dorsal/arxiv
View SchemaQuantum Computation as Geometry
| Authors | Michael A. Nielsen, Mark R. Dowling, Mile Gu, Andrew C. Doherty |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603161 |
| URL | https://arxiv.org/abs/quant-ph/0603161 |
| DOI | 10.1126/science.1121541 |
| Journal | M. A. Nielsen, M. Dowling, M. Gu, A. Doherty, Science 311, 1133 (2006) |
Abstract
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms, or to prove limitations on the power of quantum computers.
{
"annotation_id": "5a0a0e91-f5c1-4dbd-bbd3-c1aaa26158df",
"date_created": "2026-03-02T18:02:23.903000Z",
"date_modified": "2026-03-02T18:02:23.903000Z",
"file_hash": "930ef1a45b4e30a256f6fbaf1016ae6da200e6108fe4eb15c0e969af9c42423f",
"private": false,
"record": {
"abstract": "Quantum computers hold great promise, but it remains a challenge to find\nefficient quantum circuits that solve interesting computational problems. We\nshow that finding optimal quantum circuits is essentially equivalent to finding\nthe shortest path between two points in a certain curved geometry. By recasting\nthe problem of finding quantum circuits as a geometric problem, we open up the\npossibility of using the mathematical techniques of Riemannian geometry to\nsuggest new quantum algorithms, or to prove limitations on the power of quantum\ncomputers.",
"arxiv_id": "quant-ph/0603161",
"authors": [
"Michael A. Nielsen",
"Mark R. Dowling",
"Mile Gu",
"Andrew C. Doherty"
],
"categories": [
"quant-ph"
],
"doi": "10.1126/science.1121541",
"journal_ref": "M. A. Nielsen, M. Dowling, M. Gu, A. Doherty, Science 311, 1133\n (2006)",
"title": "Quantum Computation as Geometry",
"url": "https://arxiv.org/abs/quant-ph/0603161"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "0e438386-9cb4-4364-bcb7-ef784dfec7b2",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}