2025/02/03 by Alexander Gresch, Gresch, Alexander, Uğur Tepe +3 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2502.01730
openalex publication_date 2025/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy estimates with error bounds, as captured by guarantees on the problem's sampling complexity. In particular, when limited to Pauli basis measurements, the smallest sampling complexity guarantee comes from a simple single-shot estimator via a straightforward argument based on Hoeffding's inequality. In this work, we construct an adaptive estimator using the state's actual variance. Technically, our estimation method is based on the Empirical Bernstein stopping (EBS) algorithm and grouping schemes, and we provide a rigorous tail bound, which leverages the state's empirical variance. In a numerical benchmark of estimating ground-state energies of several Hamiltonians, we demonstrate that EBS consistently improves upon elementary readout guarantees up to one order of magnitude.