Quantum geometry and quantum algorithms
Abstract
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 colored Jones polynomial. The construction is based on the complete solution of Chern-Simons topological quantum field theory and its connection to Wess-Zumino-Witten conformal field theory. The colored 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 expectation value. The latter is efficiently approximated using a standard sampling procedure in quantum computation.
Cite
@article{arxiv.quant-ph/0607203,
title = {Quantum geometry and quantum algorithms},
author = {S. Garnerone and A. Marzuoli and M. Rasetti},
journal= {arXiv preprint arXiv:quant-ph/0607203},
year = {2008}
}
Comments
Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirardi