Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1806.01249 · Physical review. B./Physical review. B

Bayesian estimation for quantum sensing in the absence of single-shot detection

Hossein T. Dinani, Dominic William Berry, Raúl González Brouwer, Jeronimo R. Maze, Cristian Bonato

Published Mar 11, 2019• 50 citations
arXivHTMLPDF

Abstract

Quantum information protocols, such as quantum error correction and quantum phase estimation, have been widely used to enhance the performance of quantum sensors. While these protocols have relied on single-shot detection, in most practical applications only an averaged readout is available, as in the case of room-temperature sensing with the electron spin associated with a nitrogen-vacancy center in diamond. Here, we theoretically investigate the application of the quantum phase estimation algorithm for high dynamic-range magnetometry, when single-shot readout is not available. We show that, even in this case, Bayesian estimation provides a natural way to efficiently use the available information. We apply Bayesian analysis to achieve an optimized sensing protocol for estimating a time-independent magnetic field with a single electron spin associated to a nitrogen-vacancy center at room temperature and show that this protocol improves the sensitivity over previous protocols by more than a factor of 3. Moreover, we show that an extra enhancement can be achieved by considering the timing information in the detector clicks.

DOI
10.1103/physrevb.99.125413

Related papers

Efficient Real-Time Spin Readout of Nitrogen-Vacancy Centers Based on Bayesian Estimation

Jixing Zhang, Tianzheng Liu, Heng Yuan +8 more

This article introduces a real-time Bayesian estimation algorithm aimed at enhancing the spin readout efficiency of the nitrogen vacancy (NV) center ensemble in the diamond. By integrating both the prior probability distribution and the fluorescence likelihood function, stemming from the implementation of the NV center dynamics model, we offered an innovative solution to surpass the Cramer–Rao lower bound of the readout variance and improve the readout efficiency. The proposed real-time Bayesian estimation readout algorithm was experimentally realized by combining high-performance acquisition and processing hardware, and the Rabi oscillation experiments divulged that the signal-to-noise ratio of our approach was improved by 28.6%. This research illustrates the potential of the Bayesian estimation readout to enhance the NV ensemble's sensing capabilities and support the development of compact and scalable quantum sensors devices on a monolithic platform.

arXiv:2302.06310•IEEE Transactions on Industrial Electronics•Jan 24, 2024•6 citations

Application of phase estimation algorithms to improve diamond spin magnetometry

Naufer Nusran

Precision measurements of weak magnetic fields with nanoscale spatial resolution is an outstanding challenge in many fields including medicine, biology, material science and physical science. It has already been demonstrated that a single electronic spin formed by a defect color center in diamond, known as the nitrogen-vacancy (NV) center, can serve as a highly sensitive magnetometer with nanoscale resolution, even under ambient conditions. However, standard quantum sensing methods have significant drawbacks. These include the limited dynamic range due to quantum phase ambiguity, the non-linearity in sensitivity over the detectable field range, the requirement of prior knowledge of a working point for accurate deconvolution, etc. This thesis explores novel quantum control techniques such as the use of phase estimation algorithms (PEA) for magnetic field detection to address these issues. Unlike in the standard approach, PEA readout is linearly dependent on the field being sensed. PEA employed on oscillating (AC) magnetic fields can not only detect unknown field amplitudes but also allows detection of the field phase. The thesis also compares the performance of nonadaptive-PEA (NAPEA) with that of adaptive-PEA (QPEA) and conclude that NAPEA is superior to QPEA due to (a) better sensitivity on average, (b) consistency in sensitivity throughout the full field range, (c) comparatively less demanding measurement fidelity, and (d) for simplicity in its experimental realization. The techniques developed here can potentially have broad applicability to a wide variety of solid-state quantum systems and in the field of quantum control and measurement.

•May 29, 2014•0 citations

A two-stage optimization method for wide-range single-electron quantum magnetic sensing

Shiqian Guo, Jianqing Liu, Thinh Le +1 more

Quantum magnetic sensing is a new paradigm for detecting ultra-weak magnetic fields. Its protocol design concerns the devise of optimal sensing parameters to estimate the underlying signals of interest (SoI). Existing studies mainly rely on adaptive algorithms based on black-box AI models or formula-driven principled searches. However, when the SoI spans a wide range and the quantum sensor has physical constraints, these methods may fail to converge efficiently or optimally, causing prolonged interrogation times and reduced accuracy. This work presents a new protocol using a two-stage optimization method, consisting of a Bayesian neural network to first narrow the SoI range and a federated reinforcement learning agent to subsequently calibrate the SoI. The protocol is developed and evaluated in the challenging context of an NV-center spin system with single-shot readout and limited sensing time; and yet it achieves significant improvements in both accuracy and resource efficiency compared to the state-of-the-art.

