Magnetic field intensity estimation method based on dynamic decoupling sequence and machine learning assistance

Abstract

The invention provides a magnetic field intensity estimation method based on a dynamic decoupling sequence and machine learning assistance, and belongs to the field of precise quantum measurement. The defects of a traditional magnetometer estimation method in the aspects of calculation complexity, noise interference, precision and the like are overcome; according to the method, on the premise of reducing the data volume, a dynamic decoupling technology is introduced, interference of environmental noise on an estimation result is effectively reduced through signal decoupling, a de-coherence effect caused by environmental interaction is inhibited, measurement data of a magnetometer system is collected and preprocessed, and the estimation accuracy is improved. And then intelligent analysis and training are carried out on the preprocessed data in combination with a machine learning algorithm, and the accuracy of magnetic field measurement and the precision of magnetic field intensity estimation are remarkably improved through autonomous learning and optimization of an estimation model. The method not only improves the performance of the magnetometer system, but also expands the application range of the magnetometer system, especially the application in a complex system and a big data environment.

Description

Technical Field

[0001] The present application relates to the field of quantum precision measurement technology, and in particular to a magnetic field intensity estimation method based on a dynamic decoupling sequence and assisted by machine learning. Background Art

[0002] An AC magnetometer based on NV color centers is an instrument that measures magnetic field strength based on the dependence of the phase information of the NV color center on the AC magnetic field signal. In traditional AC magnetic field measurement methods, commonly used technologies include sensors based on the principle of electromagnetic induction, Hall effect probes, and magnetic sensitive elements such as superconducting quantum interference devices to detect magnetic field strength. Although these methods are effective, they are often limited by accuracy, sensitivity or spatial resolution. With the rapid development of quantum technology, magnetic field measurement methods based on NV color centers have gradually become an emerging technical means. Compared with traditional methods, magnetic field measurement technology based on NV color centers has the advantages of non-invasiveness, high spatial resolution and extremely high sensitivity, and can be used for nanoscale magnetic field imaging and precision magnetic field detection.

[0003] Typically, AC magnetic field measurements based on NV centers measure the changes in the NV center's spin state under an external magnetic field and perform a fitting analysis on the data to determine the magnetic field strength. This method, which typically relies on experimental data fitting, can provide magnetic field information with high sensitivity and high spatial resolution. However, this method has limitations in terms of data processing speed and noise immunity.

[0004] In some specific application scenarios, such as those requiring fast measurement, real-time feedback, and high precision, existing estimation methods often face the following problems:

[0005] 1. High computational complexity: Traditional NV color center-based AC magnetic field measurement methods require the acquisition and processing of large and complex data volumes, which makes this method inefficient in real-time applications.

[0006] 2. Noise interference: Magnetometer signals are often affected by factors such as environmental noise, temperature changes, and instrument errors. Traditional estimation methods find it difficult to suppress noise quickly and accurately.

[0007] 3. Accuracy issue: The algorithms in traditional estimation methods may not provide sufficient accuracy in some complex dynamic scenarios, especially when the strength and direction of the external magnetic field change rapidly. Summary of the Invention

[0008] In order to overcome the shortcomings of traditional magnetometer estimation methods in terms of computational complexity, noise interference and accuracy, this application proposes a magnetic field strength estimation method based on dynamic decoupling sequence and machine learning assistance. While reducing the amount of data, by introducing dynamic decoupling sequence and combining it with machine learning algorithm, the environmental noise is effectively suppressed, and the accuracy and real-time response capability of magnetic field strength estimation are improved.

[0009] The technical solution adopted in this application is: a magnetic field strength estimation method based on dynamic decoupling sequence and machine learning assistance, comprising the following steps:

[0010] Step S1: specifying an initial state, applying a matching dynamic decoupling sequence to the AC magnetic field signal to be predicted to perform evolution, and obtaining a relationship between the cumulative phase and the intensity value of the AC magnetic field signal to be measured; averaging the population numbers obtained by repeating N measurements, performing Fourier curve fitting on the data, obtaining the value of the fitting parameter angular frequency, and further obtaining the intensity value based on the relationship between the angular frequency and the intensity value to be measured;

[0011] Step S2: Using the intensity value obtained by fitting as a preprocessing value and the averaged population number as input, a gradient boosting model is used for machine learning training to obtain a predicted value of the magnetic field intensity to be measured;

[0012] Step S3: When N is greater than 50, the prediction result is obtained by using the machine learning model method with preprocessing; when N is less than 50, it is compared with the direct prediction without preprocessing, and the intensity prediction value with a root mean square error closer to 0 and a determination coefficient closer to 1 is used as the prediction result.

