Localized statistics decoding for quantum low-density parity-check codes
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908546047672320 |
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| author | Hillmann, Timo Berent, Lucas Quintavalle, Armanda O. Eisert, Jens Wille, Robert Roffe, Joschka |
| author_facet | Hillmann, Timo Berent, Lucas Quintavalle, Armanda O. Eisert, Jens Wille, Robert Roffe, Joschka |
| contents | Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination, to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localized statistics decoding for quantum low-density parity-check codes Hillmann, Timo Berent, Lucas Quintavalle, Armanda O. Eisert, Jens Wille, Robert Roffe, Joschka Quantum Physics Information Theory Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to their implementation. In this work, we introduce localized statistics decoding, a reliability-guided inversion decoder that is highly parallelizable and applicable to arbitrary quantum low-density parity-check codes. Our approach employs a parallel matrix factorization strategy, which we call on-the-fly elimination, to identify, validate, and solve local decoding regions on the decoding graph. Through numerical simulations, we show that localized statistics decoding matches the performance of state-of-the-art decoders while reducing the runtime complexity for operation in the sub-threshold regime. Importantly, our decoder is more amenable to implementation on specialized hardware, positioning it as a promising candidate for decoding real-time syndromes from experiments. |
| title | Localized statistics decoding for quantum low-density parity-check codes |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2406.18655 |