The computational complexity of knot and link problems
Journal of the ACM (JACM)
Quantum computing and quadratically signed weight enumerators
Information Processing Letters
A polynomial quantum algorithm for approximating the Jones polynomial
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computing with highly mixed states
Journal of the ACM (JACM)
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Quantum Information & Computation
Estimating Jones polynomials is a complete problem for one clean qubit
Quantum Information & Computation
Permutational quantum computing
Quantum Information & Computation
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The Jones and HOMFLY polynomials are link invariants with close connections to quan-tum computing. It was recently shown that finding a certain approximation to the Jonespolynomial of the trace closure of a braid at the fifth root of unity is a complete problemfor the one clean qubit complexity class[18]. This is the class of problems solvable inpolynomial time on a quantum computer acting on an initial state in which one qubitis pure and the rest are maximally mixed. Here we generalize this result by showingthat one clean qubit computers can efficiently approximate the Jones and single-variableHOMFLY polynomials of the trace closure of a braid at any root of unity.