An Image Classification Method Based on a Hybrid Quantum Neural Network Model with PQC

Abstract

This invention discloses an image classification method based on a hybrid quantum neural network model using PQC, belonging to the field of quantum computing technology. Based on the classical neural network structure, this invention replaces the classical convolutional layers with parameterized quantum circuits, reducing the number of trainable parameters in the network structure. Furthermore, a designed entanglement structure Ub is added to the parameterized quantum circuit to improve the feature extraction capability and the overall learning efficiency of the network. Utilizing the hybrid quantum neural network architecture, a corresponding entanglement structure Ub is designed based on given label samples and applied to the parameterized quantum circuit. This structure is then combined with a classification module composed of a classical matrix-product state network structure, continuously improving the feature extraction capability of the parameterized quantum circuit structure and enhancing the overall network performance, thereby achieving better classification results. Prediction is performed on a test set to evaluate the model's performance. Finally, classical optimization methods are used to optimize and iteratively update the parameters in the model, resulting in a hybrid quantum neural network structure with superior performance. Compared to existing network structures, this method achieves a significant performance improvement.

Description

Technical Field

[0001] This invention relates to the field of image classification, and more specifically, to an image classification method based on a hybrid quantum neural network model using a parameterized quantum circuit. Background Technology

[0002] Image classification is a fundamental problem in computer vision, and machine learning models, represented by deep convolutional neural networks (CNNs), have become the mainstream technology for solving such problems. Like other neural network models, it does not require manually designed feature operators, achieving end-to-end learning. Its basic structure generally consists of multiple convolutional layers, pooling layers, and fully connected layers, capable of automatically learning extremely complex hierarchical features from massive amounts of data. For example, in the recognition and classification of handwritten digit datasets, using convolutional neural networks to automatically extract complex features can achieve a classification accuracy of over 90%.

[0003] To address the issue of insufficient refinement in upsampling methods of convolutional neural networks (CNNs), this paper improves the model structure and enhances its understanding of multidimensional information in the scene through optimization techniques such as data augmentation, multi-scale fusion, self-attention mechanisms, and additional features (elevation information, vegetation index, and spectral features). This significantly improves the model's ability to capture features from samples. Common CNNs, such as fully convolutional networks (FCNs), U-nets, and generative adversarial networks (GANs), have become ideal models for various image classification tasks, demonstrating enormous potential in image classification.

[0004] Despite the tremendous success of convolutional neural networks, some challenging problems remain in classification. The main reasons are as follows:

[0005] (1) Images are diverse, covering various objects that differ significantly in size, color, position, and orientation. Spectral characteristics alone are often insufficient to effectively distinguish these objects; therefore, spatial location information and other features are also needed for identification. Thus, combining rich spectral information with spatial features to complement each other and significantly improve the performance of deep learning models in image classification tasks has become a key research direction.

[0006] (2) In practical applications, it is often difficult to obtain a large number of labeled datasets. This is not only due to the insufficient amount of data, but also to the challenge of accurately defining category labels for the dataset. At the same time, current complex deep neural networks usually require setting a large number of hyperparameters, resulting in an overly complex network structure that is difficult to optimize effectively. Therefore, using a small amount of dataset to train a deep neural network can easily lead to overfitting.

[0007] (3) While the current "end-to-end" learning strategy has enabled deep learning to achieve excellent performance in classification tasks, the prediction logic behind it is difficult to explain. In addition to the final output, understanding the reasoning process inside the network becomes very difficult, which also poses a challenge to the in-depth analysis and processing of image classification tasks.

[0008] Considering the above points, we designed a hybrid quantum neural network model to replace the traditional convolutional neural network built with scalar neurons and convolutional kernels. The hybrid quantum neural network model combines a parameterized quantum circuit containing a designed entangled structure Ub with a matrix product state. Its output is a high-dimensional vector that can represent various attribute information of an entity, such as attitude, illumination, and deformation. The magnitude of the vector represents the probability of the entity's occurrence; the larger the magnitude of the high-dimensional vector, the greater the probability of the entity's existence. The vector can represent the orientation and spatial relative relationships of ground objects, greatly compensating for the shortcomings of convolutional neural networks. The training method of the hybrid quantum neural network mainly uses the classic Adam optimization method. With a network structure containing fewer trainable parameters, it can improve the model's learning efficiency and prediction robustness while reducing the required number of samples. Summary of the Invention

