Spatially Correlated Qubit Errors and Burst-Correcting Quantum Codes

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dc.creatorVatan, F.
dc.creatorRoychowdhury, V. P.
dc.creatorAnantram, M. P.
dc.date1997-04-09
dc.date1997-05-16
dc.date.accessioned2026-07-07T09:09:01Z
dc.date.available2026-07-07T09:09:01Z
dc.descriptionWe 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) .
dc.description15 pages, no figures, LaTeX. Updated version includes one more example, also some minor errors are corrected
dc.identifierhttps://arxiv.org/abs/quant-ph/9704019
dc.identifierhttp://arxiv.org/abs/quant-ph/9704019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150929
dc.subjectQuantum Physics
dc.titleSpatially Correlated Qubit Errors and Burst-Correcting Quantum Codes
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