dorsal/arxiv
View SchemaGeneral error estimate for adiabatic quantum computing
| Authors | Gernot Schaller, Sarah Mostame, Ralf Schützhold |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510183 |
| URL | https://arxiv.org/abs/quant-ph/0510183 |
| DOI | 10.1103/PhysRevA.73.062307 |
| Journal | Phys. Rev. A 73, 062307 (2006) |
Abstract
Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction ${\bra{\Psi_{\rm ground}(t)}\dot H(t)\ket{\Psi_{\rm excited}(t)} /\Delta E^2(t)\ll1}$. However, it is demonstrated that this first-order correction does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections as well and shows that the computational error can be made exponentially small -- which facilitates significantly shorter evolution times than the above first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time $T$ of order of the inverse minimum energy gap $\Delta E_{\rm min}$ is sufficient and necessary, i.e., $T=\ord(\Delta E_{\rm min}^{-1})$. For some examples, these analytical investigations are confirmed by numerical simulations. PACS: 03.67.Lx, 03.67.-a.
{
"annotation_id": "60219c76-80b6-4844-8cca-5bf64d19b2c7",
"date_created": "2026-03-02T18:02:20.028000Z",
"date_modified": "2026-03-02T18:02:20.028000Z",
"file_hash": "89fbbe9efe69699abcfa70af3458631cfbcd55605289ded55263074146ab0bcd",
"private": false,
"record": {
"abstract": "Most investigations devoted to the conditions for adiabatic quantum computing\nare based on the first-order correction ${\\bra{\\Psi_{\\rm ground}(t)}\\dot\nH(t)\\ket{\\Psi_{\\rm excited}(t)} /\\Delta E^2(t)\\ll1}$. However, it is\ndemonstrated that this first-order correction does not yield a good estimate\nfor the computational error. Therefore, a more general criterion is proposed,\nwhich includes higher-order corrections as well and shows that the\ncomputational error can be made exponentially small -- which facilitates\nsignificantly shorter evolution times than the above first-order estimate in\ncertain situations. Based on this criterion and rather general arguments and\nassumptions, it can be demonstrated that a run-time $T$ of order of the inverse\nminimum energy gap $\\Delta E_{\\rm min}$ is sufficient and necessary, i.e.,\n$T=\\ord(\\Delta E_{\\rm min}^{-1})$. For some examples, these analytical\ninvestigations are confirmed by numerical simulations. PACS: 03.67.Lx,\n03.67.-a.",
"arxiv_id": "quant-ph/0510183",
"authors": [
"Gernot Schaller",
"Sarah Mostame",
"Ralf Sch\u00fctzhold"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.062307",
"journal_ref": "Phys. Rev. A 73, 062307 (2006)",
"title": "General error estimate for adiabatic quantum computing",
"url": "https://arxiv.org/abs/quant-ph/0510183"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "bb77ec64-6d0f-4dbe-ad49-de3942d13624",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}