dorsal/arxiv
View SchemaMinimal Universal Two-qubit Quantum Circuits
| Authors | Vivek V. Shende, Igor L. Markov, Stephen S. Bullock |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308033 |
| URL | https://arxiv.org/abs/quant-ph/0308033 |
| DOI | 10.1103/PhysRevA.69.062321 |
| Journal | V. V. Shende, I. L. Markov, and S. S. Bullock, ``Minimal Universal Two-qubit Controlled-NOT-based Circuits,'' APS Physical Review A 69, 062321 (2004). |
Abstract
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare favorably to previously published results. Temporary storage is not used because it tends to be expensive in physical implementations. For each gate library, best gate counts can be achieved by a single universal circuit. To compute gate parameters in universal circuits, we only use closed-form algebraic expressions, and in particular do not rely on matrix exponentials. Our algorithm has been coded in C++.
{
"annotation_id": "288b54dc-7ed9-49a5-ba43-892a42101a83",
"date_created": "2026-03-02T18:01:59.936000Z",
"date_modified": "2026-03-02T18:01:59.936000Z",
"file_hash": "95a2dc484ebfd3f763fa538852ac3dde0042158447094f907e1e437ff98d8929",
"private": false,
"record": {
"abstract": "We give quantum circuits that simulate an arbitrary two-qubit unitary\noperator up to global phase. For several quantum gate libraries we prove that\ngate counts are optimal in worst and average cases. Our lower and upper bounds\ncompare favorably to previously published results. Temporary storage is not\nused because it tends to be expensive in physical implementations.\n For each gate library, best gate counts can be achieved by a single universal\ncircuit. To compute gate parameters in universal circuits, we only use\nclosed-form algebraic expressions, and in particular do not rely on matrix\nexponentials. Our algorithm has been coded in C++.",
"arxiv_id": "quant-ph/0308033",
"authors": [
"Vivek V. Shende",
"Igor L. Markov",
"Stephen S. Bullock"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.69.062321",
"journal_ref": "V. V. Shende, I. L. Markov, and S. S. Bullock, ``Minimal Universal\n Two-qubit Controlled-NOT-based Circuits,\u0027\u0027 APS Physical Review A 69, 062321\n (2004).",
"title": "Minimal Universal Two-qubit Quantum Circuits",
"url": "https://arxiv.org/abs/quant-ph/0308033"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7c4d7851-d797-4722-a106-8c69830959af",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}