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Entanglement Theory Quantum Correlations Topological Quantum Computing Quantum Simulation Quantum State Preparation Representation

Quregisters, symmetry groups and Clifford algebras

arXiv
Authors: Dalia Cervantes, Guillermo Morales-Luna

Year

2015

Paper ID

25900

Status

Preprint

Abstract Read

~2 min

Abstract Words

115

Citations

N/A

Abstract

The Clifford algebra over the three-dimensional real linear space includes its linear structure and its exterior algebra, the subspaces spanned by multivectors of the same degree determine a gradation of the Clifford algebra. Through these geometric notions, natural one-to-one and two-to-one homomorphisms from mbox{SO}(3) into mbox{SU}(2) are built conventionally, and the set of qubits, is identified with a subgroup of mbox{SU}(2). These constructions are suitable to be extended to corresponding tensor powers. The notions of qubits, quregisters and qugates are translated into the language of symmetry groups. The corresponding elements to entangled states in the tensor product of Hilber spaces. realise a notion of entanglement in the tensor product of symmetry groups.

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  • The Clifford algebra over the three-dimensional real linear space includes its linear structure and its exterior algebra, the subspaces spanned by multivectors of the same...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1511.09004 [2] arXiv https://arxiv.org/abs/1511.09004 [3] Publisher https://arxiv.org/abs/1511.09004

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