Distributed estimation of many-body Hamiltonians via punctured surface code
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909034107371520 |
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| author | Qiao, Linmu Ouyang, Zhichun Zhou, Sisi |
| author_facet | Qiao, Linmu Ouyang, Zhichun Zhou, Sisi |
| contents | We study how a punctured surface code can turn many local $Z$-type couplings into one protected logical signal for distributed quantum metrology, where the goal is to estimate a weighted average of the coupling strengths. We consider an ordinary planar patch with two $X$-cut holes and provide a distributed sensing protocol where all $Z$-type couplings correspond to the same nontrivial logical $\bar{Z}$ for the punctured surface code. When the couplings are disjoint, we show that the relevant global condition is equivalent to the existence of a closed dual loop, called a witness, that has an odd number of intersections with every chain. Together with a local clean opening condition, this witness criterion gives a concrete punctured-code construction in which all signal chains implement the same nontrivial logical $\bar Z$. For three-body interactions with overlapping supports, we also identify the class of interactions where our punctured surface code protocol applies. Overall, our results provide a novel, noise-robust distributed sensing protocol for many-body interactions, with corresponding topological design criteria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11092 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributed estimation of many-body Hamiltonians via punctured surface code Qiao, Linmu Ouyang, Zhichun Zhou, Sisi Quantum Physics We study how a punctured surface code can turn many local $Z$-type couplings into one protected logical signal for distributed quantum metrology, where the goal is to estimate a weighted average of the coupling strengths. We consider an ordinary planar patch with two $X$-cut holes and provide a distributed sensing protocol where all $Z$-type couplings correspond to the same nontrivial logical $\bar{Z}$ for the punctured surface code. When the couplings are disjoint, we show that the relevant global condition is equivalent to the existence of a closed dual loop, called a witness, that has an odd number of intersections with every chain. Together with a local clean opening condition, this witness criterion gives a concrete punctured-code construction in which all signal chains implement the same nontrivial logical $\bar Z$. For three-body interactions with overlapping supports, we also identify the class of interactions where our punctured surface code protocol applies. Overall, our results provide a novel, noise-robust distributed sensing protocol for many-body interactions, with corresponding topological design criteria. |
| title | Distributed estimation of many-body Hamiltonians via punctured surface code |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.11092 |