Itinerant Quantum Integers: The Language of Quantum Computers
The concept of positively and negatively compatible null vectors arises in
the study of Clifford geometric algebras with a Lorentz-Minkowski metric. In
previous works, the basic properties of such algebras have been set down in
terms of a new principle of quantum duality. In the present work, the same
structure is studied in terms of real and complex quantum integers, which
generalize the real and complex number systems. It seems natural to identify a
qubit as a pair of compatible null vectors; the up state of the qubit being
their sum, and the down state being their difference. Basic identities are
developed to make calculations routine, and two different representations of
the symmetric group are given.
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