[0013] Furthermore, the relationship between the accumulated phase and the AC magnetic field signal strength value to be measured is as follows:

[0014]

[0015] Where Φ is the phase, g c is the amplitude of the alternating magnetic field signal, t is the evolution time, W xy-8 (w s ,ξ) is the weighting function, w s is the angular frequency of the alternating magnetic field signal, ξ is the initial phase of the alternating magnetic field signal, and k is the harmonic order.

[0016] Furthermore, the expression of the weighting function is as follows:

[0017]

[0018] Where k is the harmonic order, k=1 and ξ=0.

[0019] Furthermore, the expression of the fitting parameter angular frequency is as follows:

[0020]

[0021] Where w is the Fourier fitting angular frequency;

[0022] It means that the Fourier fitting angular frequency is proportional to the magnetic field intensity value, and the value of the angular frequency w obtained by fitting is further used to obtain the magnetic field preprocessing intensity value.

[0023] Furthermore, the HGboost model is selected as the machine learning model.

[0024] The beneficial effects of this application compared to the prior art are:

[0025] 1. This application adopts dynamic decoupling technology to decouple the signal and suppress the decoupling effect caused by environmental interaction. At the same time, it uses machine learning algorithms, combined with the modeling of dynamic decoupling sequences and pre-processed data for training, and through autonomous learning and optimization of the estimation model, the root mean square error of the measurement results is reduced from 10 -3 Reduced to 10 -6 , ensuring that the magnetic field estimation results are more stable and reliable in complex and changing environments, achieving high-precision measurements.

[0026] 2. This application uses the evaluation indicators MSE and R 2 Under the condition that the values ​​of are close, the amount of data required to estimate magnetic field strength is reduced from 500*60 to 65*60, and the average calculation time is reduced from 13 seconds to 3.5 seconds. The optimized data processing process enables accurate data processing and rapid estimation of magnetic field strength within 3.5 seconds, enabling fast measurement. This also enables the system to respond in real time in dynamic environments, meeting the demand for rapid feedback on magnetic field measurement and estimation, such as in application scenarios requiring real-time data processing, such as real-time monitoring and dynamic adjustment.

[0027] 3. This application utilizes dynamic decoupling technology and machine learning algorithms, which can be adaptively adjusted according to different environments and data characteristics, especially with better adaptability in complex dynamic scenarios. Therefore, this method can be flexibly applied in a variety of different scenarios (such as geological exploration, navigation and positioning, etc.) to meet diverse needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The present application will be further described below with reference to the accompanying drawings:

[0029] Figure 1 A flowchart of the method steps provided in the embodiment of the present application;

[0030] Figure 2A schematic diagram showing the correspondence between the dynamic decoupling XY-8 sequence and the AC magnetic field signal provided in an embodiment of the present application;

[0031] Figure 3 This is a diagram showing the prediction effect of the AC magnetic field strength provided in the embodiment of the present application;

[0032] Figure 4 The machine learning provided in this application embodiment is preprocessed and the accuracy evaluation indicators MSE and R of traditional methods are 2 Comparison diagram;

[0033] Figure 5 Schematic diagram comparing the data volume and computing time of the machine learning preprocessing method provided in the embodiment of the present application and the traditional method. DETAILED DESCRIPTION

[0034] like Figures 1 to 5 As shown, this application provides a method for rapidly estimating the magnetic field strength of an AC magnetometer based on a dynamic decoupling sequence and machine learning. The method collects and preprocesses the measurement data of the magnetometer system. The preprocessed data is then intelligently analyzed and trained using a machine learning algorithm. Through autonomous learning and optimization of the estimation model, the accuracy of magnetic field measurements and the precision of magnetic field strength estimation are significantly improved.

[0035] like Figure 1 As shown, the specific implementation steps of this application method are as follows:

[0036] Step S1: Specify the initial state, according to the AC magnetic field signal to be predicted B(t)=g c cos(w s t+ξ), construct the Hamiltonian expression of the NV color center two-level system under noise; where g c is the amplitude of the alternating magnetic field signal, w s is the angular frequency of the alternating magnetic field signal, t is the evolution time, ξ is the initial phase of the alternating magnetic field signal;

[0037] The Hamiltonian H(t) of the two-level system under noise is constructed. H(t) can be decomposed into Hamiltonian terms with different effects, as shown in formula (1):

[0038] H(t)=H c +H g (t)+H n (t)(1);

[0039] Among them, H c is the control field Hamiltonian, H g (t) is the interaction term between the AC magnetic field to be measured and the spin, H n (t) is the noise term.

