Local distillation from Reed Muller codes unfolding
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918488310808576 |
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| author | Londe, Vivien |
| author_facet | Londe, Vivien |
| contents | We generalize the unfolding of a Reed Muller distillation factory of Ruiz et. al. by exhibiting the algebraic structure that the unfolding is based on. We describe a 2D local layout for the Z stabilizers of a distance 4 Reed Muller distillation factory and a 3D local layout for the Z stabilizer of a distance 4 and a distance 7 Reed Muller distillation factory. Given input T states with infidelities $p=10^{-3}$, the 2D local distillation factory with distance 4 outputs a CCZ state with infidelity $p=8.256 \times 10^{-9}$ and the 3D local distillation factory with distance 7 outputs a T state with infidelity $p=1.1811 \times 10^{-17}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06284 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local distillation from Reed Muller codes unfolding Londe, Vivien Quantum Physics We generalize the unfolding of a Reed Muller distillation factory of Ruiz et. al. by exhibiting the algebraic structure that the unfolding is based on. We describe a 2D local layout for the Z stabilizers of a distance 4 Reed Muller distillation factory and a 3D local layout for the Z stabilizer of a distance 4 and a distance 7 Reed Muller distillation factory. Given input T states with infidelities $p=10^{-3}$, the 2D local distillation factory with distance 4 outputs a CCZ state with infidelity $p=8.256 \times 10^{-9}$ and the 3D local distillation factory with distance 7 outputs a T state with infidelity $p=1.1811 \times 10^{-17}$. |
| title | Local distillation from Reed Muller codes unfolding |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.06284 |