Characterizing errors in parameter estimation by local measurements
Ghosh R, Gilchrist A, Burgarth D (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 8
Article Number: 023120
Journal Issue: 2
DOI: 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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APA:
Ghosh, R., Gilchrist, A., & Burgarth, D. (2026). Characterizing errors in parameter estimation by local measurements. Physical Review Research, 8(2). https://doi.org/10.1103/4czy-q998
MLA:
Ghosh, Riddhi, Alexei Gilchrist, and Daniel Burgarth. "Characterizing errors in parameter estimation by local measurements." Physical Review Research 8.2 (2026).
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