2006/07/28 by S. Garnerone, S Garnerone, A. Marzuoli +3
Computer Science · Physics and Astronomy · #Polynomial and algebraic computation #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #gr-qc #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/12/s10
published as J.Phys.A40:3047-3066,2007 · Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirardi
arxiv created 2006/07/28 · openalex publication_date 2007/03/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the coloured Jones polynomial. The construction is based on the complete solution of the Chern–Simons topological quantum field theory and its connection to Wess–Zumino–Witten conformal field theory. The coloured Jones polynomial is expressed as the expectation value of the evolution of the q -deformed spin-network quantum automaton. A quantum circuit is constructed capable of simulating the automaton and hence of computing such an expectation value. The latter is efficiently approximated using a standard sampling procedure in quantum computation.