Fault-tolerant syndrome extraction in [[n,1,3]] non-CSS code family generated using measurements on graph states
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909028578230272 |
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| author | Gupta, Harsh Bhattacharyya, Mainak Jain, Ritik Raina, Ankur |
| author_facet | Gupta, Harsh Bhattacharyya, Mainak Jain, Ritik Raina, Ankur |
| contents | The reliability of quantum computation critically depends on the performance of quantum error-correcting codes (QECCs). Performance of QECCs can be severely degraded by hook errors, which effectively reduce the code distance. In this work, we construct a family of $[[n,1,3]]$ non-CSS QECCs, which are fault-tolerant (FT) against noisy syndrome measurements. We employ the bare-ancilla method of Muyuan Li \emph{et al.} to demonstrate fault tolerance against hook errors during syndrome extraction. We present a systematic protocol for generating these QECCs using graph codes and propose a family of $[[n,1,3]]$ codes that preserve the fault-tolerant properties of the bare ancilla codes. We use a custom lookup-table decoder and simulate the code's performance under both anisotropic and circuit-level depolarizing noise. Our results reveal a trade-off in performance with respect to the code rate and identify optimized codes under these noise models. We benchmark our results against the flag-qubit method of Chao \emph{et al}. Notably, we report a new bare ancilla code with improved code rate while maintaining the same distance compared to the bare code used in the work of Muyuan Li \emph{et al.} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fault-tolerant syndrome extraction in [[n,1,3]] non-CSS code family generated using measurements on graph states Gupta, Harsh Bhattacharyya, Mainak Jain, Ritik Raina, Ankur Quantum Physics Information Theory The reliability of quantum computation critically depends on the performance of quantum error-correcting codes (QECCs). Performance of QECCs can be severely degraded by hook errors, which effectively reduce the code distance. In this work, we construct a family of $[[n,1,3]]$ non-CSS QECCs, which are fault-tolerant (FT) against noisy syndrome measurements. We employ the bare-ancilla method of Muyuan Li \emph{et al.} to demonstrate fault tolerance against hook errors during syndrome extraction. We present a systematic protocol for generating these QECCs using graph codes and propose a family of $[[n,1,3]]$ codes that preserve the fault-tolerant properties of the bare ancilla codes. We use a custom lookup-table decoder and simulate the code's performance under both anisotropic and circuit-level depolarizing noise. Our results reveal a trade-off in performance with respect to the code rate and identify optimized codes under these noise models. We benchmark our results against the flag-qubit method of Chao \emph{et al}. Notably, we report a new bare ancilla code with improved code rate while maintaining the same distance compared to the bare code used in the work of Muyuan Li \emph{et al.} |
| title | Fault-tolerant syndrome extraction in [[n,1,3]] non-CSS code family generated using measurements on graph states |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2501.12072 |