Quantum metrology via partial quantum error correction

Abstract:We introduce a quantum metrology scheme in which partial quantum error correction suppresses local noise while preserving sensitivity beyond the standard quantum limit. The probes are superpositions of energetically distinct stabilizer sectors, whose sensing coherence is protected by measuring only a subset of local checks. We propose an adaptive weight strategy to balance two competing effects. Increasing the stabilizer-generator weight suppresses parallel noise to $O(p^{\delta})$, with $\delta$ increasing with the weight, but also increases susceptibility to perpendicular noise. Our main theorem establishes a sufficient noise condition under which adapting this weight to the system size preserves superlinear quantum Fisher information under simultaneous independent $X$ and $Z$ noise. We illustrate this strategy using repetition, Bacon-Shor, and toric codes, and analyze noise both before and after phase imprinting. In all examples, the error-correction checks and phase-imprinting operators are local and require no nonlocal connectivity.

Substantially revised version. Added Theorem 1, providing a general performance guarantee for super-SQL scaling; reorganized the presentation and updated the figures

arXiv:2605.08341 [quant-ph]

(or arXiv:2605.08341v3 [quant-ph] for this version)