In this work, we hybridize the Genetic Quantum Algorithm with the Support Vector Machines classifier for gene selection and classification of high dimensional Microarray Data. We named our algorithm GQASVM. Its purpose is to identify a small subset of genes that could be used to separate two classes of samples with high accuracy. A comparison of the approach with different methods of literature, in particular GASVM and PSOSVM [2], was realized on six different datasets issued of microarray experiments dealing with cancer (leukemia, breast, colon, ovarian, prostate, and lung) and available on Web. The experiments clearified the very good performances of the method. The first contribution shows that the algorithm GQASVM is able to find genes of interest and improve the classification on a meaningful way. The second important contribution consists in the actual discovery of new and challenging results on datasets used.