dorsal/arxiv
View SchemaBraiding Operators are Universal Quantum Gates
| Authors | Louis H. Kauffman, Samuel J. Lomonaco Jr |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401090 |
| URL | https://arxiv.org/abs/quant-ph/0401090 |
| DOI | 10.1088/1367-2630/6/1/134 |
Abstract
This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots, and links. Other solutions of the Yang-Baxter Equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, teleportation, and the structure of braiding in a topological quantum field theory.
{
"annotation_id": "3016d74a-9dd2-43ac-9dd1-ba39956755ac",
"date_created": "2026-03-02T18:02:03.123000Z",
"date_modified": "2026-03-02T18:02:03.123000Z",
"file_hash": "69766f24a1a5040673d893f298f3c5f527d9f5ac22343da45bc902d1b378284d",
"private": false,
"record": {
"abstract": "This paper explores of the role of unitary braiding operators in quantum\ncomputing. We show that a single specific solution R (the Bell basis change\nmatrix) of the Yang-Baxter Equation is a universal gate for quantum computing,\nin the presence of local unitary transformations. We show that this same R\ngenerates a new non-trivial invariant of braids, knots, and links. Other\nsolutions of the Yang-Baxter Equation are also shown to be universal for\nquantum computation. The paper discusses these results in the context of\ncomparing quantum and topological points of view. In particular, we discuss\nquantum computation of link invariants, the relationship between quantum\nentanglement and topological entanglement, teleportation, and the structure of\nbraiding in a topological quantum field theory.",
"arxiv_id": "quant-ph/0401090",
"authors": [
"Louis H. Kauffman",
"Samuel J. Lomonaco Jr"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/6/1/134",
"title": "Braiding Operators are Universal Quantum Gates",
"url": "https://arxiv.org/abs/quant-ph/0401090"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "05d765a4-eafc-4482-b6c8-f213db4db0b1",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}