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 coloured Jones polynomial. The construction is based on the complete solution of the ChernSimons topological quantum field theory and its connection to WessZuminoWitten conformal field theory. The coloured Jones polynomial is expressed as the expectation value of the evolution of the qdeformed spinnetwork 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2007
 DOI:
 10.1088/17518113/40/12/S10
 arXiv:
 arXiv:quantph/0607203
 Bibcode:
 2007JPhA...40.3047G
 Keywords:

 Quantum Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 Submitted to J. Phys. A: MathGen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirardi