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Artificial intelligence enhanced two-dimensional nanoscale nuclear magnetic resonance spectroscopy

MetadataDetails
Publication Date2020-09-16
Journalnpj Quantum Information
AuthorsXi Kong, Leixin Zhou, Zhijie Li, Zhiping Yang, Bensheng Qiu
InstitutionsNanjing University, University of Science and Technology of China
Citations18
AnalysisFull AI Review Included

This research introduces the Deep Learning Matrix Completion (DLMC) protocol, significantly enhancing the efficiency and sensitivity of two-dimensional (2D) nanoscale Nuclear Magnetic Resonance (NMR) spectroscopy using Nitrogen-Vacancy (NV) centers in diamond.

  • Core Value Proposition: DLMC enables the recovery of a full 2D NMR spectrum from highly sparse (as low as 10%) sampled data, drastically reducing experimental acquisition time by an order of magnitude.
  • Sensitivity Improvement: The artificial intelligence (AI) protocol intrinsically suppresses observation noise, resulting in a Signal-to-Noise Ratio (SNR) enhancement of 5.7 ± 1.3 dB compared to the original Fast Fourier Transform (FFT) result.
  • Hybrid Methodology: DLMC combines a trained Convolutional Neural Network (CNN) (DLNet) for complex non-linear feature mapping with the classical Singular Value Thresholding (SVT) Matrix Completion (MC) algorithm for post-processing.
  • Domain Shift Mitigation: The two-step DLMC approach utilizes MC post-processing to enforce the low-rank property of the spectrum map, effectively mitigating the domain shift problem arising from training the DLNet solely on simulated data.
  • Robustness: DLMC demonstrated superior performance (higher SNR, lower Root Mean Square Error (RMSE)) compared to MC-only or DL-only methods, even when recovering a 2D spectrum from 10% random sampling.
  • Enhanced Sensitivity Metric: The bond length sensitivity is projected to be enhanced from 0.8 nm/sqrt(Hz) to 0.3 nm/sqrt(Hz) by maintaining high fidelity across low sampling coverages (80% down to 10%).
ParameterValueUnitContext
Quantum SensorSingle Nitrogen-Vacancy (NV) CenterN/AFabricated in CVD-grown diamond.
Target SystemCoupled 13C Nuclear Spin DimerN/ANatural abundance (1.1%) in diamond.
External Magnetic Field (B)1580 (158 mT)GaussApplied along the main axis of the NV sensor.
13C Larmor Frequency (ωL)1.69MHzCalculated based on the magnetic field.
Time Domain Matrix Size50 x 50N/AData collected by sweeping t1 and t2.
Time Step (t1, t2)18”sUsed for sweeping the duration times.
Time Range (t1, t2)4 ”s to 0.9msRange of free evolution times.
Sampling Coverage Tested10%, 40%, 80%%Randomly generated masks used for sparse data input.
SNR Enhancement (10% coverage)5.7 ± 1.3dBDLMC result compared to original FFT.
MC-only SNR Enhancement (40% coverage)3.2 ± 3.1dBComparison showing DLMC superiority.
DLNet ArchitectureEncoder-Decoder CNNN/AUtilizes Res blocks, Pooling, and Transposed Convolution.
DLNet Training Epochs500N/ATraining performed on simulated data.
DLNet Learning Rate5 x 10-4N/AUsed with the Adam optimizer.
DLNet Loss FunctionL1 LossN/AUsed for back propagation during training.

The DLMC method integrates deep learning and matrix completion to accelerate 2D nanoscale NMR spectroscopy.

  1. Experimental Setup and Control:

    • A single NV center in a CVD diamond is used as the quantum sensor.
    • The target is a coupled 13C nuclear spin cluster.
    • The 2D NMR spectrum is acquired using a control protocol analogous to the conventional COSY sequence (Initialization, Free Evolution t1, π/2 pulse, Free Evolution t2, Correlation Read).
    • Data acquisition is performed by sweeping t1 and t2, collecting the nuclear spin transverse component via Optical Detected Magnetic Resonance (ODMR).
  2. Training Data Generation (Simulation):

    • Due to the high time cost of real experiments, the training dataset (pairs of partially sampled maps and full-resolution ground truth maps) is generated via numerical simulation using the Schrödinger equation for the NV-13C system.
  3. Deep Learning Network (DLNet) Construction and Training:

    • An encoder-decoder Convolutional Neural Network (CNN) is utilized (DLNet).
    • The encoder extracts multi-resolutional features using hierarchical convolutional filters, residual blocks (Res blocks), and pooling layers.
    • The decoder recovers the full-resolution spectrum map using transposed convolution layers and horizontal skipping connections (Skipping conn) to preserve detail and alleviate gradient vanishing.
    • The DLNet is trained on the simulated data using L1 loss and the Adam optimizer.
  4. DLMC Reconstruction Protocol (Two-Step Inference):

    • Step 1 (Deep Learning): The sparse experimental input matrix (M) is fed into the trained DLNet to generate a preliminary full-resolution reconstruction, DL(M).
    • Step 2 (Matrix Completion - MC): The traditional Singular Value Thresholding (SVT) algorithm is applied as a post-processing step to DL(M). This step enforces the low-rank property inherent to the NV spectrum map, thereby mitigating the bias introduced by the simulated training data (domain shift) and further reducing artifacts.

The development of high-speed, high-sensitivity nanoscale 2D NMR spectroscopy has significant implications for several advanced technological fields:

  • Quantum Sensing and Metrology:
    • Enables rapid, high-fidelity characterization of quantum systems (e.g., spin clusters, quantum dots) essential for building quantum computers and sensors.
    • Provides a robust method for characterizing noise and coupling interactions in solid-state quantum devices.
  • Drug Discovery and Structural Biology:
    • Allows for non-destructive, room-temperature structure analysis of single molecules and proteins, overcoming the limitations of conventional bulk NMR.
    • The ability to quickly obtain 2D spectra facilitates the determination of chemical bond lengths and angles, crucial for constructing 3D molecular structures.
  • Advanced Materials Characterization:
    • High-resolution nanoscale NMR is vital for analyzing the structure and defects in advanced materials, particularly those involving coupled nuclear spin systems (e.g., specialized CVD diamond substrates).
  • Artificial Intelligence in Scientific Instrumentation:
    • The DLMC methodology provides a template for integrating AI (specifically hybrid DL/MC approaches) into other time-consuming spectroscopic and imaging techniques (e.g., MRI, high-dimensional NMR) to accelerate data acquisition and processing.
View Original Abstract

Abstract Two-dimensional nuclear magnetic resonance (NMR) is indispensable to molecule structure determination. Nitrogen-vacancy center in diamond has been proposed and developed as an outstanding quantum sensor to realize NMR in nanoscale or even single molecule. However, like conventional multi-dimensional NMR, a more efficient data accumulation and processing method is necessary to realize applicable two-dimensional (2D) nanoscale NMR with a high spatial resolution nitrogen-vacancy sensor. Deep learning is an artificial algorithm, which mimics the network of neurons of human brain, has been demonstrated superb capability in pattern identifying and noise canceling. Here we report a method, combining deep learning and sparse matrix completion, to speed up 2D nanoscale NMR spectroscopy. The signal-to-noise ratio is enhanced by 5.7 ± 1.3 dB in 10% sampling coverage by an artificial intelligence protocol on 2D nanoscale NMR of a single nuclear spin cluster. The artificial intelligence algorithm enhanced 2D nanoscale NMR protocol intrinsically suppresses the observation noise and thus improves sensitivity.