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Zbl 1110.81157
Garnerone, S.; Marzuoli, A.; Rasetti, M.
Quantum geometry and quantum algorithms. (English)
[J] J. Phys. A, Math. Theor. 40, No. 12, 3047-3066 (2007). ISSN 1751-8113; ISSN 1751-8121/e

Summary: 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 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.

MSC 2000:: *81T80 Simulation and numerical modelling of fields
81P68 Quantum computation and quantum cryptography
81R50 Quantum groups and related algebraic methods in quantum theory
81Q60 Supersymmetric quantum mechanics

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Zentralblatt MATH Berlin [Germany]