Quantum geometry and quantum algorithms
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirardi
Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirardi