dorsal/arxiv
View SchemaAn Introduction to Quantum Error Correction
| Authors | Daniel Gottesman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0004072 |
| URL | https://arxiv.org/abs/quant-ph/0004072 |
| Journal | in Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, ed. S. J. Lomonaco, Jr., pp. 221-235 (American Mathematical Society, Providence, Rhode Island, 2002) |
Abstract
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. Many quantum codes can be described in terms of the stabilizer of the codewords. The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements.
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"abstract": "Quantum states are very delicate, so it is likely some sort of quantum error\ncorrection will be necessary to build reliable quantum computers. The theory of\nquantum error-correcting codes has some close ties to and some striking\ndifferences from the theory of classical error-correcting codes. Many quantum\ncodes can be described in terms of the stabilizer of the codewords. The\nstabilizer is a finite Abelian group, and allows a straightforward\ncharacterization of the error-correcting properties of the code. The stabilizer\nformalism for quantum codes also illustrates the relationships to classical\ncoding theory, particularly classical codes over GF(4), the finite field with\nfour elements.",
"arxiv_id": "quant-ph/0004072",
"authors": [
"Daniel Gottesman"
],
"categories": [
"quant-ph"
],
"journal_ref": "in Quantum Computation: A Grand Mathematical Challenge for the\n Twenty-First Century and the Millennium, ed. S. J. Lomonaco, Jr., pp. 221-235\n (American Mathematical Society, Providence, Rhode Island, 2002)",
"title": "An Introduction to Quantum Error Correction",
"url": "https://arxiv.org/abs/quant-ph/0004072"
},
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