© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2004.12674 · Optics Express

Adaptive Bayesian algorithm for achieving a desired magneto-sensitive transition

Chengyin Han, Jiahao Huang, Xunda Jiang, Ruihuan Fang, Yuxiang Qiu, Bo Lü, Chaohong Lee

Published Jun 11, 2021• 8 citations

Abstract

Bayesian methods that utilize Bayes’ theorem to update the knowledge of desired parameters after each measurement are used in a wide range of quantum science. For various applications in quantum science, efficiently and accurately achieving a quantum transition frequency is essential. However, the exact relation between a desired transition frequency and the controllable experimental parameters is usually absent. Here, we propose an efficient scheme to search the suitable conditions for a desired magneto-sensitive transition via an adaptive Bayesian algorithm and experimentally demonstrate it by using coherent population trapping in an ensemble of laser-cooled 87 Rb atoms. The transition frequency is controlled by an external magnetic field, which can be tuned in realtime by applying a d.c. voltage. Through an adaptive Bayesian algorithm, the voltage can automatically converge to the desired one from a random initial value only after few iterations ( N ≥ 10). The response time is limited by the time of obtaining the spectrum signal, which is about 50 s for 10 iterations in our experiment. In particular, when the relation between the target frequency and the applied voltage is nonlinear (e.g., quadratic), our algorithm shows significant advantages over traditional methods. This work provides a simple and efficient way to determine a transition frequency, which can be widely applied in the fields of precision spectroscopy, such as atomic clocks, magnetometers, and nuclear magnetic resonance.

DOI: 10.1364/oe.431334

Related papers

Atomic clock locking with Bayesian quantum parameter estimation: Scheme and experiment

Chengyin Han, Zhu Ma, Yuxiang Qiu +7 more

Atomic clocks are crucial for fundamental science and practical technology, but their sensitivity is often constrained by the standard quantum limit. With a cold-atom coherent-population-trapping clock, the authors design and experimentally demonstrate an adaptive Bayesian quantum frequency estimation protocol that approaches the Heisenberg scaling with respect to total interrogation time. This atomic clock also yields improved fractional frequency stability and enhanced robustness against technical noises. This work provides a high-precision approach to atomic clock locking, and holds promising applications in various interferometry-based quantum sensors.

arXiv:2306.06608•Physical Review Applied•Oct 23, 2024•12 citations

Versatile Atomic Magnetometry Assisted by Bayesian Inference

Ricardo Puebla, Yue Ban, Jan F. Haase +3 more

Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an 171Yb+ trapped-ion quantum sensor but stress the general applicability of this approach to different systems.

•Jan 1, 2021•2 citations

Time-adaptive phase estimation

Brennan de Neeve, A. V. Lebedev, Vlad Negnevitsky +1 more

Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present a Bayesian method that adaptively chooses a control phase and the time of coherent evolution. The uniqueness of the approach is to use analytics to implement an efficient numerical algorithm that offers exact calculation of the Bayesian probability and associated utility functions, even in the presence of noise. We determine the utility of control parameter values using functions of the prior probability of the phase that quantify expected knowledge gain in terms of either expected narrowing of the posterior or expected information gain. We find that by maximizing the of expected gain we obtain phase estimates having standard deviation a factor of 1.43 larger than the Heisenberg limit using a classical sequential strategy for noise-free experiments. In the presence of dephasing, we find near-optimal performance with respect to the Cramér-Rao bound. We also demonstrate some robustness of the estimates to noise that is not accounted for in the model of the estimator, making the methods suitable for calibrating operations in quantum computers. The rate of gain can be adjusted to account for times in the experiment other than the coherent evolution of the unknown phase, such as times required for state preparation or readout. The combined features of the method make it well suited to single-qubit gate calibration in trapped-ion or neutral atom experiments and promises a wide range of other applications by offering near-optimal phase estimation that straightforwardly accounts for experimental imperfections.

arXiv:2405.08930•Physical Review Research•Apr 21, 2025•2 citations

Versatile Atomic Magnetometry Assisted by Bayesian Inference

R. Puebla, Y. Ban, J.F. Haase +3 more

Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an ${}^{171}{\mathrm{Yb}}^{+}$ trapped-ion quantum sensor but stress the general applicability of this approach to different systems.

arXiv:2003.02151•Physical Review Applied•Aug 25, 2021•12 citations

Adaptive cold-atom magnetometry mitigating the trade-off between sensitivity and dynamic range

Zhu Ma, Chengyin Han, Zhi Tan +7 more

Cold-atom magnetometers can achieve an exceptional combination of superior sensitivity and high spatial resolution. One key challenge that these quantum sensors face is improving the sensitivity within a given timeframe while preserving a high dynamic range. Here, we experimentally demonstrate an adaptive entanglement-free cold-atom magnetometry with both superior sensitivity and high dynamic range. Using a tailored adaptive Bayesian quantum estimation algorithm designed for Ramsey interferometry using coherent population trapping (CPT), cold-atom magnetometry facilitates adaptive high-precision detection of a dc magnetic field with high dynamic range. Through implementing a sequence of correlated CPT-Ramsey interferometry, the sensitivity significantly surpasses the standard quantum limit with respect to total interrogation time. We yield a sensitivity of 6.8 ± 0.1 picotesla per square root of hertz over a range of 145.6 nanotesla, exceeding the conventional frequentist protocol by 3.3 ± 0.1 decibels. Our study opens avenues for the next generation of adaptive cold-atom quantum sensors, wherein real-time measurement history is leveraged to improve their performance.

