ESTIMATING JONES AND HOMELY POLYNOMIALS WITH ONE CLEAN QUBIT
The Jones and HOMELY 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 HOMELY polynomials of the trace closure of a braid at any root of unity.
Quantum Information & Computation
"ESTIMATING JONES AND HOMELY POLYNOMIALS WITH ONE CLEAN QUBIT" (2009). Faculty Bibliography 2000s. 1677.