arXiv:2506.13469•Scientific Reports•Oct 17, 2026•0 citations

Room Temperature Magnetic Field Learning with Optically Readout Single NV-Centers

Antonio A. Gentile, Jianwei Wang, Mark G. Thompson +11 more

We propose and test a Magnetic Field Learning (MFL) protocol for high-resolution, high dynamic range and high-sensitivity magnetometry with a single NV-center electron spin. Our approach leverages recent proposals that analyze the benefits of adopting classical machine learning to post-process quantum data in quantum sensing protocols [1]. MFL was tested at room-temperature using a setup detecting state-dependent fluorescence via confocal microscopy, and a microwave controlled NV defect in bulk diamond as a sensor [2]. This setup senses the intensity of a magnetic field B in the proximity of the quantum sensor via Ramsey interferometry [3]. In our protocol, the Ramsey precession time τ is adaptively chosen at each step via an efficient particle guess heuristic [1].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2019•0 citations

Dual-channel lock-in magnetometer with a single spin in diamond

Naufer Nusran, M. V. Gurudev Dutt

We present an experimental method to perform dual-channel lock-in magnetometry of time-dependent magnetic fields using a single spin associated with a nitrogen-vacancy color center in diamond. We incorporate multipulse quantum sensing sequences with phase estimation algorithms to achieve linearized field readout and constant, nearly decoherence-limited sensitivity over a wide dynamic range. Furthermore, we demonstrate unambiguous reconstruction of the amplitude and phase of the magnetic field. We show that our technique can be applied to measure random phase jumps in the magnetic field, as well as phase-sensitive readout of the frequency.

arXiv:1309.1911•Physical Review B•Dec 23, 2013•14 citations

Real-time frequency estimation of a qubit without single-shot-readout

Inbar Zohar, Ben Haylock, Yoav Romach +8 more

Abstract Quantum sensors can potentially achieve the Heisenberg limit of sensitivity over a large dynamic range using quantum algorithms. The adaptive phase estimation algorithm (PEA) is one example that was proven to achieve such high sensitivities with single-shot readout (SSR) sensors. However, using the adaptive PEA on a non-SSR sensor is not trivial due to the low contrast nature of the measurement. The standard approach to account for the averaged nature of the measurement in this PEA algorithm is to use a method based on ‘majority voting’. Although it is easy to implement, this method is more prone to mistakes due to noise in the measurement. To reduce these mistakes, a binomial distribution technique from a batch selection was recently shown theoretically to be superior, as all ranges of outcomes from an averaged measurement are considered. Here we apply, for the first time, real-time non-adaptive PEA on a non-SSR sensor with the binomial distribution approach. We compare the mean square error of the binomial distribution method to the majority-voting approach using the nitrogen-vacancy center in diamond at ambient conditions as a non-SSR sensor. Our results suggest that the binomial distribution approach achieves better accuracy with the same sensing times. To further shorten the sensing time, we propose an adaptive algorithm that controls the readout phase and, therefore, the measurement basis set. We show by numerical simulation that adding the adaptive protocol can further improve the accuracy in a future real-time experiment.

