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Limits to error correction in quantum chaos

P. G. Silvestrov·H. Schomerus·C. W. J. Beenakker
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Abstract

We study the correction of errors that have accumulated in an entangled state of spins as a result of unknown local variations in the Zeeman energy (B) and spin-spin interaction energy (J). A non-degenerate code with error rate kappa can recover the original state with high fidelity within a time kappa^1/2 / max(B,J) -- independent of the number of encoded qubits. Whether the Hamiltonian is chaotic or not does not affect this time scale, but it does affect the complexity of the error-correcting code.

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P. G. Silvestrov, H. Schomerus, C. W. J. Beenakker. 2000-12-21. Limits to error correction in quantum chaos. https://doi.org/10.1103/physrevlett.86.5192

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