In recent years, special attention has been paid to deep learning-based quantum state estimation (QSE). In this paper, we apply deep complex convolutional neural networks (DC-CNNs) to the field of QSE and optimize the network architecture by employing the attention mechanism. The DCCNN-based estimator is trained to fit the mapping from Pauli measurements to each target density matrix, and then each output density matrix is projected onto the nearest subspace that satisfies quantum state constraints. A major advantage of the proposed scheme is that it is capable of extracting sufficient features from incomplete measurements, which contributes to its ability to overcome the absence of partial measurement values. Finally, the superiority of the proposed scheme is highlighted in comparison with the QSE schemes based on the conventional least squares estimation (LSE) and maximum likelihood estimation (MLE).
In recent years, special attention has been paid to deep learning-based quantum state estimation (QSE). In this paper, we apply deep complex convolutional neural networks (DC-CNNs) to the field of QSE and optimize the network architecture by employing the attention mechanism. The DCCNN-based estimator is trained to fit the mapping from Pauli measurements to each target density matrix, and then each output density matrix is projected onto the nearest subspace that satisfies quantum state constraints. A major advantage of the proposed scheme is that it is capable of extracting sufficient features from incomplete measurements, which contributes to its ability to overcome the absence of partial measurement values. Finally, the superiority of the proposed scheme is highlighted in comparison with the QSE schemes based on the conventional least squares estimation (LSE) and maximum likelihood estimation (MLE).
In recent years, deep learning-based quantum state estimation (QSE) has attracted extensive attention, and the generative adversarial network (GAN) is a popular model in the field of deep learning. In this paper, we apply GANs into the field of QSE and design a custom neural network layer which makes the original network outputs satisfy quantum state constraints. It is worth noting that our designed custom neural-network layers are applicable to arbitrary feed-forward neural networks used for QSE. GANs are trained and tested by randomly generated pure state density matrices. Simulation results show that the designed neural network estimator is capable of achieving a fidelity higher than 99% for both eigenstates and superposition states.
We apply deep-neural-network-based techniques to quantum state classification and reconstruction. Our methods demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feed-forward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed QST technique with conditional generative adversarial networks (QST-CGAN) [Ahmed et al., Phys. Rev. Lett. 127, 140502 (2021)]. We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than iterative and accelerated projected-gradient-based maximum-likelihood estimation (MLE) methods. We also demonstrate that the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than these MLE methods. Our paper opens possibilities to use state-of-the-art deep-learning methods for quantum state classification and reconstruction under various types of noise.
Human experts cannot efficiently access physical information of a quantum many-body states by simply “reading” its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. We demonstrate that convolutional neural network (CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.
Abstract Quantum compressed sensing is a fundamental technique for tomographic reconstruction of low-rank density matrices in informationally incomplete scenarios. However, when the available measurement data is insufficient, standard compressed sensing, like other algorithmic estimators such as maximum-likelihood, can yield imprecise or noisy estimates. To mitigate this, we propose a deep neural network-based post-processing to enhance the initial reconstruction. By treating the compressed sensing-estimated quantum state as a noisy input, the network performs a supervised denoising task. After the network is applied, a projection onto the space of feasible density matrices is performed to obtain an improved final state estimation. We demonstrate the effectiveness of our method through numerical experiments. Additionally, we explore iterative application of the inference process to further enhance performance, and we analyze the network’s generalization ability by testing its performance on states and noise models not seen during training.
In the field of image processing, a well-known model is the Convolutional Neural Network, or CNN. The unique benefit that sets this model apart is its exceptional ability to use the correlation information included in the data. Even with their amazing accomplishment, conventional CNNs could have trouble improving further in terms of generalization, accuracy, and computing economy. However, it could be challenging to train CNN correctly and process information quickly if the model or data dimensions are too large. This is since it will cause the data processing to lag. The Quantum Convolutional Neural Network, or QCNN for short, is a novel proposed quantum solution that might either enhance the functionality of an existing learning model or solve a problem requiring the combination of quantum computing with CNN. To highlight the flexibility and versatility of quantum circuits in improving feature extraction capabilities, this paper compares deep quantum circuit architecture designed for image-based tasks with classical Convolutional Neural Networks (CNNs) and a novel quantum circuit architecture. The covidx-cxr4 dataset was used to train quantum-CNN models, and their results were compared against those of other models. The results show that when paired with innovative feature extraction methods, the suggested deep Quantum Convolutional Neural Network (QCNN) outperformed the conventional CNN in terms of processing speed and recognition accuracy. Even though it required more processing time, QCNN outperformed CNN in terms of recognition accuracy. When training on the covidx-cxr4 dataset, this dominance becomes much more apparent, demonstrating how deeper quantum computing has the potential to completely transform image classification problems.
Quantum computing, based on fundamental quantum-mechanical principles and phenomena such as superposition, entanglement, and interference, offers access to high-dimensional quantum feature spaces and complex correlations that may be difficult to efficiently represent using classical computing, along with potential computational advantages through quantum hardware. Therefore, quantum computing has emerged as a promising paradigm for addressing limitations of classical deep learning (DL) through fundamentally different computational mechanisms. Quantum computing-based DL approaches have been applied to image classification; however, most rely on existing quantum computing libraries that impose substantial computational costs, limiting their broader applicability. In this study, hybrid quantum convolutional neural networks (HQCNNs) are proposed for structural damage classification without relying on existing quantum computing libraries. The proposed architectures integrate quanvolutional layers, composed of encoding, variational quantum circuits, and measurement, with conventional convolutional layers in a CNN architecture, enabling quantum-enhanced feature extraction while maintaining compatibility with classical computing systems. The scratch-implemented HQCNN (HQCNN(S)), its library-based counterpart (HQCNN(P)), and the classical CNN are compared in terms of test accuracy, computational cost, and training efficiency. Experimental results demonstrate that HQCNN(S) ( at ) achieves up to 176.57 faster computation than HQCNN(P) and 3.1% higher test accuracy than the classical CNN, while reducing the number of trainable parameters by 60.2%. Moreover, HQCNN(S) achieves comparable performance to the best-performing classical CNN using 75% less training data.