[0009] The technical problem this invention aims to solve is: how to effectively solve the image classification problem in the field of computer vision and improve the structural performance of the network model. It provides an image classification method based on a hybrid quantum neural network model. First, pooling operations are used to obtain a compressed image of primary features. Then, parameterized quantum circuits are used to further extract high-level features. The expected value measured by each quantum circuit is used as a tensor in the input node of the matrix product state network. This tensor is then condensed with parameter nodes containing trainable parameters to obtain a predicted classification vector. A softmax function is then applied to output the probability distribution of the class. Finally, the Adam optimizer is used to calculate and update the gradients of the parameters in the entire hybrid quantum neural network, further improving and optimizing the overall network performance and the model's generalization ability, thus finding a superior performance structure.

[0010] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0011] Step S1: Perform data preprocessing on the handwritten dataset, dividing the preprocessed image data into training set data and validation set data;

[0012] Step S2: Using parameterized quantum circuits as the basic network architecture, integrate matrix multiplication state models to establish a hybrid quantum neural network model;

[0013] The hybrid quantum neural network model includes:

[0014] The compression processing module includes a convolutional layer and a pooling layer. The convolutional layer is used to extract primary features from the input handwritten image. The pooling layer is used to process the primary features extracted by the convolutional layer and transform them into a smaller feature map.

[0015] The parameterized quantum circuit module includes an encoding layer, an entanglement layer, and a measurement layer. The entire module is composed of an alternating encoding layer (RY gate) and an entanglement layer (CX gate), and finally a measurement layer is applied to the quantum circuit. The entire parameterized quantum circuit module is used to perform high-level feature extraction on the feature map obtained by the compression processing module.

[0016] The classification module includes a matrix multiplication state structure, which includes multiple tensor nodes. The dimensions of these multiple tensor nodes are mainly used to calculate the shrinkage of the input feature values ​​and weight parameters, and finally calculate the shrinkage vector with a dimension of the number of classes, which is used to calculate the predicted probability of each class instance.

[0017] Step S3: Train the hybrid quantum neural network model using the training set data and the validation set data to obtain the trained hybrid quantum neural network model;

[0018] Step S4: Classify the image data to be classified using the trained hybrid quantum neural network model.

[0019] Furthermore, step S1 also includes a preprocessing method using pooling compression, which takes the original 28×28 grayscale image and performs an average pooling operation with a kernel size of 6 to obtain a compressed feature map containing the primary features.

[0020] Furthermore, step S2 also includes the selection and design of the entanglement structure in the parameterized quantum circuit module, mainly the use of two entanglement structures. The first selection is the CX dual quantum gate, whose corresponding matrix form is as follows:

[0021]

[0022] The second structure is the entanglement structure Ub designed for selected sample labels, and its design process is as follows:

[0023] Input: A 28x28 normalized pixel matrix

[0024] Output: Entanglement module Ub

[0025] Process steps:

[0026] 1. Obtain a processing matrix U with a size of 4x4.

[0027] % Perform pooling compression on the pixel matrix, reducing the 28x28 dimension to 4x4.

[0028] 2. Construct a binary matrix B.

[0029] By setting a threshold or applying a mask, matrix U is processed to obtain binary matrix B.

[0030] 3. Calculate the symmetric matrix V and generate the undirected graph G:

[0031] V = B * B^T

[0032] % Calculate the autocorrelation matrix of V and map it to an undirected graph G.

[0033] 4. Construct matrix Hb based on undirected graph G:

[0034]

[0035] %Dj represents the number of edges between node j and its neighboring nodes.

[0036] 5. Construct matrix Ub based on matrix Hb:

[0037]

[0038] %γ ζ This is the adjustment parameter used in the experiment, set to 1.

[0039] Return: Ub.

[0040] Furthermore, step S2 also includes a parameter node update method in the classification module, which, like the parameter update method in the quantum circuit part, uses the Adam optimizer to perform gradient calculation and parameter iterative update.

[0041] Furthermore, step S3 also includes a step of verifying the hybrid quantum neural network model using the verification set data, including setting a given threshold or stopping the training iteration when the maximum number of iterations is met, thus completing the training of the hybrid quantum neural network model.

