Optimal Decoder for the Error Correcting Parity Code
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917091125231616 |
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| author | Tiurev, Konstantin Goeller, Christophe Stenzel, Leo Schnabl, Paul Messinger, Anette Fellner, Michael Lechner, Wolfgang |
| author_facet | Tiurev, Konstantin Goeller, Christophe Stenzel, Leo Schnabl, Paul Messinger, Anette Fellner, Michael Lechner, Wolfgang |
| contents | We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes while yielding near-optimal decoding for intermediate code sizes and achieving optimality in the limit of large codes. In the regime of unreliable measurements, the decoder demonstrates fault-tolerant thresholds above 5% at the cost of decoding a series of independent repetition codes in (1 + 1) dimensions. Such high thresholds, in conjunction with a practical decoder, efficient long-range logical gates, and suitability for planar implementation, position the parity architecture as a promising candidate for demonstrating quantum advantage on qubit platforms with strong noise bias. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Decoder for the Error Correcting Parity Code Tiurev, Konstantin Goeller, Christophe Stenzel, Leo Schnabl, Paul Messinger, Anette Fellner, Michael Lechner, Wolfgang Quantum Physics We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes while yielding near-optimal decoding for intermediate code sizes and achieving optimality in the limit of large codes. In the regime of unreliable measurements, the decoder demonstrates fault-tolerant thresholds above 5% at the cost of decoding a series of independent repetition codes in (1 + 1) dimensions. Such high thresholds, in conjunction with a practical decoder, efficient long-range logical gates, and suitability for planar implementation, position the parity architecture as a promising candidate for demonstrating quantum advantage on qubit platforms with strong noise bias. |
| title | Optimal Decoder for the Error Correcting Parity Code |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.05210 |