[0040] Step S2: Perform sensor evolution of time t under the dynamic decoupling sequence (XY-8 sequence) to obtain the phase relationship related to the weight function accumulated by the AC signal;

[0041] The sensing evolution of time t is performed by dynamically decoupling the XY-8 sequence, and the sensing time is t = 8N (T pulse +τ), where N is the number of cycles of the XY-8 pulse sequence, T pulse is the pulse width, τ is the free evolution time between the two pulses, and the phase accumulation expressed as a weighted function is obtained as shown in formula (2);

[0042]

[0043] Where W xy-8 (w s ,ξ) is the weighting function, y(t) = ±1 is the filtering function to describe the behavior of the dynamic decoupling sequence XY-8, Φ is the phase, and γ is the gyromagnetic ratio of the NV color center.

[0044] It has been verified that when the number of pulses in the dynamic decoupling sequence is greater than or equal to 3, the form of the weighted function is approximately simplified to obtain the relationship between the cumulative phase and the strength of the AC magnetic field signal to be measured;

[0045] When the number of pulses in the dynamic decoupling sequence is greater than or equal to 3, the sinc term (i.e. ) becomes very sharp, and the filter bandwidth (full width at half maximum) becomes very narrow. The relationship of the weighting function is rewritten as shown in formula (3):

[0046]

[0047] Where k is the harmonic order, k = 1, ξ = 0, and the relationship between the cumulative phase and the measured intensity value is further obtained, as shown in formula (4):

[0048]

[0049] After the last π / 2 pulse, the average population transfer transition probability P is read out, as shown in formula (5):

[0050]

[0051] Where w is the Fourier fitting angular frequency, That is, the Fourier fitting angular frequency is proportional to the magnetic field intensity value. The value of the angular frequency w obtained by fitting can be used to further determine the magnetic field pretreatment intensity value. When measuring the population, the measurement is repeated N times and the population values ​​obtained from these N measurements are averaged. Then, a Fourier curve is fitted to the data, and the fitting form must be a Fourier linear term. Through this process, the value of the fitting parameter angular frequency is obtained, and further the intensity value is obtained.

[0052] Step S3: The intensity value obtained by fitting is used as the preprocessing value and the average population number as the input. After verifying a large number of models, the best performing histogram-based gradient boosting machine learning model (HGboost) is selected for machine learning training, and then the intensity prediction value with a root mean square error reduced by more than one order of magnitude is obtained, such as Figure 3 shown.

[0053] Step S4: When N is greater than 50, a machine learning model with preprocessing is used to obtain a prediction result. When N is less than 50, the prediction result is compared with a direct prediction without preprocessing, and the intensity prediction value with a root mean square error closer to 0 and a coefficient of determination closer to 1 is used as the prediction result. The direct prediction method without preprocessing uses the averaged population number as the input and performs machine learning training using the HGboost machine learning model.

[0054] The effectiveness of this application is verified by comparing the effects of numerical simulation data:

[0055] The initial state is |0> state, and the interaction term H between the AC magnetic field and the spin to be measured is g (t) and the noise term H n (t) is σ z direction, the noise δ(t) is δ(t) = δ c +δ d (t), where, where the static noise δ c is the detuning term of the normal distribution due to the inhomogeneous local environment between the sets, with an expected value of 0 and a full width at half maximum (FWHM) The standard deviation is The probability density is Gaussian distribution, where is the corresponding transverse relaxation time; the dynamic noise term δ varies with time d (t) obeys the Ornstein-Uhlenbeck process.

[0056]

[0057] Among them, τ d= 20μs and c = 2π × 50kHz, respectively, and n ~ N(0,1). The XY-8 dynamic decoupling of the NV center is used to perform Ramsey measurement, as shown in Figure 2 As shown. The sensing time is t=8N(T pulse +τ). The total Hamiltonian in the rotating wave approximation is:

[0058]

[0059] For rectangular pulses, during the pulse application (XY-8) period, apply π x Pulse time Apply π y Pulse time The rest of the time is 0.

[0060] Through analysis Figure 3-5 It can be concluded that:

[0061] 1) If Figure 3 As shown in the figure, by training the HGboost machine learning model and combining it with preprocessing steps, the predicted values ​​of alternating magnetic field intensity are evenly distributed on both sides of the true value within a small range, demonstrating that the model can effectively capture patterns in the data and reduce prediction bias. This precise prediction can effectively improve the model's generalization ability, enhance its adaptability to different types of data, improve the model's robustness, and further enhance its reliability and accuracy in practical applications.

