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Topological Quantum Computing
Quantum Simulation
Quantum Foundations
Very ample line bundles, contextuality and quantum computation
arXiv
Authors: Raouf Dridi
Year
2014
Paper ID
46001
Status
Preprint
Abstract Read
~2 min
Abstract Words
91
Citations
N/A
Abstract
I relate contextuality to line bundles. Line bundles are important in algebraic geometry, they determine through their global sections rational maps to projective spaces. I explain how such maps, if they exist, relate rationally the input and output of measurement based computation (MBQC) and show geometrically that, indeed, contextuality is a necessary resource for the computational advantage in MBQC. I also leverage the definition of MBQC to category theory and present it as a "subfunctor" of the spectral presheaf. In general, the MBQC functor is pointless whereas the computation is trivial.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- I relate contextuality to line bundles.
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