arXiv:2210.05542•Quantum Science and Technology•May 10, 2023•8 citations
Quantum information protocols, such as quantum error correction and quantum phase estimation, have been widely used to enhance the performance of quantum sensors. While these protocols have relied on single-shot detection, in most practical applications only an averaged readout is available, as in the case of room-temperature sensing with the electron spin associated with a nitrogen-vacancy center in diamond. Here, we theoretically investigate the application of the quantum phase estimation algorithm for high dynamic-range magnetometry, when single-shot readout is not available. We show that, even in this case, Bayesian estimation provides a natural way to efficiently use the available information. We apply Bayesian analysis to achieve an optimized sensing protocol for estimating a time-independent magnetic field with a single electron spin associated to a nitrogen-vacancy center at room temperature and show that this protocol improves the sensitivity over previous protocols by more than a factor of 3. Moreover, we show that an extra enhancement can be achieved by considering the timing information in the detector clicks.
This article introduces a real-time Bayesian estimation algorithm aimed at enhancing the spin readout efficiency of the nitrogen vacancy (NV) center ensemble in the diamond. By integrating both the prior probability distribution and the fluorescence likelihood function, stemming from the implementation of the NV center dynamics model, we offered an innovative solution to surpass the Cramer–Rao lower bound of the readout variance and improve the readout efficiency. The proposed real-time Bayesian estimation readout algorithm was experimentally realized by combining high-performance acquisition and processing hardware, and the Rabi oscillation experiments divulged that the signal-to-noise ratio of our approach was improved by 28.6%. This research illustrates the potential of the Bayesian estimation readout to enhance the NV ensemble's sensing capabilities and support the development of compact and scalable quantum sensors devices on a monolithic platform.
Precision measurements of weak magnetic fields with nanoscale spatial resolution is an outstanding challenge in many fields including medicine, biology, material science and physical science. It has already been demonstrated that a single electronic spin formed by a defect color center in diamond, known as the nitrogen-vacancy (NV) center, can serve as a highly sensitive magnetometer with nanoscale resolution, even under ambient conditions. However, standard quantum sensing methods have significant drawbacks. These include the limited dynamic range due to quantum phase ambiguity, the non-linearity in sensitivity over the detectable field range, the requirement of prior knowledge of a working point for accurate deconvolution, etc. This thesis explores novel quantum control techniques such as the use of phase estimation algorithms (PEA) for magnetic field detection to address these issues. Unlike in the standard approach, PEA readout is linearly dependent on the field being sensed. PEA employed on oscillating (AC) magnetic fields can not only detect unknown field amplitudes but also allows detection of the field phase. The thesis also compares the performance of nonadaptive-PEA (NAPEA) with that of adaptive-PEA (QPEA) and conclude that NAPEA is superior to QPEA due to (a) better sensitivity on average, (b) consistency in sensitivity throughout the full field range, (c) comparatively less demanding measurement fidelity, and (d) for simplicity in its experimental realization. The techniques developed here can potentially have broad applicability to a wide variety of solid-state quantum systems and in the field of quantum control and measurement.
Quantum magnetic sensing is a new paradigm for detecting ultra-weak magnetic fields. Its protocol design concerns the devise of optimal sensing parameters to estimate the underlying signals of interest (SoI). Existing studies mainly rely on adaptive algorithms based on black-box AI models or formula-driven principled searches. However, when the SoI spans a wide range and the quantum sensor has physical constraints, these methods may fail to converge efficiently or optimally, causing prolonged interrogation times and reduced accuracy. This work presents a new protocol using a two-stage optimization method, consisting of a Bayesian neural network to first narrow the SoI range and a federated reinforcement learning agent to subsequently calibrate the SoI. The protocol is developed and evaluated in the challenging context of an NV-center spin system with single-shot readout and limited sensing time; and yet it achieves significant improvements in both accuracy and resource efficiency compared to the state-of-the-art.
We propose and test a Magnetic Field Learning (MFL) protocol for high-resolution, high dynamic range and high-sensitivity magnetometry with a single NV-center electron spin. Our approach leverages recent proposals that analyze the benefits of adopting classical machine learning to post-process quantum data in quantum sensing protocols [1]. MFL was tested at room-temperature using a setup detecting state-dependent fluorescence via confocal microscopy, and a microwave controlled NV defect in bulk diamond as a sensor [2]. This setup senses the intensity of a magnetic field B in the proximity of the quantum sensor via Ramsey interferometry [3]. In our protocol, the Ramsey precession time τ is adaptively chosen at each step via an efficient particle guess heuristic [1].
We present an experimental method to perform dual-channel lock-in magnetometry of time-dependent magnetic fields using a single spin associated with a nitrogen-vacancy color center in diamond. We incorporate multipulse quantum sensing sequences with phase estimation algorithms to achieve linearized field readout and constant, nearly decoherence-limited sensitivity over a wide dynamic range. Furthermore, we demonstrate unambiguous reconstruction of the amplitude and phase of the magnetic field. We show that our technique can be applied to measure random phase jumps in the magnetic field, as well as phase-sensitive readout of the frequency.
Abstract Quantum sensors can potentially achieve the Heisenberg limit of sensitivity over a large dynamic range using quantum algorithms. The adaptive phase estimation algorithm (PEA) is one example that was proven to achieve such high sensitivities with single-shot readout (SSR) sensors. However, using the adaptive PEA on a non-SSR sensor is not trivial due to the low contrast nature of the measurement. The standard approach to account for the averaged nature of the measurement in this PEA algorithm is to use a method based on ‘majority voting’. Although it is easy to implement, this method is more prone to mistakes due to noise in the measurement. To reduce these mistakes, a binomial distribution technique from a batch selection was recently shown theoretically to be superior, as all ranges of outcomes from an averaged measurement are considered. Here we apply, for the first time, real-time non-adaptive PEA on a non-SSR sensor with the binomial distribution approach. We compare the mean square error of the binomial distribution method to the majority-voting approach using the nitrogen-vacancy center in diamond at ambient conditions as a non-SSR sensor. Our results suggest that the binomial distribution approach achieves better accuracy with the same sensing times. To further shorten the sensing time, we propose an adaptive algorithm that controls the readout phase and, therefore, the measurement basis set. We show by numerical simulation that adding the adaptive protocol can further improve the accuracy in a future real-time experiment.