account gas efficiency). But if you choose another routes, the amount of gas you burn will vary accordingly. That is similar with heat and work which depend on route you take.
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