dorsal/arxiv
View SchemaBoth Toffoli and Controlled-NOT need little help to do universal quantum computation
| Authors | Yaoyun Shi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205115 |
| URL | https://arxiv.org/abs/quant-ph/0205115 |
Abstract
What additional gates are needed for a set of classical universal gates to do universal quantum computation? We answer this question by proving that any single-qubit real gate suffices, except those that preserve the computational basis. The result of Gottesman and Knill[quant-ph/9807006] implies that any quantum circuit involving only the Controlled-NOT and Hadamard gates can be efficiently simulated by a classical circuit. In contrast, we prove that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its alike) are universal for quantum computing. Previously only a ``generic'' gate, namely a rotation by an angle incommensurate with pi, is known to be sufficient in both problems, if only one single-qubit gate is added.
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"date_created": "2026-03-02T18:01:51.785000Z",
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"abstract": "What additional gates are needed for a set of classical universal gates to do\nuniversal quantum computation? We answer this question by proving that any\nsingle-qubit real gate suffices, except those that preserve the computational\nbasis.\n The result of Gottesman and Knill[quant-ph/9807006] implies that any quantum\ncircuit involving only the Controlled-NOT and Hadamard gates can be efficiently\nsimulated by a classical circuit. In contrast, we prove that Controlled-NOT\nplus any single-qubit real gate that does not preserve the computational basis\nand is not Hadamard (or its alike) are universal for quantum computing.\n Previously only a ``generic\u0027\u0027 gate, namely a rotation by an angle\nincommensurate with pi, is known to be sufficient in both problems, if only one\nsingle-qubit gate is added.",
"arxiv_id": "quant-ph/0205115",
"authors": [
"Yaoyun Shi"
],
"categories": [
"quant-ph"
],
"title": "Both Toffoli and Controlled-NOT need little help to do universal quantum computation",
"url": "https://arxiv.org/abs/quant-ph/0205115"
},
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"source": {
"execution_id": "3d29fc1c-a633-4446-b4ac-9097dc25d8f0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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