[0062] 2) If Figure 4 、 5 As shown in the figure, after preprocessing, the evaluation index MSE (mean square error) is increased from 10 -3 Reduced to 10 -6 , R 2 The coefficient of determination decreased from 182 to 0.85, and the accuracy indicated by the mean square error and the coefficient of determination increased by more than an order of magnitude, indicating that the model's prediction error is small and the fitting effect is excellent. This means that the model can fit the training data more accurately, reducing the error and improving the prediction accuracy. A lower MSE indicates that the model is more accurate in predicting the target variable, and an R closer to 1 indicates that the model is more accurate in predicting the target variable. 2 The value indicates that the model can well explain the variability of the data, has strong predictive ability and higher stability, thereby improving the effectiveness of the model in practical applications.

[0063] 3) If Figure 5 As shown in the evaluation indicators MSE and R 2Under the condition that the values ​​of are close, the amount of data required to estimate magnetic field strength is reduced from 500*60 to 65*60, and the average calculation time is reduced from 13 seconds to 3.5 seconds. The optimized data processing process enables accurate data processing and rapid estimation of magnetic field strength within 3.5 seconds, enabling fast measurement. This also enables the system to respond in real time in dynamic environments, meeting the demand for rapid feedback on magnetic field measurement and estimation, such as in application scenarios requiring real-time data processing, such as real-time monitoring and dynamic adjustment.

[0064] While reducing the amount of data, this application utilizes a dynamic decoupling sequence to suppress the effects of system noise, particularly the decoherence effect caused by interactions with the environment. The method collects and preprocesses the measurement data of the magnetometer system, and then combines it with a machine learning algorithm for training to rapidly estimate the magnetic field strength. This method offers significant advantages in addressing computational complexity, noise interference, real-time performance, and accuracy issues. It can provide efficient, accurate, and real-time magnetic field strength estimation, improving the performance of the magnetometer system, particularly in high-precision, dynamic scenarios, and expanding its application scope, particularly in complex systems and big data environments.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A magnetic field strength estimation method based on a dynamic decoupling sequence and assisted by machine learning, characterized by: The following steps are involved: Step S1: specifying an initial state, applying a matching dynamic decoupling sequence to the AC magnetic field signal to be predicted to perform evolution, and obtaining a relationship between the cumulative phase and the intensity value of the AC magnetic field signal to be measured; averaging the population numbers obtained by repeating N measurements, performing Fourier curve fitting on the data, obtaining the value of the fitting parameter angular frequency, and further obtaining the intensity value based on the relationship between the angular frequency and the intensity value to be measured; Step S2: Using the intensity value obtained by fitting as a preprocessing value and the averaged population number as input, a gradient boosting model is used for machine learning training to obtain a predicted value of the magnetic field intensity to be measured; Step S3: When N is greater than 50, the prediction result is obtained by using the machine learning model method with preprocessing; when N is less than 50, it is compared with the direct prediction without preprocessing, and the intensity prediction value with a root mean square error closer to 0 and a determination coefficient closer to 1 is used as the prediction result.

2. The magnetic field strength estimation method based on dynamic decoupling sequence and machine learning assistance according to claim 1, characterized in that: The relationship between the accumulated phase and the AC magnetic field signal strength to be measured is as follows: Where Φ is the phase, g c is the amplitude of the alternating magnetic field signal, t is the evolution time, W xy-8 (w s ,ξ) is the weighting function, w s is the angular frequency of the alternating magnetic field signal, ξ is the initial phase of the alternating magnetic field signal, and k is the harmonic order.

3. The method for estimating magnetic field strength based on a dynamic decoupling sequence and machine learning according to claim 2, characterized in that: The expression of the weighting function is as follows: Where k is the harmonic order, k=1 and ξ=0.

4. The method for estimating magnetic field strength based on a dynamic decoupling sequence and machine learning according to claim 2, characterized in that: The expression of the fitting parameter angular frequency is as follows: Where w is the Fourier fitting angular frequency; It means that the Fourier fitting angular frequency is proportional to the magnetic field intensity value, and the value of the angular frequency w obtained by fitting is further used to obtain the magnetic field preprocessing intensity value.

5. The method for estimating magnetic field strength based on a dynamic decoupling sequence and machine learning according to claim 1, characterized in that: The HGboost model is selected as the machine learning model.

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