dorsal/arxiv
View SchemaGeneralized Performance of Concatenated Quantum Codes -- A Dynamical Systems Approach
| Authors | Jesse Fern, Julia Kempe, Slobodan Simic, Shankar Sastry |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409084 |
| URL | https://arxiv.org/abs/quant-ph/0409084 |
| DOI | 10.1109/TAC.2006.871942 |
| Journal | IEEE Trans. on Automatic Control 51:448-459 (March 2006) |
Abstract
We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn et al. [1] to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing on particular types of noise channels, we study the geometry of the coding map as a discrete-time dynamical system on the entire space of noise channels. In the case of diagonal channels, we show that any code with distance at least three corrects (in the infinite concatenation limit) an open set of errors. For Calderbank-Shor-Steane (CSS) codes, we give a more precise characterization of that set. We show how to incorporate noise in the gates, thus completing the framework. We derive some general bounds for noise channels, which allows us to analyze several codes in detail.
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"abstract": "We apply a dynamical systems approach to concatenation of quantum error\ncorrecting codes, extending and generalizing the results of Rahn et al. [1] to\nboth diagonal and nondiagonal channels. Our point of view is global: instead of\nfocusing on particular types of noise channels, we study the geometry of the\ncoding map as a discrete-time dynamical system on the entire space of noise\nchannels. In the case of diagonal channels, we show that any code with distance\nat least three corrects (in the infinite concatenation limit) an open set of\nerrors. For Calderbank-Shor-Steane (CSS) codes, we give a more precise\ncharacterization of that set. We show how to incorporate noise in the gates,\nthus completing the framework. We derive some general bounds for noise\nchannels, which allows us to analyze several codes in detail.",
"arxiv_id": "quant-ph/0409084",
"authors": [
"Jesse Fern",
"Julia Kempe",
"Slobodan Simic",
"Shankar Sastry"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TAC.2006.871942",
"journal_ref": "IEEE Trans. on Automatic Control 51:448-459 (March 2006)",
"title": "Generalized Performance of Concatenated Quantum Codes -- A Dynamical Systems Approach",
"url": "https://arxiv.org/abs/quant-ph/0409084"
},
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