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Quantum computation and link polynomials
Jon Yard
LANL
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Quantum computation and link polynomials Jon Yard LANL |
| ABSTRACT Abstract: In this talk, I will present a quantum algorithm for approximating topological invariants of knots and links coming from Markov traces on centralizer algebras of quantum groups. The method is based on a general formalism for efficiently implementing, on a quantum computer, representations of braid groups associated with path algebras. The general framework presented accommodates known quantum algorithms for approximately evaluating the Jones and HOMFLYPT polynomials - which arise from Markov traces on Temperley-Lieb and Hecke algebras associated to deformations of unitary groups. The framework also allows one to approximately evaluate the Kauffman polynomial invariants which arise from Markov traces on Birman-Wenzl-Murakami algebras associated to deformations of the orthogonal and symplectic groups. Time permitting, I will also comment on the cases in which approximating these polynomials is a universal quantum algorithm. |