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arXiv · 2605.11092

Distributed estimation of many-body Hamiltonians via punctured surface code

Linmu Qiao·Zhichun Ouyang·Sisi Zhou
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Abstract

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 sum of the coupling strengths. We consider an ordinary planar patch with two $X$-cut holes and develop a distributed sensing protocol in which all $Z$-type couplings correspond to the same nontrivial logical $\bar{Z}$ of the punctured surface code. When the couplings have prescribed placements on the lattice, we show that the relevant global condition is equivalent to the existence of a simple closed dual loop, called a witness, that has an odd number of intersections with every signal path. Together with a local clean-opening condition, this witness criterion gives a concrete punctured-code construction in which all signal paths realize the same nontrivial logical $\bar Z$. When only the abstract support structure is specified, disjoint supports are straightforward to realize, while overlapping supports are constrained by a stabilizer-difference condition, which we illustrate for three-body interactions. Overall, our results provide a novel, noise-robust distributed sensing protocol for many-body interactions, with corresponding topological design criteria.

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Linmu Qiao, Zhichun Ouyang, Sisi Zhou. 2026-05-11. Distributed estimation of many-body Hamiltonians via punctured surface code. https://arxiv.org/abs/2605.11092

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