Decoding general error correcting codes and the role of complementarity
Abstract Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper, we show that a decoding circuit for Calderbank-Shor-...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-024-00951-5 |
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| _version_ | 1841544469112946688 |
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| author | Yoshifumi Nakata Takaya Matsuura Masato Koashi |
| author_facet | Yoshifumi Nakata Takaya Matsuura Masato Koashi |
| author_sort | Yoshifumi Nakata |
| collection | DOAJ |
| description | Abstract Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper, we show that a decoding circuit for Calderbank-Shor-Steane (CSS) codes can be straightforwardly extended to handle general QECCs. The key to the extension lies in the use of a pair of classical-quantum (CQ) codes associated with the QECC to be decoded. The decoding error of the proposed decoding circuit depends on the classical decoding errors of the CQ codes and their degree of complementarity. We demonstrate the power of the decoding circuit in a toy model of the black hole information paradox, improving decoding errors compared to previous results. In addition, we reveal that black hole dynamics may optimally encode quantum information but poorly encode classical information. |
| format | Article |
| id | doaj-art-d92032412f2c4a948616583163fa83e2 |
| institution | Kabale University |
| issn | 2056-6387 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj-art-d92032412f2c4a948616583163fa83e22025-01-12T12:34:09ZengNature Portfolionpj Quantum Information2056-63872025-01-0111111910.1038/s41534-024-00951-5Decoding general error correcting codes and the role of complementarityYoshifumi Nakata0Takaya Matsuura1Masato Koashi2Yukawa Institute for Theoretical Physics, Kyoto University, Oiwake-cho, KitashirakawaRIKEN Center for Quantum Computing (RQC)Photon Science Center, Graduate School of Engineering, The University of TokyoAbstract Among various classes of quantum error correcting codes (QECCs), non-stabilizer codes have rich properties and are of theoretical and practical interest. Decoding non-stabilizer codes is, however, a highly non-trivial task. In this paper, we show that a decoding circuit for Calderbank-Shor-Steane (CSS) codes can be straightforwardly extended to handle general QECCs. The key to the extension lies in the use of a pair of classical-quantum (CQ) codes associated with the QECC to be decoded. The decoding error of the proposed decoding circuit depends on the classical decoding errors of the CQ codes and their degree of complementarity. We demonstrate the power of the decoding circuit in a toy model of the black hole information paradox, improving decoding errors compared to previous results. In addition, we reveal that black hole dynamics may optimally encode quantum information but poorly encode classical information.https://doi.org/10.1038/s41534-024-00951-5 |
| spellingShingle | Yoshifumi Nakata Takaya Matsuura Masato Koashi Decoding general error correcting codes and the role of complementarity npj Quantum Information |
| title | Decoding general error correcting codes and the role of complementarity |
| title_full | Decoding general error correcting codes and the role of complementarity |
| title_fullStr | Decoding general error correcting codes and the role of complementarity |
| title_full_unstemmed | Decoding general error correcting codes and the role of complementarity |
| title_short | Decoding general error correcting codes and the role of complementarity |
| title_sort | decoding general error correcting codes and the role of complementarity |
| url | https://doi.org/10.1038/s41534-024-00951-5 |
| work_keys_str_mv | AT yoshifuminakata decodinggeneralerrorcorrectingcodesandtheroleofcomplementarity AT takayamatsuura decodinggeneralerrorcorrectingcodesandtheroleofcomplementarity AT masatokoashi decodinggeneralerrorcorrectingcodesandtheroleofcomplementarity |