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Discrete Quantum Computing
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See https://arxiv.org/pdf/1101.3764.pdf and https://arxiv.org/pdf/1010.2929.pdf

[[
Discrete quantum theory is obtained by instantiating the mathematical framework
of Hilbert spaces with a finite field instead of the field of complex numbers.
This instantiation collapses much the structure of actual quantum mechanics but
retains several of its distinguishing characteristics including the notions of
superposition, interference, and entanglement. Furthermore, discrete quantum
theory excludes local hidden variable models, has a no-cloning theorem, and can
express natural counterparts of quantum information protocols such as superdense
coding and teleportation.

Surprisingly discrete quantum computing is identical to conventional logic
programming except for a small twist that is responsible for all the
"quantum-ness". The twist occurs when merging sets of answers computed by
several alternatives: the answers are combined using an exclusive version of
logical disjunction. In other words, the two branches of a choice junction
exhibit an interference effect: an answer is produced from the junction if it
occurs in one or the other branch but not both.
]]
