Quantum Computation of Jones' Polynomials

Details Quantum Computation of Jones' Polynomials Quantum Computation of Jones' Polynomials

2002-10-12

arxiv.org/abs/quant-ph/0210095v2

Physics

Quantum Physics

14pages, 2 figures, included references, made significant modification

Scientific paper

It is a challenging problem to construct an efficient quantum algorithm which can compute the Jones' polynomial for any knot or link obtained from platting or capping of a $2n$-strand braid. We recapitulate the construction of braid-group representations from vertex models. We present the eigenbases and eigenvalues for the braiding generators and its usefulness in direct evaluation of Jones' polynomial. The calculation suggests that it is possible to associate a series of unitary operators for any braid word. Hence we propose a quantum algorithm using these unitary operators as quantum gates acting on a $2n$ qubit state. We show that the quantum computation gives Jones' polynomial for achiral knots and links.

Affiliated with

Also associated with

No associations

Rating

Quantum Computation of Jones' Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Computation of Jones' Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Computation of Jones' Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-372601