Abstract
We develop a new geometric approach to deal with qubit information systems using colored graph theory. More precisely, we present a one to one correspondence between graph theory, and qubit systems, which may be explored to attack qubit information problems using toric geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with CP1, CP1 × CP1 and CP1 × CP1 × CP1 toric varieties respectively. Using a geometric procedure referred to as a colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of hypercube graph theory. Operations on toric information can produce universal quantum gates.
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