  We use our Clifford algebra technique, that is nilpotents and projectors
which are binomials of the Clifford algebra objects $\gamma^a$ with the
property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum
gates and quantum algorithms needed in quantum computers in an elegant way. We
identify $n$-qubits with spinor representations of the group SO(1,3) for a
system of $n$ spinors. Representations are expressed in terms of products of
projectors and nilpotents. An algorithm for extracting a particular information
out of a general superposition of $2^n$ qubit states is presented. It
reproduces for a particular choice of the initial state the Grover's algorithm.
