An important problem in algebra is to give algebraic descriptions for automorphism groups of noncommutative algebras. In this talk I define quantum polynomial algebras and describe their graded automorphisms. I do this by finding the systems of parameters $Q$ for which a fixed subgroup $G$ of $\text{GL}(V)$ is an automorphism. I will start by demonstrating interesting theorems for cyclic monomial subgroups and then generalize the ideas to the non-cyclic and non-monomial subgroups of $\text{GL}(V)$.