We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information theory. This one to one correspondence may be explored to attack qubit system problems using 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 CP 1 , CP 1 ×CP 1 and CP 1 ×CP 1 ×CP 1 toric varieties respectively. Using a geometric procedure referred to as colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of Adinkra graph theory. Operations on toric information can produce universal quantum gates.

Using Hodge diagram combinatorial data, we study qubit and fermionic Fock spaces from the point of view of type II superstring black holes based on complex compactifications. Concretely, we establish a one-to-one correspondence between qubits, fermionic spaces and extremal black holes in maximally supersymmetric supergravity obtained from type II superstring on complex toroidal and Calabi-Yau compactifications. We interpret the differential forms of the n-dimensional complex toroidal compactification as states of n-qubits encoding information on extremal black hole charges. We show that there are 2 n copies of n qubit systems which can be split as 2 n = 2 n−1 + 2 n−1 . More precisely, 2 n−1 copies are associated with even D-brane charges in type IIA superstring and the other 2 n−1 ones correspond to odd D-brane charges in IIB superstring. This correspondence is generalized to a class of Calabi-Yau manifolds. In connection with black hole charges in type IIA superstring, an n-qubit system has been obtained from a canonical line bundle of n factors of one dimensional projective space CP 1 .

Using M-theory compactification, we develop a three factor separation for the scalar submanifold of N = 2 seven dimensional supergravity associated with 2-cycles of the K3 surface. Concretely, we give an interplay between the three scalar submanifold factors and the extremal black holes obtained from M2-branes wrapping such 2-cycles. Then, we show that the corresponding black hole charges are linked to one, two and four qubit systems.

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.

Using dyonic solutions in the type IIA superstring theory on Calabi-Yau manifolds, we reconsider the study of black objects and quantum information theory using string/string duality in six dimensions. Concretely, we relate four-qubits with a stringy quaternionic moduli space of type IIA compactification associated with a dyonic black solution formed by black holes (BH) and black 2-branes (B2B) carrying 8 electric charges and 8 magnetic charges. This connection is made by associating the cohomology classes of the heterotic superstring on T 4 to four-qubit states. These states are interpreted in terms of such dyonic charges resulting from the quaternionic symmetric space SO(4,4) SO(4)×SO(4) corresponding to a N = 4 sigma model superpotential in two dimensions. The superpotential is considered as a functional depending on four quaternionic fields mapped to a class of Clifford algebras denoted as Cl 0,4 . A link between such an algebra and the cohomology classes of T 4 in heterotic superstring theory is also given.