@techreport{oai:ipsj.ixsq.nii.ac.jp:00220428,
 author = {Kaito, Wada and Kazuma, Fukuchi and Naoki, Yamamoto and Kaito, Wada and Kazuma, Fukuchi and Naoki, Yamamoto},
 issue = {24},
 month = {Oct},
 note = {Estimating the mean values of quantum observables is a fundamental task in quantum computing. In particular, efficient estimation in a noisy environment requires us to develop a sophisticated measurement strategy. Here, we propose a quantum-enhanced estimation method for the mean values, that adaptively optimizes the measurement (POVM) for each circuit; as a result of optimization, the estimation precision gets close to the quantum Cramer-Rao lower bound, that is, inverse of the quantum Fisher information. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimation method such as consistency and asymptotic normality. Furthermore, several numerical simulations with large system dimension are provided to show that the estimator needs only a reasonable number of measurements to almost saturate the quantum Cramer-Rao bound., Estimating the mean values of quantum observables is a fundamental task in quantum computing. In particular, efficient estimation in a noisy environment requires us to develop a sophisticated measurement strategy. Here, we propose a quantum-enhanced estimation method for the mean values, that adaptively optimizes the measurement (POVM) for each circuit; as a result of optimization, the estimation precision gets close to the quantum Cramer-Rao lower bound, that is, inverse of the quantum Fisher information. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimation method such as consistency and asymptotic normality. Furthermore, several numerical simulations with large system dimension are provided to show that the estimator needs only a reasonable number of measurements to almost saturate the quantum Cramer-Rao bound.},
 title = {Quantum-enhanced mean value estimation via adaptive measurement},
 year = {2022}
}