dorsal/arxiv
View SchemaThe query complexity of order-finding
| Authors | Richard Cleve |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911124 |
| URL | https://arxiv.org/abs/quant-ph/9911124 |
Abstract
We consider the problem where P is an unknown permutation on {0,1,...,2^n - 1}, y is an element of {0,1,...,2^n - 1}, and the goal is to determine the minimum r > 0 such that P^r(y) = y (where P^r is P composed with itself r times). Information about P is available only via queries that yield P^x(y) from any x in {0,1,...,2^m - 1} and y in {0,1,...,2^n - 1} (where m is polynomial in n). The main resource under consideration is the number of these queries. We show that the number of queries necessary to solve the problem in the classical probabilistic bounded-error model is exponential in n. This contrasts sharply with the quantum bounded-error model, where a constant number of queries suffices.
{
"annotation_id": "f9ca13cd-09d7-43bb-b2c5-c812a0c99b85",
"date_created": "2026-03-02T18:02:48.537000Z",
"date_modified": "2026-03-02T18:02:48.537000Z",
"file_hash": "3feaba8c4e1c53975fd8f14aca267f46231e8faf0b1af9d3c4301c326ad6fafb",
"private": false,
"record": {
"abstract": "We consider the problem where P is an unknown permutation on {0,1,...,2^n -\n1}, y is an element of {0,1,...,2^n - 1}, and the goal is to determine the\nminimum r \u003e 0 such that P^r(y) = y (where P^r is P composed with itself r\ntimes). Information about P is available only via queries that yield P^x(y)\nfrom any x in {0,1,...,2^m - 1} and y in {0,1,...,2^n - 1} (where m is\npolynomial in n). The main resource under consideration is the number of these\nqueries. We show that the number of queries necessary to solve the problem in\nthe classical probabilistic bounded-error model is exponential in n. This\ncontrasts sharply with the quantum bounded-error model, where a constant number\nof queries suffices.",
"arxiv_id": "quant-ph/9911124",
"authors": [
"Richard Cleve"
],
"categories": [
"quant-ph"
],
"title": "The query complexity of order-finding",
"url": "https://arxiv.org/abs/quant-ph/9911124"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "bd1c71b7-16ab-46f0-b12e-2d9683b2b0c2",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}