Title

ESTIMATING JONES AND HOMELY POLYNOMIALS WITH ONE CLEAN QUBIT

Authors

Authors

S. P. Jordan;P. Wocjan

Comments

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Abstract

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[18]. 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.

Journal Title

Quantum Information & Computation

Volume

9

Issue/Number

3-4

Publication Date

1-1-2009

Document Type

Article

First Page

264

Last Page

289

WOS Identifier

WOS:000264937400006

ISSN

1533-7146

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