2009/09/30 by G. Passante, Gina Passante, O. Moussa +5
Computer Science · Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #quant-ph #semigroups and automata theory
paper · pdf · doi:10.1103/physrevlett.103.250501
published as PRL 103, 250501 (2009) · 5 figures. Version 2 changes: published version, minor errors corrected, slight changes to improve readability
arxiv created 2009/12/18 · openalex publication_date 2009/12/18 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.