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  • Open Access

Characterizing errors in parameter estimation by local measurements

Riddhi Ghosh1,*, Alexei Gilchrist1, and Daniel Burgarth2

  • *Contact author: riddhighosh22@gmail.com
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Phys. Rev. Research 8, 023120 – Published 5 May, 2026

DOI: https://doi.org/10.1103/4czy-q998

Abstract

The indirect estimation of couplings in quantum dynamics relies on the measurement of the spectrum and the overlap of eigenvectors with some reference states. These data can be obtained by local measurements on some sites and eliminate the need for full Hamiltonian tomography. For a one-dimensional (1D) chain, access to only one edge site is sufficient to compute all the couplings between the adjacent sites, and consequently to reconstruct the full Hamiltonian. However, its robustness in the presence of perturbations remains a critical question, particularly when sites interact with other lattice sites beyond nearest neighbors. Our work studies the applicability of schemes designed for 1D chains to topologies with interactions beyond nearest neighbor. We treat interactions between the next-nearest sites as perturbation of strength ɛ and show that the error in estimation of couplings scales linearly with ɛ in the presence of such interactions. Further, we show that, on average, the existence of couplings between sites beyond the next-nearest neighbor results in higher error. We also study the length of the chain that can be estimated (up to a fixed precision) as a function of ɛ, in the presence of next-nearest-neighbor interactions. Typically, for weak interactions, chains of 30 sites can be estimated within reasonable error. Thus, we study the robustness of estimation scheme designed for a 1D chain when exposed to such multisite perturbations, offering valuable insights into its applicability and limitations.

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Phys. Rev. Research 8, 023120– Published 5 May, 2026
  • Received 18 June 2025
  • Accepted 2 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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