Multi-qubits and Polyvalent Singularity in Type II Supestring Theory

TL;DR

This paper explores the connection between multi-qubit quantum systems and polyvalent singularities in local Calabi-Yau manifolds within type II superstring theory, using geometric engineering and mirror symmetry.

Contribution

It establishes a novel correspondence between multi-qubits and polyvalent singularities in Calabi-Yau manifolds, linking quantum information to string theory geometry.

Findings

1-qubit corresponds to D2-brane probing su(2) singularity.

Multi-qubits relate to multiple su(2) singularities via Cartan decomposition.

4-qubits linked to tetravalent singularity and wrapped D4-branes.

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.