dorsal/arxiv
View SchemaOverhead and noise threshold of fault-tolerant quantum error correction
| Authors | Andrew M. Steane |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207119 |
| URL | https://arxiv.org/abs/quant-ph/0207119 |
| DOI | 10.1103/PhysRevA.68.042322 |
Abstract
Fault tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is calculated for a variety of CSS codes, including large block codes and concatenated codes. Recent insights into the syndrome extraction process, which render the whole process more efficient and more noise-tolerant, are incorporated. The average number of recoveries which can be completed without failure is thus estimated as a function of various parameters. The main parameters are the gate (gamma) and memory (epsilon) failure rates, the physical scale-up of the computer size, and the time t_m required for measurements and classical processing. The achievable computation size is given as a surface in parameter space. This indicates the noise threshold as well as other information. It is found that concatenated codes based on the [[23,1,7]] Golay code give higher thresholds than those based on the [[7,1,3]] Hamming code under most conditions. The threshold gate noise gamma_0 is a function of epsilon/gamma and t_m; example values are {epsilon/gamma, t_m, gamma_0} = {1, 1, 0.001}, {0.01, 1, 0.003}, {1, 100, 0.0001}, {0.01, 100, 0.002}, assuming zero cost for information transport. This represents an order of magnitude increase in tolerated memory noise, compared with previous calculations, which is made possible by recent insights into the fault-tolerant QEC process.
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"abstract": "Fault tolerant quantum error correction (QEC) networks are studied by a\ncombination of numerical and approximate analytical treatments. The probability\nof failure of the recovery operation is calculated for a variety of CSS codes,\nincluding large block codes and concatenated codes. Recent insights into the\nsyndrome extraction process, which render the whole process more efficient and\nmore noise-tolerant, are incorporated. The average number of recoveries which\ncan be completed without failure is thus estimated as a function of various\nparameters. The main parameters are the gate (gamma) and memory (epsilon)\nfailure rates, the physical scale-up of the computer size, and the time t_m\nrequired for measurements and classical processing. The achievable computation\nsize is given as a surface in parameter space. This indicates the noise\nthreshold as well as other information. It is found that concatenated codes\nbased on the [[23,1,7]] Golay code give higher thresholds than those based on\nthe [[7,1,3]] Hamming code under most conditions. The threshold gate noise\ngamma_0 is a function of epsilon/gamma and t_m; example values are\n{epsilon/gamma, t_m, gamma_0} = {1, 1, 0.001}, {0.01, 1, 0.003}, {1, 100,\n0.0001}, {0.01, 100, 0.002}, assuming zero cost for information transport. This\nrepresents an order of magnitude increase in tolerated memory noise, compared\nwith previous calculations, which is made possible by recent insights into the\nfault-tolerant QEC process.",
"arxiv_id": "quant-ph/0207119",
"authors": [
"Andrew M. Steane"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.042322",
"title": "Overhead and noise threshold of fault-tolerant quantum error correction",
"url": "https://arxiv.org/abs/quant-ph/0207119"
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