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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.