dorsal/arxiv
View SchemaQuantum circuits with uniformly controlled one-qubit gates
| Authors | Ville Bergholm, Juha J. Vartiainen, Mikko Mottonen, Martti M. Salomaa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410066 |
| URL | https://arxiv.org/abs/quant-ph/0410066 |
| DOI | 10.1103/PhysRevA.71.052330 |
| Journal | Phys. Rev. A 71, 052330 (2005) |
Abstract
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.
{
"annotation_id": "cb047e51-d9c8-4e92-9fa5-dcdbfcfb63ac",
"date_created": "2026-03-02T18:02:10.132000Z",
"date_modified": "2026-03-02T18:02:10.132000Z",
"file_hash": "801f2fd3c6a97b595ab5df58277d43844aee5e0f7ac8424ab97ea577e1a6b2fb",
"private": false,
"record": {
"abstract": "Uniformly controlled one-qubit gates are quantum gates which can be\nrepresented as direct sums of two-dimensional unitary operators acting on a\nsingle qubit. We present a quantum gate array which implements any n-qubit gate\nof this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit\ngates and a single diagonal n-qubit gate. The circuit is based on the so-called\nquantum multiplexor, for which we provide a modified construction. We\nillustrate the versatility of these gates by applying them to the decomposition\nof a general n-qubit gate and a local state preparation procedure. Moreover, we\nstudy their implementation using only nearest-neighbor gates. We give upper\nbounds for the one-qubit and controlled-NOT gate counts for all the\naforementioned applications. In all four cases, the proposed circuit topologies\neither improve on or achieve the previously reported upper bounds for the gate\ncounts. Thus, they provide the most efficient method for general gate\ndecompositions currently known.",
"arxiv_id": "quant-ph/0410066",
"authors": [
"Ville Bergholm",
"Juha J. Vartiainen",
"Mikko Mottonen",
"Martti M. Salomaa"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.052330",
"journal_ref": "Phys. Rev. A 71, 052330 (2005)",
"title": "Quantum circuits with uniformly controlled one-qubit gates",
"url": "https://arxiv.org/abs/quant-ph/0410066"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "eea9dc61-e21a-40f9-be2a-872eedaf3018",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}