Re: [quantum] Geometric Algebra

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
>
>
>
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