dorsal/arxiv
View SchemaRobust Control of Quantum Information
| Authors | Marco A. Pravia, Nicolas Boulant, Joseph Emerson, Amro Farid, Evan M. Fortunato, Timothy F. Havel, David G. Cory |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307062 |
| URL | https://arxiv.org/abs/quant-ph/0307062 |
| DOI | 10.1063/1.1619132 |
| Journal | J. of Chem. Phys. 119, 19: 9993-10001 (2003). |
Abstract
Errors in the control of quantum systems may be classified as unitary, decoherent and incoherent. Unitary errors are systematic, and result in a density matrix that differs from the desired one by a unitary operation. Decoherent errors correspond to general completely positive superoperators, and can only be corrected using methods such as quantum error correction. Incoherent errors can also be described, on average, by completely positive superoperators, but can nevertheless be corrected by the application of a locally unitary operation that ``refocuses'' them. They are due to reproducible spatial or temporal variations in the system's Hamiltonian, so that information on the variations is encoded in the system's spatiotemporal state and can be used to correct them. In this paper liquid-state nuclear magnetic resonance (NMR) is used to demonstrate that such refocusing effects can be built directly into the control fields, where the incoherence arises from spatial inhomogeneities in the quantizing static magnetic field as well as the radio-frequency control fields themselves. Using perturbation theory, it is further shown that the eigenvalue spectrum of the completely positive superoperator exhibits a characteristic spread that contains information on the Hamiltonians' underlying distribution.
{
"annotation_id": "4e03f2fd-069e-4f28-b155-a2efefb1cbab",
"date_created": "2026-03-02T18:01:59.974000Z",
"date_modified": "2026-03-02T18:01:59.974000Z",
"file_hash": "f34fa26c9d7e4d8efea065fa999e95f5e2c91412e1217ede228ac6c58d93872a",
"private": false,
"record": {
"abstract": "Errors in the control of quantum systems may be classified as unitary,\ndecoherent and incoherent. Unitary errors are systematic, and result in a\ndensity matrix that differs from the desired one by a unitary operation.\nDecoherent errors correspond to general completely positive superoperators, and\ncan only be corrected using methods such as quantum error correction.\nIncoherent errors can also be described, on average, by completely positive\nsuperoperators, but can nevertheless be corrected by the application of a\nlocally unitary operation that ``refocuses\u0027\u0027 them. They are due to reproducible\nspatial or temporal variations in the system\u0027s Hamiltonian, so that information\non the variations is encoded in the system\u0027s spatiotemporal state and can be\nused to correct them. In this paper liquid-state nuclear magnetic resonance\n(NMR) is used to demonstrate that such refocusing effects can be built directly\ninto the control fields, where the incoherence arises from spatial\ninhomogeneities in the quantizing static magnetic field as well as the\nradio-frequency control fields themselves. Using perturbation theory, it is\nfurther shown that the eigenvalue spectrum of the completely positive\nsuperoperator exhibits a characteristic spread that contains information on the\nHamiltonians\u0027 underlying distribution.",
"arxiv_id": "quant-ph/0307062",
"authors": [
"Marco A. Pravia",
"Nicolas Boulant",
"Joseph Emerson",
"Amro Farid",
"Evan M. Fortunato",
"Timothy F. Havel",
"David G. Cory"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1619132",
"journal_ref": "J. of Chem. Phys. 119, 19: 9993-10001 (2003).",
"title": "Robust Control of Quantum Information",
"url": "https://arxiv.org/abs/quant-ph/0307062"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "15172fde-27f3-41d2-952a-bdbffd3df97f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}