Physics – Quantum Physics
Scientific paper
2008-01-08
Physics
Quantum Physics
14 pages, presented at International Symposium "Quantum Informatics 2007", October 3rd - 5th, 2007, Moscow Zvenigorod, Russia
Scientific paper
10.1117/12.801913
Complementary idempotent paravectors and their ordered compositions, are used to represent multivector basis elements of geometric Clifford algebra for 3D Euclidean space as the states of a geometric byte in a given frame of reference. Two layers of information, available in real numbers, are distinguished. The first layer is a continuous one. It is used to identify spatial orientations of similar geometric objects in the same computational basis. The second layer is a binary one. It is used to manipulate with 8D structure elements inside the computational basis itself. An oriented unit cube representation, rather than a matrix one, is used to visualize an inner structure of basis multivectors. Both layers of information are used to describe unitary operations -- reflections and rotations -- in Euclidian and Hilbert spaces. The results are compared with ones for quantum gates. Some consequences for quantum and classical information technologies are discussed.
Nesterov Michael M.
Tarkhanov Victor I.
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