Multi-qubits and Polyvalent Singularity in Type II Supestring Theory

Abstract

Inspired by geometric engineering method, we approach qubit systems in the context of D-branes in type II superstrings. Concretely, we establish a correspondence between such quantum systems and polyvalent singularities appearing in local Calabi-Yau manifolds. First, we examine 1-qubit by considering a D2-brane probing the su(2) toric singularity associated with type IIA monovalent geometry. Then, we discuss the multi-qubits in terms of $n$ factors of su(2) singularities using the Cartan decomposition of non zero roots. Applying mirror symmetry, the 4-qubits are linked to the tetravalent singularity associated with the affine \widehat{so(8)} Lie algebra matching with the ADE-correspondences in the context of quantum information theory. Precisely, these states can be identified with wrapped D4-branes in a Calabi-Yau 4-fold near such a singularity.