Qubits from Adinkra Graph Theory via Colored Toric Geometry

Aadel, Y.; Belhaj, A.; Benslimane, Z.; Sedra, M. B.; Seguí, A.

doi:10.48550/arxiv.1506.02523

Cited by 6 publications

(7 citation statements)

References 36 publications

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“…Det A can be written explicitly as Namely, they display a discrete triality that interchanges S, T and U. Moreover, they involve an SL(2) S × SL(2) T × SL(2) U symmetry [21], and the solution of an STU black hole in the case of spherical symmetry is given in terms of 8 charges (q 0 , q 1 , q 2 , q 3 , p 0 , p 1 , p 2 , p 3 ).…”

Section: D-brane Configurationsmentioning

confidence: 99%

See 1 more Smart Citation

Qubit and fermionic Fock spaces from type II superstring black holes

Belhaj

Bensed

Benslimane

et al. 2017

Int. J. Geom. Methods Mod. Phys.

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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 .

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Section: D-brane Configurationsmentioning

confidence: 99%

“…Besides these activities, black holes in string theory compactification have been connected with quantum information using the qubit formalism [12][13][14][15][16][17][18][19][20][21][22]. Concretely, a possible link between the N = 2 STU black hole obtained from type II superstring and three qubits has been given in [15,16].…”

Section: Introductionmentioning

confidence: 99%

Qubit and fermionic Fock spaces from type II superstring black holes

Belhaj

Bensed

Benslimane

et al. 2017

Int. J. Geom. Methods Mod. Phys.

Self Cite

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“…The corresponding graphs are formed by nodes associated with bosonic and fermionic degree of freedom. These graphs have been used to classify a class of qubit black holes [12].…”

Section: Introductionmentioning

confidence: 99%

Weighted Graph Theory Representation of Quantum Information Inspired by Lie Algebras

Belhaj,

Machkouri

et al. 2016

Preprint

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Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed.In this way, the density matrix of a quantum state can be interpreted as a signless Laplacian matrix of an associated graph. Using similarities with root systems of simply laced Lie algebras, one-qubit theory is analyzed in some details and is found to be linked to a non-oriented weighted graph having two vertices. Moreover, this one-qubit theory is generalized to n-qubits. In this representation, quantum gates correspond to graph weight operations preserving the probability condition. A speculation from string theory, via D-brane quivers, is also given.

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“…The calculations on CP 2 in [9] were aimed at evaluating the Aharonov-Anandan phase for a 3-state spin-1 system using the Kähler connection. More recently there have been interesting applications using ideas from toric geometry [23]. In this paper we shall further elaborate on applications of this formalism, including the study of the quantum entanglement of qubits.…”

Section: Introductionmentioning

confidence: 99%

Compactifications of deformed conifolds, branes and the geometry of qubits

Cvetič

Gibbons

Pope

2016

J. High Energ. Phys.

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We present three families of exact, cohomogeneity-one Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces CP n+1 , written in a Stenzel form, whose principal orbits are the Stiefel manifolds V 2 (R n+2 ) = SO(n+2)/SO(n) divided by Z 2 . The second family are also Einstein-Kähler metrics, now on the Grassmannian manifolds G 2 (R n+3 ) = SO(n+3)/((SO(n+1)×SO(2)), whose principal orbits are the Stiefel manifolds V 2 (R n+2 ) (with no Z 2 factoring in this case). The third family are Einstein metrics on the product manifolds S n+1 × S n+1 , and are Kähler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the Kähler geometry of Fubini-Study metrics on CP n+1 , and we apply the formalism to study the quantum entanglement of qubits.

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Qubits from Adinkra Graph Theory via Colored Toric Geometry

Cited by 6 publications

References 36 publications

Qubit and fermionic Fock spaces from type II superstring black holes

Qubit and fermionic Fock spaces from type II superstring black holes

Weighted Graph Theory Representation of Quantum Information Inspired by Lie Algebras

Compactifications of deformed conifolds, branes and the geometry of qubits

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