Accurate determination of the temperature of trapped ion Coulomb crystals (ICCs) is critical for advancing quantum technologies. We present a deep learning approach to classify ICC temperature states from fluorescence images. A high-fidelity dataset was generated using the (py)LIon molecular dynamics toolkit, simulating ICCs containing 100--268 ions over a temperature range of 5--20 mK. In the initial 16-class problem (each class a 1-mK interval), a ConvNeXt convolutional network achieved a peak accuracy of 57%, demonstrating its ability to capture fine-grained structural features. To overcome low distinguishability among similar temperature classes, we redefined the task into four broader temperature intervals and applied a vision transformer (ViT). The ViT model achieved a test accuracy of 84%, indicating substantially improved generalization. These results highlight the complementarity of convolutional neural network and transformer architectures for noninvasive temperature diagnostics. We discuss limitations due to dataset diversity and outline future work on larger-scale simulations and physics-guided network designs to further improve ICC temperature estimation in quantum applications.
Accurate determination of the temperature of trapped ion Coulomb crystals (ICCs) is critical for advancing quantum technologies. We present a deep learning approach to classify ICC temperature states from fluorescence images. A high-fidelity dataset was generated using the (py)LIon molecular dynamics toolkit, simulating ICCs containing 100--268 ions over a temperature range of 5--20 mK. In the initial 16-class problem (each class a 1-mK interval), a ConvNeXt convolutional network achieved a peak accuracy of 57%, demonstrating its ability to capture fine-grained structural features. To overcome low distinguishability among similar temperature classes, we redefined the task into four broader temperature intervals and applied a vision transformer (ViT). The ViT model achieved a test accuracy of 84%, indicating substantially improved generalization. These results highlight the complementarity of convolutional neural network and transformer architectures for noninvasive temperature diagnostics. We discuss limitations due to dataset diversity and outline future work on larger-scale simulations and physics-guided network designs to further improve ICC temperature estimation in quantum applications.
Coulomb crystals---ordered structures of cold ions confined in ion traps---have applications in a variety of research fields. The number and temperature of the ions forming the Coulomb crystals are two key attributes of interest in many trapped-ion experiments. Here, we present a fast and accurate approach to determining these attributes from fluorescence images of the ions based on convolutional neural networks (CNNs). In this approach, we first generate a large number of images of Coulomb crystals with different numbers of ions at different temperatures using molecular-dynamics simulations and then train CNN models on these images to classify the desired attributes. The classification performance of several common pretrained CNN models is compared in example tasks. We find that for crystals with numbers of ions in the range 100--299 and secular temperatures of 5--15 mK, the best-performing model can discern variations of a single ion with an accuracy of 93% and temperature changes of 1 mK with an accuracy of 92%. Since the trained models can be directly integrated into experiments, in situ determination of these attributes can be realized in a noninvasive fashion. This has the potential to greatly enhance the analysis and control of trapped ions in real time.
Transformer neural networks, known for their ability to recognize complex patterns in high-dimensional data, offer a promising framework for capturing many-body correlations in quantum systems. We employ an adapted vision transformer (ViT) architecture to model quantum impurity models, optimizing it with a subspace expansion scheme that surpasses conventional variational Monte Carlo in both accuracy and efficiency. Benchmarks against matrix product states in single- and three-orbital Anderson impurity models show that these ViT-based neural quantum states achieve comparable or superior accuracy with significantly fewer variational parameters. We further extend our approach to compute dynamical quantities by constructing a restricted excitation space that effectively captures relevant physical processes, yielding accurate core-level x-ray absorption spectra. These findings highlight the potential of ViT-based neural quantum states for accurate and efficient modeling of quantum impurity models.
Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work, we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
Nowadays, with the discovery of the power and potential of quantum computers, developing and understanding quantum-based deep learning models has become an important research area. This study investigates Quantum Transfer Learning and Quantum Hybrid Learning models that involve feature extraction and training processes using Convolutional Neural Networks (CNN) and Vision Transformer (ViT). The study aims to explore the potential advantages and differences of quantum deep learning techniques. It is envisioned that quantum computing can provide significant advantages in terms of computational speed and efficiency, especially in complex and large-scale data sets. Therefore, this study will contribute to a better understanding of the practical applications and potential impacts of quantum deep learning techniques. In this study, we evaluate the performance of four different quantum deep learning architectures using two different datasets. The classifiers used are the pre-trained ResNet-50 with a kernel size of 5x5 and the state-of-the-art CaiT-24-XXS-224 (CaiT) transducers. Optimization was performed with Adam optimizer using the cross entropy loss function. A total of eight models were trained, each with ten iterations. Accuracy (Acc), balanced accuracy (BA), overall F𝛽 (F_beta) macro score F1 and F2, Matthew's Correlation Coefficient (MCC), sensitivity (Sens) and specificity (Spec) were used as performance measures.
Convolutional Neural Networks (CNNs) are extensively utilized for image classification due to their ability to exploit data correlations effectively. However, traditional CNNs encounter several challenges, including limitations in accuracy improvement, computational efficiency, explain ability, and generalization. As data dimensionality or model complexity increases, CNNs often become more difficult to train efficiently, leading to slower processing times. To overcome these challenges, Quantum Convolutional Neural Networks (QCNNs) offer a promising quantum-based approach to enhance existing models, particularly by improving training efficiency and reducing processing times. This paper provides a comparative analysis of classical CNNs and a novel quantum circuit architecture tailored for image-based tasks. The analysis emphasizes the adaptability and potential of quantum circuits to enhance feature extraction, recognition accuracy, and processing efficiency.We applied various QCNN architectures to the Chinese-MNIST dataset and compared their performance with traditional CNN models. Although QCNNs achieved slightly lower accuracy, they demonstrated significantly greater stability. These findings high- light QCNNs’ potential to overcome the computational limitations of conventional deep learning, offering a promising pathway for quantum-enhanced solutions in computer vision. Future work will focus on refining quantum circuit designs, developing hybrid quantum-classical models, and extending QCNN applications to larger and more diverse datasets.
Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model.For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy.However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques.In this work, we present a new thermometry method tailored for ion crystals.The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals.We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods.The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.