Quantum geometry and quantum algorithms Export

@misc{citeulike:781360, 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.}, archivePrefix = {arXiv}, author = {Garnerone, S. and Marzuoli, A. and Rasetti, M.}, citeulike-article-id = {781360}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0607203}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0607203}, day = {28}, eprint = {quant-ph/0607203}, keywords = {qait, quantum-algorithm, quantum-geometry}, month = {Jul}, posted-at = {2006-09-28 16:55:09}, priority = {2}, title = {Quantum geometry and quantum algorithms}, url = {http://arxiv.org/abs/quant-ph/0607203}, year = {2006} }

TY - ELEC ID - citeulike:781360 L3 - citeulike-article-id:781360 N2 - 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. TI - Quantum geometry and quantum algorithms KW - qait KW - quantum-algorithm KW - quantum-geometry AU - Garnerone, S AU - Marzuoli, A AU - Rasetti, M PY - 2006/Jul/28/ UR - http://arxiv.org/abs/quant-ph/0607203 ER -