Quantum Tetrahedra

TL;DR

This paper explores the Wigner 6j symbol's role as a fundamental element connecting quantum geometry, topological quantum field theory, statistical models, and quantum computing, unifying these fields through a quantum state sum framework.

Contribution

It introduces a unified SU(2)-state sum framework that merges the quantum tetrahedron interpretation with quantum computational gates, highlighting their interconnected nature.

Findings

Wigner 6j symbol serves as a unifying building block across multiple quantum fields.

The quantum tetrahedron and computational gate are shown to be aspects of the same framework.

A new unified quantum state sum model is proposed for quantum geometry and computing.

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.