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Quantum State Evolution in C2 and G3+
Science Research
Volume 3, Issue 5, October 2015, Pages: 240-247
Received: Jul. 29, 2015; Accepted: Aug. 10, 2015; Published: Aug. 19, 2015
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Author
Alexander Soiguine, Soiguine Supercomputing, Aliso Viejo, CA, USA
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Abstract
Quantum mechanical qubit states as elements of two dimensional complex Hilbert space can be generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space. The construction critically depends on generalization of formal, unspecified, complex plane to arbitrary variable, but explicitly defined, planes in 3D, and of usual Hopf fibration to special maps of the geometric algebra elements to the unit sphere in 3D generated by arbitrary unit value bivectors. Analysis of the structure of the map of the even subalgebra to the Hilbert space demonstrates that quantum state evolution in the latter gives only restricted information compared to that in geometric algebra.
Keywords
Qubits, Geometric Algebra, Clifford Translation, Berry Phase, Topological Quantum Computing
To cite this article
Alexander Soiguine, Quantum State Evolution in C2 and G3+, Science Research. Vol. 3, No. 5, 2015, pp. 240-247. doi: 10.11648/j.sr.20150305.11
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