Be aware that Hestenes has copyrighted some of his material.
Arthur On 11/14/2016 01:11 AM, Tim Daly wrote:
Current quantum computing uses 2x2 (Pauli) operators and (4x4) Dirac operators expressed as matrices. But Hestenes https://en.wikipedia.org/wiki/David_Hestenes showed that these are simple subdomains of the Clifford (aka Geometric) Algebra. Axiom implements the Clifford algebra so it should be possible to re-formulate the quantum algorithms using operations expressed in this more general form. It is possible that these more general Clifford forms would improve clarity and expressiveness for quantum algorithms. In particular, applying Clifford notation to the Bloch sphere rotations seems like an interesting idea. Also of interest is that the Hadamard gate, expressed as a matrix [[1,1],[1,-1]], is fundamental quantum operator. But it is also the method of constructing communication codes so that multiple endpoints can fully share the same channel using the full channel bandwidth. This leads to the thought that quantum communication is intimately linked with these higher codes. See http://www.uow.edu.au/~jennie/WEBPDF/2005_12.pdf A Geometric Algebra formulation of these matrix operations provides a more general, coordinate-free language. This leads to the need for more work on the Clifford domain. Tim _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org https://lists.nongnu.org/mailman/listinfo/axiom-developer
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