dorsal/arxiv
View SchemaSub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
| Authors | Navin Khaneja, Steffen J. Glaser, Roger Brockett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106099 |
| URL | https://arxiv.org/abs/quant-ph/0106099 |
| DOI | 10.1103/PhysRevA.65.032301 |
Abstract
Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces.
{
"annotation_id": "5ae92103-6988-40ca-bf01-7f90566e29f9",
"date_created": "2026-03-02T18:01:44.864000Z",
"date_modified": "2026-03-02T18:01:44.864000Z",
"file_hash": "fdcc1ff9ca4862b3e382e733f5314014faa20bb2325d0ee8070ec4e21936fcbc",
"private": false,
"record": {
"abstract": "Many coherence transfer experiments in Nuclear Magnetic Resonance\nSpectroscopy, involving network of coupled spins, use temporary spin-decoupling\nto produce desired effective Hamiltonians. In this paper, we show that\nsignificant time can be saved in producing an effective Hamiltonian, if\nspin-decoupling is avoided. We provide time optimal pulse sequences for\nproducing an important class of effective Hamiltonians in three spin networks.\nThese effective Hamiltonians are useful for coherence transfer experiments and\nimplementation of quantum logic gates in NMR quantum computing. It is\ndemonstrated that computing these time optimal pulse sequences can be reduced\nto geometric problems that involve computing sub-Riemannian geodesics on\nHomogeneous spaces.",
"arxiv_id": "quant-ph/0106099",
"authors": [
"Navin Khaneja",
"Steffen J. Glaser",
"Roger Brockett"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.032301",
"title": "Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer",
"url": "https://arxiv.org/abs/quant-ph/0106099"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "fa525c55-44da-4d2b-a8c2-eb8d37f1bdfa",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}