dorsal/arxiv
View SchemaEffects of noise on quantum error correction algorithms
| Authors | Adriano Barenco, Todd A. Brun, Ruediger Schack, Tim Spiller |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9612047 |
| URL | https://arxiv.org/abs/quant-ph/9612047 |
| DOI | 10.1103/PhysRevA.56.1177 |
Abstract
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation, however, are limited by decoherence, in which the effect of an external environment causes random errors in the quantum calculation. To combat this problem, quantum error correction schemes have been proposed, in which a single quantum bit (qubit) is ``encoded'' as a state of some larger number of qubits, chosen to resist particular types of errors. Most such schemes are vulnerable, however, to errors in the encoding and decoding itself. We examine two such schemes, in which a single qubit is encoded in a state of $n$ qubits while subject to dephasing or to arbitrary isotropic noise. Using both analytical and numerical calculations, we argue that error correction remains beneficial in the presence of weak noise, and that there is an optimal time between error correction steps, determined by the strength of the interaction with the environment and the parameters set by the encoding.
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"abstract": "It has recently been shown that there are efficient algorithms for quantum\ncomputers to solve certain problems, such as prime factorization, which are\nintractable to date on classical computers. The chances for practical\nimplementation, however, are limited by decoherence, in which the effect of an\nexternal environment causes random errors in the quantum calculation. To combat\nthis problem, quantum error correction schemes have been proposed, in which a\nsingle quantum bit (qubit) is ``encoded\u0027\u0027 as a state of some larger number of\nqubits, chosen to resist particular types of errors. Most such schemes are\nvulnerable, however, to errors in the encoding and decoding itself. We examine\ntwo such schemes, in which a single qubit is encoded in a state of $n$ qubits\nwhile subject to dephasing or to arbitrary isotropic noise. Using both\nanalytical and numerical calculations, we argue that error correction remains\nbeneficial in the presence of weak noise, and that there is an optimal time\nbetween error correction steps, determined by the strength of the interaction\nwith the environment and the parameters set by the encoding.",
"arxiv_id": "quant-ph/9612047",
"authors": [
"Adriano Barenco",
"Todd A. Brun",
"Ruediger Schack",
"Tim Spiller"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.56.1177",
"title": "Effects of noise on quantum error correction algorithms",
"url": "https://arxiv.org/abs/quant-ph/9612047"
},
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