Quantum geometry and quantum algorithms

Details Quantum geometry and quantum algorithms Quantum geometry and quantum algorithms

2006-07-28

arxiv.org/abs/quant-ph/0607203v1

J.Phys.A40:3047-3066,2007

Physics

Quantum Physics

Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirardi

Scientific paper

10.1088/1751-8113/40/12/S10

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.

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