© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2210.05542 · Quantum Science and Technology

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

Inbar Zohar, Ben Haylock, Yoav Romach, Muhammad Junaid Arshad, Nir Halay, Niv Drucker, Rainer Stöhr, A. Denisenko, Y Cohen, Cristian Bonato, Amit Finkler

Published May 10, 2023• 8 citations

Abstract

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.

DOI: 10.1088/2058-9565/acd415

Related papers

Frequency Multiplexed Magnetometry via Compressive Sensing

Graciana Puentes, G. Waldherr, Philipp Neumann +1 more

Quantum sensors based on single Nitrogen-Vacancy (NV) defects in diamond are state-of-the-art tools for nano-scale magnetometry with precision scaling inversely with total measurement time $σ_{B} \propto 1/T$ (Heisenberg scaling) rather than as the inverse of the square root of $T$, with $σ_{B} =1/\sqrt{T}$ the Shot-Noise limit. This scaling can be achieved by means of phase estimation algorithms (PEAs) using adaptive or non-adaptive feedback, in combination with single-shot readout techniques. Despite their accuracy, the range of applicability of PEAs is limited to periodic signals involving single frequencies with negligible temporal fluctuations. In this Letter, we propose an alternative method for precision magnetometry in frequency multiplexed signals via compressive sensing (CS) techniques. We show that CS can provide for precision scaling approximately as $σ_{B} \approx 1/T$, both in the case of single frequency and frequency multiplexed signals, as well as for a 5-fold increase in sensitivity over dynamic-range gain, in addition to reducing the total number of resources required.

arXiv:1308.4349•Aug 20, 2013•2 citations

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

Hossein T. Dinani, Dominic William Berry, Raúl González Brouwer +2 more

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.

arXiv:1806.01249•Physical review. B./Physical review. B•Mar 11, 2019•50 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

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

Benchmarking machine learning algorithms for adaptive quantum phase estimation with noisy intermediate-scale quantum sensors

Nelson Filipe Costa, Yasser Omar, Aidar Sultanov +1 more

Abstract Quantum phase estimation is a paradigmatic problem in quantum sensing and metrology. Here we show that adaptive methods based on classical machine learning algorithms can be used to enhance the precision of quantum phase estimation when noisy non-entangled qubits are used as sensors. We employ the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to this task and we identify the optimal feedback policies which minimize the Holevo variance. We benchmark these schemes with respect to scenarios that include Gaussian and Random Telegraph fluctuations as well as reduced Ramsey-fringe visibility due to decoherence. We discuss their robustness against noise in connection with real experimental setups such as Mach–Zehnder interferometry with optical photons and Ramsey interferometry in trapped ions, superconducting qubits and nitrogen-vacancy (NV) centers in diamond.

arXiv:2108.06978•EPJ Quantum Technology•Jun 3, 2021•20 citations

Resource-efficient adaptive Bayesian tracking of magnetic fields with a quantum sensor

K Craigie, E M Gauger, Yoann Altmann +1 more

Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be minimised. Bayesian estimation and adaptive experiment optimisation can speed up the sensing process by reducing the number of measurements required. These protocols consist of computing and updating the probability distribution of the magnetic field based on measurement outcomes and of determining optimized acquisition settings for the next measurement. However, the computational steps feeding into the measurement settings of the next iteration must be performed quickly enough to allow real-time updates. This article addresses the issue of computational speed by implementing an approximate Bayesian estimation technique, where probability distributions are approximated by a finite sum of Gaussian functions. Given that only three parameters are required to fully describe a Gaussian density, we find that in many cases, the magnetic field probability distribution can be described by fewer than ten parameters, achieving a reduction in computation time by factor 10 compared to existing approaches. ForT2*=1μs, only a small decrease in computation time is achieved. However, in these regimes, the proposed Gaussian protocol outperforms the existing one in tracking accuracy.

arXiv:2008.08891•Journal of Physics Condensed Matter•Feb 5, 2021•15 citations

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.

Quantum sensors based on single Nitrogen-Vacancy (NV) defects in diamond are state-of-the-art tools for nano-scale magnetometry with precision scaling inversely with total measurement time

σ_{B} \propto 1/T

(Heisenberg scaling) rather than as the inverse of the square root of

T

, with

σ_{B} =1/\sqrt{T}

the Shot-Noise limit. This scaling can be achieved by means of phase estimation algorithms (PEAs) using adaptive or non-adaptive feedback, in combination with single-shot readout techniques. Despite their accuracy, the range of applicability of PEAs is limited to periodic signals involving single frequencies with negligible temporal fluctuations. In this Letter, we propose an alternative method for precision magnetometry in frequency multiplexed signals via compressive sensing (CS) techniques. We show that CS can provide for precision scaling approximately as

σ_{B} \approx 1/T

, both in the case of single frequency and frequency multiplexed signals, as well as for a 5-fold increase in sensitivity over dynamic-range gain, in addition to reducing the total number of resources required.

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.

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.

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.

Abstract Quantum phase estimation is a paradigmatic problem in quantum sensing and metrology. Here we show that adaptive methods based on classical machine learning algorithms can be used to enhance the precision of quantum phase estimation when noisy non-entangled qubits are used as sensors. We employ the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to this task and we identify the optimal feedback policies which minimize the Holevo variance. We benchmark these schemes with respect to scenarios that include Gaussian and Random Telegraph fluctuations as well as reduced Ramsey-fringe visibility due to decoherence. We discuss their robustness against noise in connection with real experimental setups such as Mach–Zehnder interferometry with optical photons and Ramsey interferometry in trapped ions, superconducting qubits and nitrogen-vacancy (NV) centers in diamond.

Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be minimised. Bayesian estimation and adaptive experiment optimisation can speed up the sensing process by reducing the number of measurements required. These protocols consist of computing and updating the probability distribution of the magnetic field based on measurement outcomes and of determining optimized acquisition settings for the next measurement. However, the computational steps feeding into the measurement settings of the next iteration must be performed quickly enough to allow real-time updates. This article addresses the issue of computational speed by implementing an approximate Bayesian estimation technique, where probability distributions are approximated by a finite sum of Gaussian functions. Given that only three parameters are required to fully describe a Gaussian density, we find that in many cases, the magnetic field probability distribution can be described by fewer than ten parameters, achieving a reduction in computation time by factor 10 compared to existing approaches. ForT2*=1μs, only a small decrease in computation time is achieved. However, in these regimes, the proposed Gaussian protocol outperforms the existing one in tracking accuracy.