New local stabilizer codes from local classical codes
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910894802337792 |
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| author | Gunderman, Lane G. |
| author_facet | Gunderman, Lane G. |
| contents | Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new local and low-weight stabilizer codes which are obtained from the recent progress in $2D$ local classical codes. Of note, we construct codes with weight and qubit use count of $5$ while being able to protect the information with high distance, or greater logical count. We also consider the Fibonacci code family which generates weight and qubit use count of $6$ while having parameters $[[O(l^3),O(l),Ω(l)]]$. While other weight-reduction methods centered on lowering the weight without regard to locality, this work achieves very low-weight and geometric locality. This work is exhaustive over translated classical generators of size $3\times 3$ and up to size $17\times 17$ classical bit grids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New local stabilizer codes from local classical codes Gunderman, Lane G. Quantum Physics Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new local and low-weight stabilizer codes which are obtained from the recent progress in $2D$ local classical codes. Of note, we construct codes with weight and qubit use count of $5$ while being able to protect the information with high distance, or greater logical count. We also consider the Fibonacci code family which generates weight and qubit use count of $6$ while having parameters $[[O(l^3),O(l),Ω(l)]]$. While other weight-reduction methods centered on lowering the weight without regard to locality, this work achieves very low-weight and geometric locality. This work is exhaustive over translated classical generators of size $3\times 3$ and up to size $17\times 17$ classical bit grids. |
| title | New local stabilizer codes from local classical codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.20717 |