Quantum Tetrahedra

Abstract

We discuss in details the role of Wigner 6j symbol as the basic building block unifying such different fields as state sum models for quantum geometry, topological quantum field theory, statistical lattice models and quantum computing. The apparent twofold nature of the 6j symbol displayed in quantum field theory and quantum computing -a quantum tetrahedron and a computational gate- is shown to merge together in a unified quantum-computational SU(2)-state sum framework.

References in corpus (11)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Discrete structures in gravity
• Classical 6j-symbols and the tetrahedron
• Computing Spin Networks
• Combinatorial and topological approach to the 3D Ising model
• Semiclassical analysis of Wigner $3j$-symbol
• 3nj Morphogenesis and Semiclassical Disentangling
• Quantum geometry and quantum algorithms
• Hierarchies of invariant spin models
• Quantum Knitting
• The WZW model on Random Regge Triangulations

Cited by in corpus (5)

• Symplectic and Semiclassical Aspects of the Schläfli Identity
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• A New Recursion Relation for the 6j-Symbol
• Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials
• Projective Ponzano-Regge spin networks and their symmetries