A general formulation based on algebraic spinors for the quantum computation

Abstract

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.