dorsal/arxiv
View SchemaSpatially Correlated Qubit Errors and Burst-Correcting Quantum Codes
| Authors | F. Vatan, V. P. Roychowdhury, M. P. Anantram |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9704019 |
| URL | https://arxiv.org/abs/quant-ph/9704019 |
Abstract
We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of burst errors in classical coding theory. We present several different efficient schemes for constructing families of such codes. For example, one can find one-dimensional quantum codes of length n=13 and 15 that correct burst errors of width b < 4; as a comparison, a random-error correcting quantum code that corrects t=3 errors must have length n > 18. In general, we show that it is possible to build quantum burst-correcting codes that have near optimal dimension. For example, we show that for any constant b, there exist b-burst-correcting quantum codes with length n, and dimension k=n-log n -O(b); as a comparison, the Hamming bound for the case with t (constant) random errors yields k < n - t log n - O(1) .
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"abstract": "We explore the design of quantum error-correcting codes for cases where the\ndecoherence events of qubits are correlated. In particular, we consider the\ncase where only spatially contiguous qubits decohere, which is analogous to the\ncase of burst errors in classical coding theory. We present several different\nefficient schemes for constructing families of such codes. For example, one can\nfind one-dimensional quantum codes of length n=13 and 15 that correct burst\nerrors of width b \u003c 4; as a comparison, a random-error correcting quantum code\nthat corrects t=3 errors must have length n \u003e 18. In general, we show that it\nis possible to build quantum burst-correcting codes that have near optimal\ndimension. For example, we show that for any constant b, there exist\nb-burst-correcting quantum codes with length n, and dimension k=n-log n -O(b);\nas a comparison, the Hamming bound for the case with t (constant) random errors\nyields k \u003c n - t log n - O(1) .",
"arxiv_id": "quant-ph/9704019",
"authors": [
"F. Vatan",
"V. P. Roychowdhury",
"M. P. Anantram"
],
"categories": [
"quant-ph"
],
"title": "Spatially Correlated Qubit Errors and Burst-Correcting Quantum Codes",
"url": "https://arxiv.org/abs/quant-ph/9704019"
},
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