arXiv:2503.01211•Science Advances•Feb 28, 2025•19 citations

Bayesian Phase Estimation via Active Learning

Yuxiang Qiu, Zhuang, Min, Jiahao Huang +1 more

Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable auxiliary phase. Here, we present a non-adaptive Bayesian phase estimation (BPE) algorithms with an ingenious update rule of the auxiliary phase designed via active learning. Unlike adaptive BPE algorithms, the auxiliary phase in our algorithm is determined by a pre-established update rule with simple statistical analysis of a small batch of data, instead of complex calculations in every update trails. As the number of measurements for a same amount of Bayesian updates is significantly reduced via active learning, our algorithm can work as efficient as adaptive ones and shares the advantages (such as wide dynamic range and perfect noise robustness) of non-adaptive ones. Our algorithm is of promising applications in various practical quantum sensors such as atomic clocks and quantum magnetometers.

arXiv:2107.00196•Jul 1, 2021•0 citations

Bayesian methods that utilize Bayes’ theorem to update the knowledge of desired parameters after each measurement are used in a wide range of quantum science. For various applications in quantum science, efficiently and accurately achieving a quantum transition frequency is essential. However, the exact relation between a desired transition frequency and the controllable experimental parameters is usually absent. Here, we propose an efficient scheme to search the suitable conditions for a desired magneto-sensitive transition via an adaptive Bayesian algorithm and experimentally demonstrate it by using coherent population trapping in an ensemble of laser-cooled 87 Rb atoms. The transition frequency is controlled by an external magnetic field, which can be tuned in realtime by applying a d.c. voltage. Through an adaptive Bayesian algorithm, the voltage can automatically converge to the desired one from a random initial value only after few iterations ( N ≥ 10). The response time is limited by the time of obtaining the spectrum signal, which is about 50 s for 10 iterations in our experiment. In particular, when the relation between the target frequency and the applied voltage is nonlinear (e.g., quadratic), our algorithm shows significant advantages over traditional methods. This work provides a simple and efficient way to determine a transition frequency, which can be widely applied in the fields of precision spectroscopy, such as atomic clocks, magnetometers, and nuclear magnetic resonance.

Atomic clocks are crucial for fundamental science and practical technology, but their sensitivity is often constrained by the standard quantum limit. With a cold-atom coherent-population-trapping clock, the authors design and experimentally demonstrate an adaptive Bayesian quantum frequency estimation protocol that approaches the Heisenberg scaling with respect to total interrogation time. This atomic clock also yields improved fractional frequency stability and enhanced robustness against technical noises. This work provides a high-precision approach to atomic clock locking, and holds promising applications in various interferometry-based quantum sensors.

Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an 171Yb+ trapped-ion quantum sensor but stress the general applicability of this approach to different systems.

Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present a Bayesian method that adaptively chooses a control phase and the time of coherent evolution. The uniqueness of the approach is to use analytics to implement an efficient numerical algorithm that offers exact calculation of the Bayesian probability and associated utility functions, even in the presence of noise. We determine the utility of control parameter values using functions of the prior probability of the phase that quantify expected knowledge gain in terms of either expected narrowing of the posterior or expected information gain. We find that by maximizing the of expected gain we obtain phase estimates having standard deviation a factor of 1.43 larger than the Heisenberg limit using a classical sequential strategy for noise-free experiments. In the presence of dephasing, we find near-optimal performance with respect to the Cramér-Rao bound. We also demonstrate some robustness of the estimates to noise that is not accounted for in the model of the estimator, making the methods suitable for calibrating operations in quantum computers. The rate of gain can be adjusted to account for times in the experiment other than the coherent evolution of the unknown phase, such as times required for state preparation or readout. The combined features of the method make it well suited to single-qubit gate calibration in trapped-ion or neutral atom experiments and promises a wide range of other applications by offering near-optimal phase estimation that straightforwardly accounts for experimental imperfections.

Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an

{}^{171}{\mathrm{Yb}}^{+}

trapped-ion quantum sensor but stress the general applicability of this approach to different systems.

Cold-atom magnetometers can achieve an exceptional combination of superior sensitivity and high spatial resolution. One key challenge that these quantum sensors face is improving the sensitivity within a given timeframe while preserving a high dynamic range. Here, we experimentally demonstrate an adaptive entanglement-free cold-atom magnetometry with both superior sensitivity and high dynamic range. Using a tailored adaptive Bayesian quantum estimation algorithm designed for Ramsey interferometry using coherent population trapping (CPT), cold-atom magnetometry facilitates adaptive high-precision detection of a dc magnetic field with high dynamic range. Through implementing a sequence of correlated CPT-Ramsey interferometry, the sensitivity significantly surpasses the standard quantum limit with respect to total interrogation time. We yield a sensitivity of 6.8 ± 0.1 picotesla per square root of hertz over a range of 145.6 nanotesla, exceeding the conventional frequentist protocol by 3.3 ± 0.1 decibels. Our study opens avenues for the next generation of adaptive cold-atom quantum sensors, wherein real-time measurement history is leveraged to improve their performance.

Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable auxiliary phase. Here, we present a non-adaptive Bayesian phase estimation (BPE) algorithms with an ingenious update rule of the auxiliary phase designed via active learning. Unlike adaptive BPE algorithms, the auxiliary phase in our algorithm is determined by a pre-established update rule with simple statistical analysis of a small batch of data, instead of complex calculations in every update trails. As the number of measurements for a same amount of Bayesian updates is significantly reduced via active learning, our algorithm can work as efficient as adaptive ones and shares the advantages (such as wide dynamic range and perfect noise robustness) of non-adaptive ones. Our algorithm is of promising applications in various practical quantum sensors such as atomic clocks and quantum magnetometers.