In order to explore the possibility of cross-fertilization between quantum computing and neural networks as well as to improve the classification performance of quantum neural networks, this paper proposes an improved Variable Split Shadow Quantum Circuit (VSQC-WOA) model based on the Whale Optimization Algorithm. In this model, we design a strongly entangled local shadow circuit to achieve efficient characterization of global features through local shadow feature extraction and a sliding mechanism, which provides a rich quantum feature representation for the classification task. The gradient is then computed by the parameter-shifting method, and finally the features processed by the shadow circuit are passed to the classical fully connected neural network (FCNN) for processing and classification. The model also introduces the Whale Optimization Algorithm (WOA) to further optimize the weights and biases of the fully connected neural network, which improves the expressive power and classification accuracy of the model. In this paper, we firstly use different localized shadow circuit VSQC models to achieve the binary classification task on the MNIST dataset, and our design of strongly entangled shadow circuits performs the best in terms of classification accuracy. The VSQC-WOA model is then used to multi-classify the MNIST dataset (three classifications as an example), and the effectiveness of the proposed VSQC-WOA model as well as the robustness and generalization ability of the model are verified through various comparison experiments.
In order to explore the possibility of cross-fertilization between quantum computing and neural networks as well as to improve the classification performance of quantum neural networks, this paper proposes an improved Variable Split Shadow Quantum Circuit (VSQC-WOA) model based on the Whale Optimization Algorithm. In this model, we design a strongly entangled local shadow circuit to achieve efficient characterization of global features through local shadow feature extraction and a sliding mechanism, which provides a rich quantum feature representation for the classification task. The gradient is then computed by the parameter-shifting method, and finally the features processed by the shadow circuit are passed to the classical fully connected neural network (FCNN) for processing and classification. The model also introduces the Whale Optimization Algorithm (WOA) to further optimize the weights and biases of the fully connected neural network, which improves the expressive power and classification accuracy of the model. In this paper, we firstly use different localized shadow circuit VSQC models to achieve the binary classification task on the MNIST dataset, and our design of strongly entangled shadow circuits performs the best in terms of classification accuracy. The VSQC-WOA model is then used to multi-classify the MNIST dataset (three classifications as an example), and the effectiveness of the proposed VSQC-WOA model as well as the robustness and generalization ability of the model are verified through various comparison experiments.
Abstract Convolutional neural network (CNN), as a prominent machine learning model, is crucial in image classification and feature extraction by completely utilizing the correlation information of data. Currently, the CNN is facing the challenges of slow computing speed, expanding data scale and poor interpretation for rapidly increasing Hilbert space. Fortunately, quantum convolutional neural network (QCNN) promises an elegant solution to improve the efficiency of data processing by combining the superiority of quantum computing and the feature extraction capability of the CNN. However, most of the existing QCNNs have the problem that they are feeble to extract global features effectively and coincidentally variational shadow quantum circuit (VSQC) can preferably figure out it. Accordingly, an enhanced QCNN assisted by the VSQC (VSQC‐QCNN) is developed. To be specific, the input data is primarily preprocessed by the VSQC module to establish global entanglement and extract effective features. Then the output shadow features are further processed by encoding, quantum circuit evolution and decoding through quantum convolutional layer and the dimensionality of the feature results is reduced through the pooling layer. When the data dimension is small enough, it is fed into a fully connected neural network to make classification predictions via activation functions. Experiments conducted on the MNIST dataset through the VQNet quantum framework demonstrate that the VSQC‐QCNN model is with performance surpassing the original QCNN in terms of loss function, classification accuracy and training speed. In addition, it is proved that the VSQC‐QCNN model has good astringency and stability under different circuit depths, widths and learning rates. Remarkably, the classification average accuracy of the model can reach up to 99% (even 100% for a few cases). Finally, experiments are also performed on Fashion‐MNIST and Iris datasets, indicating that the designed model has good universality.
Quantum machine learning (QML) has attracted significant research attention over the last decade. Multiple models have been developed to demonstrate the practical applications of the quantum properties. In this study, we first demonstrate that the previously proposed quanvolutional neural network (QuanvNN) using a randomly generated quantum circuit improves the image classification accuracy of a fully connected neural network against the Modified National Institute of Standards and Technology (MNIST) dataset and the Canadian Institute for Advanced Research 10 class (CIFAR-10) dataset from 92.0% to 93.0% and from 30.5% to 34.9%, respectively. We then propose a new model referred to as a Neural Network with Quantum Entanglement (NNQE) using a strongly entangled quantum circuit combined with Hadamard gates. The new model further improves the image classification accuracy of MNIST and CIFAR-10 to 93.8% and 36.0%, respectively. Unlike other QML methods, the proposed method does not require optimization of the parameters inside the quantum circuits; hence, it requires only limited use of the quantum circuit. Given the small number of qubits and relatively shallow depth of the proposed quantum circuit, the proposed method is well suited for implementation in noisy intermediate-scale quantum computers. While promising results were obtained by the proposed method when applied to the MNIST and CIFAR-10 datasets, a test against a more complicated German Traffic Sign Recognition Benchmark (GTSRB) dataset degraded the image classification accuracy from 82.2% to 73.4%. The exact causes of the performance improvement and degradation are currently an open question, prompting further research on the understanding and design of suitable quantum circuits for image classification neural networks for colored and complex data.
