01125nas a2200145 4500008004100000245006500041210006500106260001500171300001200186490000600198520068700204100002400891700001800915856004600933 2009 eng d00aEstimating Jones and HOMFLY polynomials with One Clean Qubit0 aEstimating Jones and HOMFLY polynomials with One Clean Qubit c2009/03/01 a264-2890 v93 a
The Jones and HOMFLY polynomials are link invariants with close connections to quantum computing. It was recently shown that finding a certain approximation to the Jones polynomial of the trace closure of a braid at the fifth root of unity is a complete problem for the one clean qubit complexity class. This is the class of problems solvable in polynomial time on a quantum computer acting on an initial state in which one qubit is pure and the rest are maximally mixed. Here we generalize this result by showing that one clean qubit computers can efficiently approximate the Jones and single-variable HOMFLY polynomials of the trace closure of a braid at any root of unity.
1 aJordan, Stephen, P.1 aWocjan, Pawel uhttp://dl.acm.org/citation.cfm?id=2011787