dorsal/arxiv
View SchemaQuantum Computation of Jones' Polynomials
| Authors | V. Subramaniam, P. Ramadevi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210095 |
| URL | https://arxiv.org/abs/quant-ph/0210095 |
Abstract
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.
{
"annotation_id": "74daedb9-5132-4335-83cb-7c3cf51db635",
"date_created": "2026-03-02T18:01:52.931000Z",
"date_modified": "2026-03-02T18:01:52.931000Z",
"file_hash": "3236d4b0525542abc7f3796ce7c5e7a4b8921bdb6af2924caa7ca4d5acc06074",
"private": false,
"record": {
"abstract": "It is a challenging problem to construct an efficient quantum algorithm which\ncan compute the Jones\u0027 polynomial for any knot or link obtained from platting\nor capping of a $2n$-strand braid. We recapitulate the construction of\nbraid-group representations from vertex models. We present the eigenbases and\neigenvalues for the braiding generators and its usefulness in direct evaluation\nof Jones\u0027 polynomial. The calculation suggests that it is possible to associate\na series of unitary operators for any braid word. Hence we propose a quantum\nalgorithm using these unitary operators as quantum gates acting on a $2n$ qubit\nstate. We show that the quantum computation gives Jones\u0027 polynomial for achiral\nknots and links.",
"arxiv_id": "quant-ph/0210095",
"authors": [
"V. Subramaniam",
"P. Ramadevi"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "Quantum Computation of Jones\u0027 Polynomials",
"url": "https://arxiv.org/abs/quant-ph/0210095"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "25b82107-540d-4751-afcd-28ca9f50dd47",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}