  We present a solid state implementation of quantum computation, which
improves previously proposed optically driven schemes. Our proposal is based on
vertical arrays of quantum dots embedded in a mesoporous material which can be
fabricated with present technology. We study the feasibility of performing
quantum computation with different mesoporous matrices. We analyse which matrix
materials ensure that each individual stack of quantum dots can be considered
isolated from the rest of the ensemble-a key requirement of our scheme. This
requirement is satisfied for all matrix materials for feasible structure
parameters and GaN/AlN based quantum dots. We also show that one dimensional
ensembles substantially improve performances, even of CdSe/CdS based quantum
dots.
