Adaptive estimation schemes for 2-level quantum systems

We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean-square error (MSE) that decreases at best as a power law $\ensuremath{\sim}{N}^{\ensuremath{-}2}$ in the number of measurements $N$ . By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to $\mathrm{exp}(\ensuremath{-}0.3N)$. That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in $N$ .We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean-square error (MSE) that decreases at best as a power law $\ensuremath{\sim}{N}^{\ensuremath{-}2}$ in the number of measurements $N$. By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to $\mathrm{exp}(\ensuremath{-}0.3N)$. That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in $N$.

arXiv:1102.3700Physical Review ANov 15, 201178 citations

Realization of adaptive quantum state estimation for dynamic quantum states

Saki Nohara, Ryo Okamoto, Akio Fujiwara +1 more

The Japan Society of Applied PhysicsJul 10, 20190 citations

Anisotropic efficiency of adaptive measurements in two-parameter estimation for states in manifolds with nonzero Berry curvature

Haijun Xing

The efficiency of quantum measurements in distinguishing neighboring quantum states is a central topic in quantum information sciences. We study the efficiency of vertex measurement in two-parameter estimation from the information geometry perspective, where the vertex measurement is a rare typical measurement recognized as optimal for both single-parameter estimation and multiparameter estimation of states in manifolds with vanishing Berry curvature. This article focuses explicitly on scenarios with nonzero Berry curvature. We quantify the precision of an estimation scheme with the density of distinguishable states and measure the efficiency of a given vertex measurement by comparing its precision to the maximum value. Exemplified by the three-level system with two parameters, we show that the efficiency is highly anisotropic concerning the direction of a small mismatch vector between the applied measurement and the estimated parameter. It may even vanish in some specific directions. Furthermore, the direction is hardly acknowledged prior, hindering the practical application of vertex measurement in multiparameter estimations. To remove this obstacle, we further introduce a scheme that can adaptively approach the optimal vertex measurements.The efficiency of quantum measurements in distinguishing neighboring quantum states is a central topic in quantum information sciences. We study the efficiency of vertex measurement in two-parameter estimation from the information geometry perspective, where the vertex measurement is a rare typical measurement recognized as optimal for both single-parameter estimation and multiparameter estimation of states in manifolds with vanishing Berry curvature. This article focuses explicitly on scenarios with nonzero Berry curvature. We quantify the precision of an estimation scheme with the density of distinguishable states and measure the efficiency of a given vertex measurement by comparing its precision to the maximum value. Exemplified by the three-level system with two parameters, we show that the efficiency is highly anisotropic concerning the direction of a small mismatch vector between the applied measurement and the estimated parameter. It may even vanish in some specific directions. Furthermore, the direction is hardly acknowledged prior, hindering the practical application of vertex measurement in multiparameter estimations. To remove this obstacle, we further introduce a scheme that can adaptively approach the optimal vertex measurements.

Physical Review AJul 22, 20241 citation

Effcient state estimation for quantum systems

László Ruppert

Jan 1, 20120 citations

An Adaptive Observer Design for State and Parameter Estimation of Quantum Systems via Averaging Theory

Eram Taslima, Shyam Kamal, Ram Khelawan Saket +1 more

This paper presents an adaptive asymptotic observer-based approach for estimating the states and the atom-laser coupling constant (parameter) of a two-level, closed quantum system driven by a constant control input. Using the interaction frame and averaging theory, the proposed observer ensures asymptotic estimation of both the system states and the unknown parameter. In addition to the asymptotic observer, we also propose an adaptive finite-time observer for the estimation of states in finite time, considering the parameter is unknown. The proposed finite-time observer is designed to provide the minimum output horizon required for accurate state and parameter estimation. To ensure the estimation of the unknown parameter, the extended Lyapunov method is employed. Through simulations on a two-level quantum dynamical system, the proposed observers are demonstrated to exhibit robust performance in the presence of noise in the control and output measurement.This paper presents an adaptive asymptotic observer-based approach for estimating the states and the atom-laser coupling constant (parameter) of a two-level, closed quantum system driven by a constant control input. Using the interaction frame and averaging theory, the proposed observer ensures asymptotic estimation of both the system states and the unknown parameter. In addition to the asymptotic observer, we also propose an adaptive finite-time observer for the estimation of states in finite time, considering the parameter is unknown. The proposed finite-time observer is designed to provide the minimum output horizon required for accurate state and parameter estimation. To ensure the estimation of the unknown parameter, the extended Lyapunov method is employed. Through simulations on a two-level quantum dynamical system, the proposed observers are demonstrated to exhibit robust performance in the presence of noise in the control and output measurement.

Proceedings of the ... American Control Conference/Proceedings of the American Control ConferenceJul 8, 20250 citations

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. By contrast, we present numerical simulations indicating that an adaptive Bayesian algorithm, where the time between measurements can be adjusted based on prior measurement results, yields a MSE which appears to scale close to $\mathrm{exp}(\ensuremath{-}0.3N)$. That is, measurements in a single fixed basis are sufficient to achieve exponential scaling in

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