dorsal/arxiv
View SchemaCartan Decomposition of SU(2^n), Constructive Controllability of Spin systems and Universal Quantum Computing
| Authors | Navin Khaneja, Steffen Glaser |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0010100 |
| URL | https://arxiv.org/abs/quant-ph/0010100 |
Abstract
In this paper we provide an explicit parameterization of arbitrary unitary transformation acting on n qubits, in terms of one and two qubit quantum gates. The construction is based on successive Cartan decompositions of the semi-simple Lie group, SU(2^n). The decomposition highlights the geometric aspects of building an arbitrary unitary transformation out of quantum gates and makes explicit the choice of pulse sequences for the implementation of arbitrary unitary transformation on $n coupled spins. Finally we make observations on the optimality of the design procedure.
{
"annotation_id": "b7436ee1-778c-417c-adc6-9ed2af5b01b9",
"date_created": "2026-03-02T18:01:41.423000Z",
"date_modified": "2026-03-02T18:01:41.423000Z",
"file_hash": "416f20778aef3d89523a6920961d23750681eee41c50496b4dde4aa98b1a7a17",
"private": false,
"record": {
"abstract": "In this paper we provide an explicit parameterization of arbitrary unitary\ntransformation acting on n qubits, in terms of one and two qubit quantum gates.\nThe construction is based on successive Cartan decompositions of the\nsemi-simple Lie group, SU(2^n). The decomposition highlights the geometric\naspects of building an arbitrary unitary transformation out of quantum gates\nand makes explicit the choice of pulse sequences for the implementation of\narbitrary unitary transformation on $n coupled spins. Finally we make\nobservations on the optimality of the design procedure.",
"arxiv_id": "quant-ph/0010100",
"authors": [
"Navin Khaneja",
"Steffen Glaser"
],
"categories": [
"quant-ph"
],
"title": "Cartan Decomposition of SU(2^n), Constructive Controllability of Spin systems and Universal Quantum Computing",
"url": "https://arxiv.org/abs/quant-ph/0010100"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "41dd1698-6081-43ad-8515-eae091192106",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}