  In this work we explore the structure of Clifford algebras and the
representations of the algebraic spinors in quantum information theory.
Initially we present an general formulation through elements of left minimal
ideals in tensor products of the Clifford algebra $Cl^{+}_{1,3}$. Posteriorly
we perform some applications in quantum computation: qubits, entangled states,
quantum gates, representations of the braid group, quantum teleportation,
Majorana operators and supersymmetry. Finally, we discuss advantages related to
standard Hilbert space formulation.
