An important problem in algebra is to give algebraic descriptions for automorphism groups of noncommutative algebras. In this talk, we examine quantum polynomial algebras and their graded automorphisms. We fix a subgroup $G$ of $\text{GL}(V)$ and ask for a description of all quantum polynomial rings on which $G$ acts by automorphisms. We will start by considering cyclic monomial subgroups and then discuss ideas for generalizing to the non-cyclic and non-monomial subgroups of $\text{GL}(V)$.