[0042] Furthermore, in steps S3 and S4, the hybrid quantum neural network model employs a parameterized quantum circuit with an entangled layer Ub containing specified sample labels, enabling the primary features to be extracted layer by layer to obtain higher-level features. For the same type of label sample input, the same quantum circuit structure is used for the network's forward propagation computation.

[0043] Furthermore, in steps S3 and S4, the hybrid quantum neural network model employs a parameterized quantum circuit with an entangled layer Ub containing specified sample labels, enabling the primary features to be extracted layer by layer to obtain higher-level features. The output of the measurement layer of the quantum part network is used as the tensor form of the input node in the matrix multiplication state structure of the classical part, and then the forward computation of the matrix multiplication state network part is performed. Finally, the model performance is evaluated. The model evaluation has two criteria: the first is the convergence of the loss function, the corresponding mathematical form of which is as follows:

[0044]

[0045] Where M represents the number of categories, i is the index of the training set sample, and y c It is a one-hot encoded real label vector of length M. This is a probability distribution vector of length M obtained after model prediction, where each element represents the probability that the model predicts the data to be of class c. Another evaluation criterion is the accuracy of the model's predictions, which has the following mathematical form:

[0046]

[0047] Where, N test This indicates the number of samples in the test set, where j is the index of a sample in the test set. This represents the index of the sample j to predict and return the maximum value of the prediction result, y. c This represents the true label of sample j. Therefore, When the result is true, it means that the model's prediction of sample j is consistent with the true label.

[0048] The present invention has the following advantages over the prior art:

[0049] (1) Under the hybrid quantum neural network structure, although the convergence result of the loss function in the final evaluation and the prediction accuracy of the final training robust model are comparable to the performance of the classical network structure, the improvement of the prediction accuracy of the hybrid quantum neural network model and the convergence rate of the corresponding loss function are faster than those of the convolutional neural network.

[0050] (2) With fewer trainable parameters in the overall network model, the sub-network of the quantum part we designed, namely the parameterized quantum circuit, has a stronger ability to extract structural features than the classical convolutional layer, and the overall model has higher learning efficiency.

[0051] (3) The entanglement module Ub designed for given sample labels improves the network structure performance in the PQC structure. This results in slightly better convergence of the model training loss function, a faster convergence rate, and, more importantly, higher prediction accuracy with lower time costs. This further confirms the feasibility of our structural design approach. Attached Figure Description

[0052] Figure 1 This is the network architecture of a hybrid quantum neural network based on PQC in this embodiment of the invention;

[0053] Figure 2 This is the structure of the parameterized quantum circuit in the embodiments of the present invention;

[0054] Figure 3 This is a schematic diagram illustrating the performance of the entangled structure Ub designed in this embodiment of the invention;

[0055] Figure 4 This is a schematic diagram comparing the performance of the present invention with that of a classic convolutional neural network in an embodiment of the invention. Detailed Implementation

[0056] The embodiments of the present invention will be described in detail below. These embodiments are implemented based on the technical solutions of the present invention, and detailed implementation methods and specific operation processes are given. However, the scope of protection of the present invention is not limited to the following embodiments.

[0057] This invention uses handwritten digit recognition data from MNIST to experimentally solve the image binary classification problem. It provides an image classification method based on a hybrid quantum neural network model using PQC, comprising: Step S1: First, the original samples are processed into feature maps containing primary features using a compression method; Step S2: Using the entangled module structure Ub designed for samples with given labels, and the combination of matrix product states and parameterized quantum circuits, an image classification method based on a hybrid quantum neural network model using PQC is constructed; Step S3: The hybrid quantum neural network model is trained using the training set data and the validation set data to obtain a trained hybrid quantum neural network model; Step S4: The trained hybrid quantum neural network model is used to classify the image data to be classified.

[0058] Data preprocessing

[0059] This invention utilizes the MNIST handwritten digit dataset for experiments. This dataset contains 70,000 samples, with 60,000 used for training and 10,000 for testing. Each sample is a 28×28 pixel grayscale image representing a handwritten digit. Based on this dataset, we benchmark different network architectures to evaluate model performance. Before inputting image data into the network for training, we perform preliminary feature extraction and scale compression. For this purpose, we employ average pooling with a kernel size of 6 to preprocess the original grayscale images. This step helps reduce data dimensionality, improving the network's training efficiency and generalization ability.

