dorsal/arxiv
View SchemaConvergence of coined quantum walks on d-dimensional Euclidean space
| Authors | Alex D. Gottlieb, Svante Janson, Petra F. Scudo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406072 |
| URL | https://arxiv.org/abs/quant-ph/0406072 |
Abstract
Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and a translation conditional on the spin state. Coined quantum walks on the d-dimensional lattice can be treated as special cases of coined quantum walks on d-dimensional Euclidean space. We study quantum walks on d-dimensional Euclidean space and prove that the sequence of rescaled probability distributions in position space associated to the unitary evolution of the particle converges to a limit distribution.
{
"annotation_id": "3c00210b-45af-4e5f-9427-949a198b2c6e",
"date_created": "2026-03-02T18:02:07.054000Z",
"date_modified": "2026-03-02T18:02:07.054000Z",
"file_hash": "ed84e7cda25d0f1f6f0272b18f10f1c87f8034f8f2ebcde399c8c2287a951c94",
"private": false,
"record": {
"abstract": "Coined quantum walks may be interpreted as the motion in position space of a\nquantum particle with a spin degree of freedom; the dynamics are determined by\niterating a unitary transformation which is the product of a spin\ntransformation and a translation conditional on the spin state. Coined quantum\nwalks on the d-dimensional lattice can be treated as special cases of coined\nquantum walks on d-dimensional Euclidean space. We study quantum walks on\nd-dimensional Euclidean space and prove that the sequence of rescaled\nprobability distributions in position space associated to the unitary evolution\nof the particle converges to a limit distribution.",
"arxiv_id": "quant-ph/0406072",
"authors": [
"Alex D. Gottlieb",
"Svante Janson",
"Petra F. Scudo"
],
"categories": [
"quant-ph"
],
"title": "Convergence of coined quantum walks on d-dimensional Euclidean space",
"url": "https://arxiv.org/abs/quant-ph/0406072"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "f0123b26-d020-45af-b0b0-b087478215d0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}