dorsal/arxiv
View SchemaFast Quantum Modular Exponentiation
| Authors | R. Van Meter, K. M. Itoh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408006 |
| URL | https://arxiv.org/abs/quant-ph/0408006 |
| DOI | 10.1103/PhysRevA.71.052320 |
| Journal | Phys. Rev. A 71, 052320 (2005) |
Abstract
We present a detailed analysis of the impact on modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space tradeoffs. We find that, to exponentiate an n-bit number, for storage space 100n (twenty times the minimum 5n), we can execute modular exponentiation two hundred to seven hundred times faster than optimized versions of the basic algorithms, depending on architecture, for n=128. Addition on a neighbor-only architecture is limited to O(n) time when non-neighbor architectures can reach O(log n), demonstrating that physical characteristics of a computing device have an important impact on both real-world running time and asymptotic behavior. Our results will help guide experimental implementations of quantum algorithms and devices.
{
"annotation_id": "3e557122-64f9-444a-a342-03daf1dee934",
"date_created": "2026-03-02T18:02:10.005000Z",
"date_modified": "2026-03-02T18:02:10.005000Z",
"file_hash": "96abb68fb41cffdb089ce27a8a21ddab00e702b497965d192fa3a187dad6fc18",
"private": false,
"record": {
"abstract": "We present a detailed analysis of the impact on modular exponentiation of\narchitectural features and possible concurrent gate execution. Various\narithmetic algorithms are evaluated for execution time, potential concurrency,\nand space tradeoffs. We find that, to exponentiate an n-bit number, for storage\nspace 100n (twenty times the minimum 5n), we can execute modular exponentiation\ntwo hundred to seven hundred times faster than optimized versions of the basic\nalgorithms, depending on architecture, for n=128. Addition on a neighbor-only\narchitecture is limited to O(n) time when non-neighbor architectures can reach\nO(log n), demonstrating that physical characteristics of a computing device\nhave an important impact on both real-world running time and asymptotic\nbehavior. Our results will help guide experimental implementations of quantum\nalgorithms and devices.",
"arxiv_id": "quant-ph/0408006",
"authors": [
"R. Van Meter",
"K. M. Itoh"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.052320",
"journal_ref": "Phys. Rev. A 71, 052320 (2005)",
"title": "Fast Quantum Modular Exponentiation",
"url": "https://arxiv.org/abs/quant-ph/0408006"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "bbb5f031-ca97-4e40-8cbd-969ab4294538",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}