[0060] Establishment of a hybrid quantum neural network model based on PQC

[0061] This invention proposes a hybrid quantum neural network model based on PQC for image classification. In image classification, both parameterized quantum circuits (PQC) and convolutional layers in convolutional networks act as filters to extract features; therefore, hybrid neural networks containing PQC structures are also called quantum convolutional neural networks. In classical convolutional neural networks, feature extraction is mainly handled by convolutional layers, which extract spatial features of the image through a mechanism of local receptive fields and weight sharing. Our hybrid quantum classical convolutional neural network architecture based on parameterized quantum circuits (PQC) improves upon classical convolutional neural networks in two main ways: First, it replaces convolutional layers with parameterized quantum circuits (PQC) and applies an entanglement structure Ub constructed for a given label. This part of the architecture typically involves fewer parameters because each parameterized quantum gate involves a specific parameter, and the effect of each gate is limited to a single or two qubits. This locality helps to effectively reduce the number of parameters required. Second, matrix product states (MPS), as an efficient tensor network structure, are introduced in image classification tasks to replace pooling layers and fully connected layers in classical convolutional neural networks (CNNs). Pooling layers typically reduce spatial dimensionality and mitigate the risk of overfitting through dimensionality reduction operations. However, pooling operations (especially when the kernel scale is inappropriately chosen) can lead to significant information loss, reducing the accuracy of feature extraction and the final performance of the model. Fully connected layers classify high-dimensional features by mapping them to a fixed-dimensional space, but they have a large parameter scale and high computational cost. In contrast, Matrix Product States (MPS) compress high-dimensional data while preserving its core information by transforming the input tensor into a low-rank representation. The advantage of MPS lies in its ability to progressively capture long-range correlations through local tensor operations, avoiding excessive information loss during pooling and enabling more efficient data compression. This advantage of MPS is further enhanced by combining it with quantum circuits. Specifically, the quantum states in the quantum circuit, after multiple entanglements and evolutions, provide the ability to recognize complex patterns in the input data, while MPS achieves an efficient mapping from the quantum states to the final classification output. Therefore, combining MPS with quantum circuits not only eliminates the need for pooling operations and fully connected layers in the traditional CNN framework, but also improves the model's performance in classification tasks by preserving key data features.

[0062] See Figure 1 and Figure 2The image classification model based on a PQC hybrid quantum neural network model of the present invention includes: a compression processing module, which includes convolutional layers and pooling layers. The convolutional layers are used to extract primary features from the input handwritten image; the pooling layers are used to pool the primary features extracted by the convolutional layers and transform them into a smaller-scale feature map; a parameterized quantum circuit module, which includes an encoding layer, an entanglement layer, and a measurement layer. The entire module is composed of an alternating encoding layer and an entanglement layer, and finally a measurement layer is applied to the quantum circuit. The entire parameterized quantum circuit module is used to perform high-level feature extraction on the feature map obtained by the compression processing module; and a classification module, which includes a matrix multiplication state structure. The matrix multiplication state structure includes multiple tensor nodes. The dimensions of these multiple tensor nodes are mainly used to calculate the shrinkage of the input feature values ​​and weight parameters, and finally calculate a shrinkage vector with a dimension equal to the number of classes, which is used to calculate the predicted probability corresponding to the instance of each class.

[0063] According to an optional embodiment of the present invention: in the comparative experiment, the CNN structure used has 1 input channel, 2 output channels, and a kernel size of 3×3. Therefore, the total number of parameters in the convolutional layer is 18 without considering bias terms. However, the designed quantum convolutional layer (i.e., parameterized quantum circuit) uses only 4 qubits, interleaving single-quantum rotation gate Ry(θ) and double-quantum CNOT gates in 4 layers. Thus, the total number of parameters in the entire PQC is n×d (where n is the number of qubits and d is the interleaving depth of the parameterized circuit), which is less than the total number of parameters in the corresponding structural part compared to a classical convolutional layer.

