Quantum Register Algebra: the mathematical language for quantum computing

Abstract

We introduce Quantum Register Algebra (QRA) as an efficient tool for quantum computing. We show the direct link between QRA and Dirac formalism. We present GAALOP (Geometric Algebra Algorithms Optimizer) implementation of our approach. Using the QRA basis vectors definitions given in Section 4 and the framework based on the de Witt basis presented in Section 5, we are able to fully describe and compute with QRA in GAALOP using the geometric product. We illustrate the intuitiveness of this computation by presenting the QRA form for the well known SWAP operation on a two qubit register.

Survey of New Applications of Geometric Algebra

“…In such spaces the Dirac formalism can be realized straightforwardly. Aiming to establish GA as a major language for quantum computing, the authors introduce the non-complex Quantum Register Algebra (QRA) 49 and exploit the GAALOP (Geometric Algebra Algorithms Optimizer) framework to perform numerical operations.…”