Nuclear-magnetic-resonance quantum calculations of the Jones polynomial
- Department of Chemistry, Technische Universitaet Muenchen, Lichtenbergstr. 4, D-85747 Garching (Germany)
- Biological Chemistry and Molecular Pharmacology, Harvard Medical School, 240 Longwood Avenue, Boston, Massachusetts 02115 (United States)
- University of Illinois at Chicago, 851 S. Morgan Street, Chicago, Illinois 60607-7045 (United States)
- University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250 (United States)
- Cruft Laboratory, Harvard University, 19 Oxford Street, Cambridge, Massachusetts 02138 (United States)
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 a 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.
- OSTI ID:
- 21413291
- Journal Information:
- Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
Similar Records
How the Jones polynomial give rise to physical states of quantum general relativity
Forced periodic oscillations and the Jones polynomial
Related Subjects
GENERAL PHYSICS
ABUNDANCE
ANGULAR MOMENTUM
APPROXIMATIONS
CALCULATION METHODS
CHLORINATED ALIPHATIC HYDROCARBONS
CHLOROFORM
COMPUTERS
EVALUATION
FUNCTIONS
HALOGENATED ALIPHATIC HYDROCARBONS
IMPLEMENTATION
MAGNETIC RESONANCE
MOLECULES
NUCLEAR MAGNETIC RESONANCE
NUCLEI
ORGANIC CHLORINE COMPOUNDS
ORGANIC COMPOUNDS
ORGANIC HALOGEN COMPOUNDS
PARTICLE PROPERTIES
POLYNOMIALS
QUANTUM COMPUTERS
RESONANCE
SPIN