Characterizing errors in parameter estimation by local measurements

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. This data can be obtained by local measurements on some sites and eliminates the need for full Hamiltonian tomography. For a 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-neighbour. We treat interactions between the next-nearest sites as perturbation of strength $\epsilon$ and show that the error in estimation of couplings scales linearly with $\epsilon$ in the presence of such interactions. Further, we show that on average, the existence of couplings between sites beyond the next-nearest neighbour 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 $\epsilon$, in the presence of next-nearest neighbour interactions. Typically, for weak interactions, chains of 40 sites can be estimated within reasonable error. Thus, we study the robustness of estimation scheme designed for a 1D chain when exposed to such multi-site perturbations, offering valuable insights into its applicability and limitations.

8 pages, 8 figures

References in corpus (22)

• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Efficient tomography of a quantum many-body system
• Full control by locally induced relaxation
• Learning a local Hamiltonian from local measurements
• Quantum State Tomography via Linear Regression Estimation
• Quantum Hamiltonian identification from measurement time traces
• Sample-efficient learning of quantum many-body systems
• Coupling strength estimation for spin chains despite restricted access
• Quantum System Identification
• Efficient estimation of nearly sparse many-body quantum Hamiltonians
• Indirect Hamiltonian Identification through a small gateway
• Local-measurement-based quantum state tomography via neural networks
• A Scalable Maximum Likelihood Method for Quantum State Tomography
• Evolution-free Hamiltonian parameter estimation through Zeeman markers
• Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
• Local probe of single phonon dynamics in warm ion crystals
• Compressed sensing for Hamiltonian reconstruction
• Complete Quantum-State Tomography with a Local Random Field
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
• Estimation of general Hamiltonian parameters via controlled energy measurements
• Compressed Sensing Tomography for qudits in Hilbert spaces of non-power-of-two dimensions
• Applicability of coupling strength estimation for linear chains of restricted access