Quantum Noise Spectroscopy
A Machine Learning approach for imaging magnetic noise, by Fernando Meneses.
View the Project on GitHub Fertmeneses/AI-quantum-noise-spectroscopy
Deep Learning applied to Spectral Imaging of Magnetic Noise
As a postdoc in The City College of New York (CCNY, USA), I have combined my experimental skills in quantum sensing along with artificial intelligence (AI) techniques. In collaboration with University College London (UCL, UK) and Universidad Nacional de Córdoba (UNC, Argentina), we published a research article titled Toward Deep-Learning-Assisted Spectrally Resolved Imaging of Magnetic Noise, in the journal Physical Review Applied in 2022.
Link to the research article 👈🏽.
The full list of authors include:
- Fernando Meneses (CCNY).
- David F. Wise (UCL).
- Daniela Pagliero (CCNY).
- Pablo R. Zangara (UNC).
- Siddharth Dhomkar (UCL).
- Carlos A. Meriles (CCNY).
The main concept of the work was to we probe the response of quantum defects in diamond in the presence of a magnetic environment and implement a deep neural network to extract information about the noise spectral density. Our artificial intelligence method was compared to traditional approaches, demonstrating a better performance and more precise results.
Introduction
Quantum sensing is a powerful tool where the theory of quantum mechanics can be applied to measure physical properties, for example detecting subtle changes in magnetic fields with great precision. A well-established platform for this technology is the nitrogen-vacancy (NV) center in diamond, a specific type of defect within the diamond lattice, in which a nitrogen atom has replaced a carbon atom, next to a spot in which there is a missing carbon atom (vacancy). This NV defect hosts a quantum system that is extremely sensitive to magnetic fields, and can be manipulated optically to read out very small variations in the magnetic environment.
Magnetic signals are usually convoluted with noise originated by random magnetic fluctuations. This noise, tipycally seen as an obstacle for measurements, can also become a valuable source of information, as it may encode critical properties of the local composition and structure of a sample. Consequently, understanding and characterizing the noise Power Spectral Density (PSD) is a powerful tool to extract detailed information about a sample’s physical properties.
The problem of decoding magnetic noise has a long history, and traditional approaches, which rely on theoretical models and numerical methods, have made significant progress in the area. However, they face large limitations due to oversimplifications or to the extensive experimental data that is required, compromising the accuracy of the results.
In our research, we address the challenge of reconstructing the noise PSD from experimental magnetic measurements, emphasizing the case of colored noise, where random magnetic fluctuations are mostly distributed within a reduced frequency range. The novelty of our work comes with the application of AI tools, showing that Deep Learning algorithms can efficiently predict the noise PSD, employing a minimal experimental dataset. Our results have benchmarked those of equivalent methodologies using only theoretical and numerical methods, highlighting the great potential of combining AI-based methods with quantum sensing.
Deep Learning algorithm
In order to determine the noise PSD from magnetic signals, we have designed an AI Autoencoder algorithm. This program takes magnetic timeseries as input data and determines the PSD of the underlying magnetic noise in the frequency space.
The idea behind the autoencoding process is to first extract the essential information from the magnetic timeseries into a reduced representation, and then expand it to the frequency domain to reconstruct the PSD of the magnetic noise. The main tools in the process are the one-dimensional (1D) Convolutional Layers, which scan the input data with 1D filters and extract the most relevant features. The Autoencoder algorithm consists in two main structures: first the Encoder, which combines 1D Convolutional Layers with Max-Pooling layers to reduce the information in each step, while preserving the critical features; and then the Decoder, which instead uses Up-sampling layers to progressively expand the data.
Our algorithm has a Deep Leaning structure (meaning many internal layers) which requires training on a large dataset, having at least a few tens of thousands of samples. As our application aims to predict the PSD of real magnetic measurements, the ideal dataset would comprise a large collection of experimental measurements. However, acquiring a single timeseries sample can take several minutes, then measuring just 10.000 samples would take more than a month.
An alternative solution for generating a large dataset is to use simulations that reproduce the experimental conditions within a range of colored noises. Although simulations cannot perfectly replicate real-world conditions, the AI algorithm can still learn to identify patterns and generalize its knowledge to real data. In our work, we have simulated a set of 500,000 samples, 80% used for training and 20% for testing.
Results
The colored noise studied in this work is within the range of tens to a few hundred kHz. At these frequencies, the Hahn Echo control sequence (an experimental technique) allows us to measure the relaxation time of the NV defects and to determine the coherence curve, which goes from a state of maximum to minimum information regarding the quantum state of the NV defects. The shape of this coherence curve is strongly affected by the magnetic noise, which is the main principle that we use in our AI application for determining the PSD of each particular noise.
The following Figure illustrates three examples of magnetic signals presented as coherence curves (left column), each affected by a different colored noise. The real PSD is computed on the right by solid lines, exhibiting distinct signatures for each colored noise. When the input data is processed by our Deep Learning algorithm, the PSD predictions (green dashed lines in central column) closely match the true PSD values. For comparison, we include the results obtained through a traditional approach commonly used for this experimental technique (red dotted lines in right column). This method provides only a rough estimation of the noise PSD, but the accuracy level is rather low.
The results demonstrate that the AI method significantly outperfoms its traditional counterpart, achieving very accurate predictions. Furthermore, the precision level of the AI predictions can be improved by using a larger training dataset, while designing more complex experiments can unlock the analysis of broader frequency ranges for the PSD.
Conclusions
In this research, we have developed an AI autoencoder algorithm that can be integrated with magnetic platforms, such as NV centers in diamond, to determine the Power Spectral Density of the noise behind a magnetic signal. The demonstrated superiority of our method over traditional solutions highlights the great potential of AI applied to experimental techniques. As determining the PSD for magnetic signals is key to several applications, the AI algorithm can be tailored according to the problem’s need to achieve the desired accuracy, improving the efficiency known so far by other approaches.
