  This paper deals with the stabilization of the linear Biharmonic
Schr\"odinger equation in an $n$-dimensional open bounded domain under
Dirichlet-Neumann boundary conditions considering three infinite memory terms
as damping mechanisms. We show that depending on the smoothness of initial data
and the arbitrary growth at infinity of the kernel function, this class of
solution goes to zero with a polynomial decay rate like $t^{-n}$ depending on
assumptions about the kernel function associated with the infinite memory
terms.