Long-short term memory (LSTM) neural network solves the problems of long-term dependence, gradient disappearance and gradient explosion by introducing memory units, and is widely used in time series analysis and prediction. Combining quantum computing with LSTM neural network will help to improve its computational efficiency and reduce the number of model parameters, thus significantly improving the performance of traditional LSTM neural network. This paper proposes a hybrid quantum LSTM (hybrid quantum long-short term memory, HQLSTM) network model that can be used to realize the image classification. It uses variable quantum circuits to replace the nerve cells in the classical LSTM network to realize the memory function of the quantum network. At the same time, it introduces Choquet integral operator to enhance the degree of aggregation between data. The memory cells in the HQLSTM network are composed of multiple variation quantum circuits (VQC) that can realize different functions. Each VQC consists of three parts: the coding layer, which uses angle coding to reduce the complexity of network model design; the variation layer, which is designed with quantum natural gradient optimization algorithm, so that the gradient descent direction does not target specific parameters, thereby optimizing the parameter update process and improving the generalization and convergence speed of the network model; the measurement layer, which uses the Pauli Z gate to measure, and the expected value of the measurement result is input to the next layer to extract useful information from the quantum circuit. The experimental results on the MNIST, FASHION-MNIST and CIFAR datasets show that the HQLSTM model achieves higher image classification accuracy and lower loss value than the classical LSTM model and quantum LSTM model. At the same time, the network space complexity of HQLSTM and quantum LSTM are significantly reduced compared with the classical LSTM network.
This research endeavor centers on augmenting the quantum circuitry of the Quantum Support Vector Machine (QSVM), a pivotal algorithm in the realm of quantum machine learning, via a hybrid optimization methodology that amalgamates Quantum Natural Gradient Descent (QNGD) with the Whale Optimization Algorithm (WOA). QSVM harnesses the power of quantum computing to facilitate proficient classification within high-dimensional spaces; however, its efficacy is frequently compromised by suboptimal circuit parameters and quantum noise prevalent in near-term quantum devices. The proposed hybrid optimization paradigm integrates the global search proficiency of WOA with the effective parameter refinement capabilities of QNGD, culminating in expedited convergence (38 iterations), enhanced classification accuracy (96.8%), optimized circuit complexity (44 quantum gates), and increased resilience against noise (fidelity: 0.985). In comparison to conventional optimization techniques such as Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Firefly Algorithm (FA), our methodology demonstrates superior efficacy by refining quantum kernel computation, entanglement configurations, and circuit depth, while concurrently alleviating the impacts of quantum noise.
Classification of quantum data is essential for quantum machine learning and near-term quantum technologies. In this paper, we propose a new hybrid quantum-classical framework for supervised quantum learning, which we call Variational Shadow Quantum Learning (VSQL). Our method in particular utilizes the classical shadows of quantum data, which fundamentally represent the side information of quantum data with respect to certain physical observables. Specifically, we first use variational shadow quantum circuits to extract classical features in a convolution way and then utilize a fully-connected neural network to complete the classification task. We show that this method could sharply reduce the number of parameters and thus better facilitate quantum circuit training. Simultaneously, less noise will be introduced since fewer quantum gates are employed in such shadow circuits. Moreover, we show that the Barren Plateau issue, a significant gradient vanishing problem in quantum machine learning, could be avoided in VSQL. Finally, we demonstrate the efficiency of VSQL in quantum classification via numerical experiments on the classification of quantum states and the recognition of multi-labeled handwritten digits. In particular, our VSQL approach outperforms existing variational quantum classifiers in the test accuracy in the binary case of handwritten digit recognition and notably requires much fewer parameters.
We redesign the parameterized quantum circuit in the quantum deep neural network, construct a three-layer structure as the hidden layer, and then use classical optimization algorithms to train the parameterized quantum circuit, thereby propose a novel hybrid quantum deep neural network (HQDNN) used for image classification. After bilinear interpolation reduces the original image to a suitable size, an improved novel enhanced quantum representation (INEQR) is used to encode it into quantum states as the input of the HQDNN. Multi-layer parameterized quantum circuits are used as the main structure to implement feature extraction and classification. The output results of parameterized quantum circuits are converted into classical data through quantum measurements and then optimized on a classical computer. To verify the performance of the HQDNN, we conduct binary classification and three classification experiments on the MNIST (Modified National Institute of Standards and Technology) data set. In the first binary classification, the accuracy of 0 and 4 exceeds 98%. Then we compare the performance of three classification with other algorithms, the results on two datasets show that the classification accuracy is higher than that of quantum deep neural network and general quantum convolutional neural network.