An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909722289897472 |
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| author | iOlius, Antonio deMarti Martinez, Imanol Etxezarreta Roffe, Joschka Martinez, Josu Etxezarreta |
| author_facet | iOlius, Antonio deMarti Martinez, Imanol Etxezarreta Roffe, Joschka Martinez, Josu Etxezarreta |
| contents | Fault-tolerant quantum computers must be designed in conjunction with classical co-processors that decode quantum error correction measurement information in real-time. In this work, we introduce the belief propagation plus ordered Tanner forest (BP+OTF) algorithm as an almost-linear time decoder for quantum low-density parity-check codes. The OTF post-processing stage removes qubits from the decoding graph until it has a tree-like structure. Provided that the resultant loop-free OTF graph supports a subset of qubits that can generate the syndrome, BP decoding is then guaranteed to converge. To enhance performance under circuit-level noise, we introduce a technique for sparsifying detector error models. This method uses a transfer matrix to map soft information from the full detector graph to the sparsified graph, preserving critical error propagation information from the syndrome extraction circuit. Our BP+OTF implementation first applies standard BP to the full detector graph, followed by BP+OTF post-processing on the sparsified graph. Numerical simulations show that the BP+OTF decoder achieves similar logical error suppression compared to state-of-the-art inversion-based and matching decoders for bivariate bicycle and surface codes, respectively, while maintaining almost-linear runtime complexity across all stages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise iOlius, Antonio deMarti Martinez, Imanol Etxezarreta Roffe, Joschka Martinez, Josu Etxezarreta Quantum Physics Fault-tolerant quantum computers must be designed in conjunction with classical co-processors that decode quantum error correction measurement information in real-time. In this work, we introduce the belief propagation plus ordered Tanner forest (BP+OTF) algorithm as an almost-linear time decoder for quantum low-density parity-check codes. The OTF post-processing stage removes qubits from the decoding graph until it has a tree-like structure. Provided that the resultant loop-free OTF graph supports a subset of qubits that can generate the syndrome, BP decoding is then guaranteed to converge. To enhance performance under circuit-level noise, we introduce a technique for sparsifying detector error models. This method uses a transfer matrix to map soft information from the full detector graph to the sparsified graph, preserving critical error propagation information from the syndrome extraction circuit. Our BP+OTF implementation first applies standard BP to the full detector graph, followed by BP+OTF post-processing on the sparsified graph. Numerical simulations show that the BP+OTF decoder achieves similar logical error suppression compared to state-of-the-art inversion-based and matching decoders for bivariate bicycle and surface codes, respectively, while maintaining almost-linear runtime complexity across all stages. |
| title | An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2409.01440 |