Distributed estimation of many-body Hamiltonians via punctured surface code

TL;DR

This paper introduces a topological quantum sensing protocol using punctured surface codes to robustly estimate many-body Hamiltonian couplings in a distributed manner.

Contribution

It develops a novel, noise-robust distributed sensing protocol based on punctured surface codes, with explicit topological design criteria for many-body interactions.

Findings

The protocol converts local couplings into a protected logical signal.

A witness condition involving a closed dual loop determines the applicability.

Applicable to certain three-body interactions with overlapping supports.

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 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.