title: Nuclear-magnetic-resonance quantum calculations of the Jones polynomial.
abstract: The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation, however, involves many known experimental challenges. Here we present experimental results for small-scale approximate evaluation of the Jones polynomial by nuclear magnetic resonance (NMR); in addition, we show how to escape from the limitations of NMR approaches that employ pseudopure states. Specifically, we use two spin-1/2 nuclei of natural abundance chloroform and apply a sequence of unitary transforms representing the trefoil knot, the figure-eight knot, and the Borromean rings. After measuring the nuclear spin state of the molecule in each case, we are able to estimate the value of the Jones polynomial for each of the knots.
authors: Department of Chemistry, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany.
authors: Raimund
authors: R
authors: Marx
authors: Amr
authors: A
authors: Fahmy
authors: Louis
authors: L
authors: Kauffman
authors: Samuel
authors: S
authors: Lomonaco
authors: Andreas
authors: A
authors: Spörl
authors: Nikolas
authors: N
authors: Pomplun
authors: Thomas
authors: T
authors: Schulte-Herbrüggen
authors: John M
authors: JM
authors: Myers
authors: Steffen J
authors: SJ
authors: Glaser