Quantum codes do not fix isotropic errors

• URL: http://arxiv.org/abs/2502.07075v1
• Date: Mon, 27 Jan 2025 12:35:34 GMT
• Title: Quantum codes do not fix isotropic errors
• Authors: Jesús García López de Lacalle, Luis Miguel Pozo Coronado, André L. Fonseca de Oliveira,
• Abstract summary: We say that a quantum code does not fix a quantum computing error if its application does not reduce the variance of the error. We also prove for isotropic errors that, if the correction circuit of a quantum code detects an error, the corrected logical $m-$qubit has uniform distribution and as a result, it already loses all the computing information.
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• Abstract: In this work we prove that quantum error correcting codes do not fix isotropic errors, even assuming that their correction circuits do not introduce new errors. We say that a quantum code does not fix a quantum computing error if its application does not reduce the variance of the error. We also prove for isotropic errors that, if the correction circuit of a quantum code detects an error, the corrected logical $m-$qubit has uniform distribution and as a result, it already loses all the computing information.

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