Unitary metaplectic representations of the group \(\varvec{SL}_{\textbf{2}}(\mathbb {Z}_{\textbf{2}^{\varvec{n}}})\) are necessary to describe the time evolution of \(\textbf{2}^{\varvec{n}}\) -dimensional quantum systems, such as systems involving n qubits. It is shown that in order for the metaplectic property to be fulfilled, an increase in the dimensionality of the involved n-qubit Hilbert spaces, from \(\textbf{2}^{\varvec{n}}\) to \(\textbf{2}^{\textbf{2}{\varvec{n}}}\) , is necessary. Thus we construct the general matrix form of such representations based on the magnetic translations of the diagonal subgroup \(\varvec{HW}_{\textbf{2}{\varvec{n}}} \otimes \varvec{HW}_{\textbf{2}{\varvec{n}}}\) . Comparisson with other approaches on this problem of the literature are discussed.
