dorsal/arxiv
View SchemaUniversal quantum gates
| Authors | Jean-Luc Brylinski, Ranee Brylinski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108062 |
| URL | https://arxiv.org/abs/quant-ph/0108062 |
Abstract
In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit gates together with V produces all n-qudit gates up to arbitrary precision, or (ii) the collection of all 1-qudit gates together with V produces all n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions on V, and they hold if and only if V is not a primitive gate. Here we say V is primitive if it transforms any decomposable tensor into a decomposable tensor. We discuss some applications and also relations with work of other authors.
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"abstract": "In this paper we study universality for quantum gates acting on qudits.Qudits\nare states in a Hilbert space of dimension d where d is at least two. We\ndetermine which 2-qudit gates V have the properties (i) the collection of all\n1-qudit gates together with V produces all n-qudit gates up to arbitrary\nprecision, or (ii) the collection of all 1-qudit gates together with V produces\nall n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions\non V, and they hold if and only if V is not a primitive gate. Here we say V is\nprimitive if it transforms any decomposable tensor into a decomposable tensor.\nWe discuss some applications and also relations with work of other authors.",
"arxiv_id": "quant-ph/0108062",
"authors": [
"Jean-Luc Brylinski",
"Ranee Brylinski"
],
"categories": [
"quant-ph"
],
"title": "Universal quantum gates",
"url": "https://arxiv.org/abs/quant-ph/0108062"
},
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"execution_id": "d161b78b-05bf-4a08-b3af-9b1cbe28624d",
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"variant": "snapshot-2026-03-01",
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