dorsal/arxiv
View SchemaAn efficient quantum algorithm for the one-dimensional Burgers equation
| Authors | Jeffrey Yepez |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210092 |
| URL | https://arxiv.org/abs/quant-ph/0210092 |
Abstract
We analyze one-dimensional classical and quantum microscopic lattice-gas models governed by a lattice Boltzmann equation at the mesoscopic scale, achieved by ensemble averaging over microscopic realizations. The models are governed by the Burgers equation at the macroscopic scale, achieved by taking the limit where the grid size and time step both approach zero and by performing a perturbative Chapman-Enskog expansion. The quantum algorithm exploiting superposition and entanglement is more efficient than the classical one because the quantum algorithm requires less memory. Furthermore, its viscosity can be made arbitrarily small.
{
"annotation_id": "0bd72b4e-87f4-4d31-a8eb-5f99f91ec538",
"date_created": "2026-03-02T18:01:52.931000Z",
"date_modified": "2026-03-02T18:01:52.931000Z",
"file_hash": "0f59510874317ba7151c123802d46dd854b8fdccef5dfeff6322afdd16541d31",
"private": false,
"record": {
"abstract": "We analyze one-dimensional classical and quantum microscopic lattice-gas\nmodels governed by a lattice Boltzmann equation at the mesoscopic scale,\nachieved by ensemble averaging over microscopic realizations. The models are\ngoverned by the Burgers equation at the macroscopic scale, achieved by taking\nthe limit where the grid size and time step both approach zero and by\nperforming a perturbative Chapman-Enskog expansion. The quantum algorithm\nexploiting superposition and entanglement is more efficient than the classical\none because the quantum algorithm requires less memory. Furthermore, its\nviscosity can be made arbitrarily small.",
"arxiv_id": "quant-ph/0210092",
"authors": [
"Jeffrey Yepez"
],
"categories": [
"quant-ph"
],
"title": "An efficient quantum algorithm for the one-dimensional Burgers equation",
"url": "https://arxiv.org/abs/quant-ph/0210092"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "0a8de7ea-9df9-4963-ae31-935e6b3016b0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}