Spin networks, quantum automata and link invariants

TL;DR

This paper explores the spin network simulator as a bridge between quantum computation and topological quantum field theories, focusing on quantum automata for braid groups and link polynomial estimation.

Contribution

It introduces a finite state quantum automaton model that encodes SU(2) algebra and braid group representations for topological quantum computations.

Findings

Develops a quantum automaton for braid group language recognition.

Connects spin networks with topological quantum field theory models.

Proposes applications to estimate link polynomials in Chern--Simons theory.

Abstract

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological quantum computation models. Such a quantum combinatorial scheme, which essentially encodes SU(2) Racah--Wigner algebra and its braided counterpart, is particularly suitable to address problems in topology and group theory and we discuss here a finite states--quantum automaton able to accept the language of braid group in view of applications to the problem of estimating link polynomials in Chern--Simons field theory.