Qubits from Adinkra Graph Theory via Colored Toric Geometry
arXiv:1506.02523
Abstract
We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information theory. This one to one correspondence may be explored to attack qubit system problems using geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with \bf CP^1, \bf CP^1\times CP^1 and \bf CP^1\times CP^1\times CP^1 toric varieties respectively. Using a geometric procedure referred to as colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of Adinkra graph theory. Operations on toric information can produce universal quantum gates.
arXiv comment13 pages, 2 figures
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Cited by in corpus (4)
- Weighted Graph Theory Representation of Quantum Information Inspired by Lie Algebras
- Compactifications of Deformed Conifolds, Branes and the Geometry of Qubits
- Multi-qubits and Polyvalent Singularity in Type II Supestring Theory
- Fractional Quantum Hall Filling Factors from String Theory using Toric Geometry