Minimising surface-code failures using a color-code decoder
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced by the depolarising noise model. The decoder is obtained by...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-02-17-1632/pdf/ |
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| _version_ | 1850024279814438912 |
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| author | Asmae Benhemou Kaavya Sahay Lingling Lao Benjamin J. Brown |
| author_facet | Asmae Benhemou Kaavya Sahay Lingling Lao Benjamin J. Brown |
| author_sort | Asmae Benhemou |
| collection | DOAJ |
| description | The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced by the depolarising noise model. The decoder is obtained by mapping the syndrome of the surface code onto that of the color code, thereby allowing us to adopt more sophisticated color-code decoding algorithms. Analytical arguments and exhaustive testing show that the resulting decoder can find a least-weight correction for all weight $d/2$ depolarising errors for even code distance $d$. This improves the logical error rate by an exponential factor $O(2^{d/2})$ compared with decoders that treat bit-flip and dephasing errors separately. We demonstrate this improvement with analytical arguments and supporting numerical simulations at low error rates. Of independent interest, we also demonstrate an exponential improvement in logical error rate for our decoder used to correct independent and identically distributed bit-flip errors affecting the color code compared with more conventional color-code decoding algorithms. |
| format | Article |
| id | doaj-art-5bac2e7771f04065a50a7e5a8a7d3f6c |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-5bac2e7771f04065a50a7e5a8a7d3f6c2025-08-20T03:01:10ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-02-019163210.22331/q-2025-02-17-163210.22331/q-2025-02-17-1632Minimising surface-code failures using a color-code decoderAsmae BenhemouKaavya SahayLingling LaoBenjamin J. BrownThe development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced by the depolarising noise model. The decoder is obtained by mapping the syndrome of the surface code onto that of the color code, thereby allowing us to adopt more sophisticated color-code decoding algorithms. Analytical arguments and exhaustive testing show that the resulting decoder can find a least-weight correction for all weight $d/2$ depolarising errors for even code distance $d$. This improves the logical error rate by an exponential factor $O(2^{d/2})$ compared with decoders that treat bit-flip and dephasing errors separately. We demonstrate this improvement with analytical arguments and supporting numerical simulations at low error rates. Of independent interest, we also demonstrate an exponential improvement in logical error rate for our decoder used to correct independent and identically distributed bit-flip errors affecting the color code compared with more conventional color-code decoding algorithms.https://quantum-journal.org/papers/q-2025-02-17-1632/pdf/ |
| spellingShingle | Asmae Benhemou Kaavya Sahay Lingling Lao Benjamin J. Brown Minimising surface-code failures using a color-code decoder Quantum |
| title | Minimising surface-code failures using a color-code decoder |
| title_full | Minimising surface-code failures using a color-code decoder |
| title_fullStr | Minimising surface-code failures using a color-code decoder |
| title_full_unstemmed | Minimising surface-code failures using a color-code decoder |
| title_short | Minimising surface-code failures using a color-code decoder |
| title_sort | minimising surface code failures using a color code decoder |
| url | https://quantum-journal.org/papers/q-2025-02-17-1632/pdf/ |
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