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Updated: Jun 3, 2026

Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy
Published on: September 17, 2017
Nuclear-magnetic-resonance quantum calculations of the Jones polynomial
Raimund Marx1, Amr Fahmy, Louis Kauffman
1Department of Chemistry, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany.
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.
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