2016/09/12 by Abdelilah Belhaj, A. Belhaj, Belhaj, Abdelilah +7
Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1609.03534
openalex publication_date 2016/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.