dorsal/arxiv
View SchemaError threshold estimation by means of the [[7,1,3]] CSS quantum code
| Authors | Pedro J. Salas, Angel L. Sanz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411042 |
| URL | https://arxiv.org/abs/quant-ph/0411042 |
Abstract
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting codes. In this work, we estimate the threshold conditions necessary to make a long enough quantum computation. The [[7,1,3]] CSS quantum code, together with the Shor method to measure the error syndrome is used. No concatenation is included. The decoherence is introduced by means of the depolarizing channel error model, obtaining several thresholds from the numerical simulation. Regarding the maintenance of a qubit stabilized in the memory, the error probability must be smaller than 2.9 10-5. In order to implement a one or two qubit encoded gate in an effective fault-tolerant way, it is possible to choose an adequate non-encoded noisy gate if the memory error probability is smaller than 1.3 10-5. In addition, fulfilling this last condition permits us to assume a more efficient behaviour compared to the equivalent non-encoded process.
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"abstract": "The states needed in a quantum computation are extremely affected by\ndecoherence. Several methods have been proposed to control error spreading.\nThey use two main tools: fault-tolerant constructions and concatenated quantum\nerror correcting codes. In this work, we estimate the threshold conditions\nnecessary to make a long enough quantum computation. The [[7,1,3]] CSS quantum\ncode, together with the Shor method to measure the error syndrome is used. No\nconcatenation is included. The decoherence is introduced by means of the\ndepolarizing channel error model, obtaining several thresholds from the\nnumerical simulation. Regarding the maintenance of a qubit stabilized in the\nmemory, the error probability must be smaller than 2.9 10-5. In order to\nimplement a one or two qubit encoded gate in an effective fault-tolerant way,\nit is possible to choose an adequate non-encoded noisy gate if the memory error\nprobability is smaller than 1.3 10-5. In addition, fulfilling this last\ncondition permits us to assume a more efficient behaviour compared to the\nequivalent non-encoded process.",
"arxiv_id": "quant-ph/0411042",
"authors": [
"Pedro J. Salas",
"Angel L. Sanz"
],
"categories": [
"quant-ph"
],
"title": "Error threshold estimation by means of the [[7,1,3]] CSS quantum code",
"url": "https://arxiv.org/abs/quant-ph/0411042"
},
"schema_id": "dorsal/arxiv",
"source": {
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"variant": "snapshot-2026-03-01",
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