Quantum geometry and quantum algorithms

@article{Garnerone2007QuantumGA,
title={Quantum geometry and quantum algorithms},
author={Silvano Garnerone and Annalisa Marzuoli and Mario Rasetti},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2007},
volume={40},
pages={3047 - 3066}
}
• Published 28 July 2006
• Computer Science, Physics
• Journal of Physics A: Mathematical and Theoretical
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…
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