[0064] Model training and validation

[0065] The runtime environment of this invention uses PyTorch and the quantum machine learning framework TorchQuantum. TorchQuantum is an open-source library based on PyTorch, focused on accelerating quantum computing. This library provides additional libraries and modules, enabling users to easily build, optimize, and deploy quantum-classical applications. To build a hybrid network model, we implemented the classical module using PyTorch and the quantum module using TorchQuantum. We optimized the parameters of the quantum circuit using classical optimization algorithms (such as gradient descent and Adam). In this process, we called the PyTorch interface to calculate the gradient of the quantum part and performed backpropagation to update the parameters. Each model was trained from scratch using the Adam optimizer with a training batch size of 256 samples and a learning rate of 0.005, iterating for 10 rounds. Furthermore, we used a cosine-based learning rate annealing strategy, CosineAnnealingLR, to periodically adjust the learning rate with each training round, improving the model's generalization ability.

[0066] Classification

[0067] In the classification phase, the trained PQC-based hybrid quantum neural network model is used to classify the test sample data. Matrix product states (MPS) are utilized to transform the input tensor into a low-rank representation, compressing high-dimensional data while preserving its core information. The advantage of MPS lies in its ability to progressively capture long-range correlations through local tensor operations. This serves as the final classification layer.

[0068] According to an optional embodiment of the present invention, four input tensor nodes are selected as classical value inputs after the quantum convolutional layer measurement is completed, and they are condensed and calculated with three trainable parameter tensor nodes to finally obtain a classification vector of dimension L, corresponding to the category prediction value of each label.

[0069] Evaluation methods

[0070] This invention will conduct comparative experiments on two different network models, selecting the classic CNN network structure and its improvements and structural innovations. Convolutional Neural Networks (CNNs) extract features through operations such as convolution and pooling, mapping data to a high-dimensional feature space, and then classifying or regressing these features through fully connected layers. Their core characteristics include weight sharing and local connectivity, which give CNNs a significant advantage in processing spatially structured data such as images. See also... Figure 3 This mainly compares the performance of the entangled Ub structure with and without Ub in the main hybrid network structure HQCNN. (See also...) Figure 4 In another set of experiments, we proposed a hybrid quantum convolutional network structure, HQCNN (PQC+MPS), corresponding to CNN. This structure primarily uses a designed parameterized quantum circuit structure as a sub-network of the quantum part for forward computation, replacing the classical convolutional and pooling network forward propagation. This is combined with a classification layer constructed from matrix multiplication states (a sub-network of the classical part). Finally, we selected the convergence of the loss function (Loss) and the accuracy of the model's predictions on the test set as evaluation metrics to assess and compare our proposed framework structure with classical network structures. The loss function (Loss) is a function commonly used in machine learning to evaluate the difference between model predictions and actual values. Specifically, in image classification problems, the loss function measures the degree of inconsistency between the model's predicted image category and the actual label. The equation is as follows:

[0071]

[0072] Accuracy, the accuracy of model predictions, is one of the important metrics for evaluating the overall performance of a model. It represents the proportion of samples that are correctly classified out of the total number of samples, as shown in the following equation:

[0073]

[0074] In summary, this invention discloses an image classification method based on a hybrid quantum neural network model. First, pooling operations are used to obtain a compressed image of primary features. Then, parameterized quantum circuits are used to further extract higher-level features. The expected value measured by each quantum circuit is used as a tensor in the input node of the matrix product state network. This tensor is then condensed with parameter nodes containing trainable parameters to obtain a predicted classification vector. A softmax function is then applied to output the probability distribution of the class. Finally, the Adam optimizer is used to calculate and update the gradients of the parameters in the entire hybrid quantum neural network, further improving and optimizing the performance of the entire network and the generalization ability of the model, thus finding a more optimal performance structure.

[0075] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. An image classification method based on a hybrid quantum neural network model using PQC, comprising: Step S1: Perform data preprocessing on the handwritten dataset, dividing the preprocessed image data into training set data and validation set data; Step S2: Using parameterized quantum circuits as the basic network architecture, integrate matrix multiplication state models to establish a hybrid quantum neural network model; The hybrid quantum neural network model includes: The compression processing module includes a convolutional layer and a pooling layer. The convolutional layer is used to extract primary features from the input handwritten image. The pooling layer is used to process the primary features extracted by the convolutional layer and transform them into a smaller feature map. The parameterized quantum circuit module includes an encoding layer, an entanglement layer, and a measurement layer. The entire module is composed of an alternating encoding layer and an entanglement layer, and a measurement layer is applied at the end of the quantum circuit. The entire parameterized quantum circuit module is used to perform high-level feature extraction on the feature map obtained by the compression processing module. The classification module includes a matrix multiplication state structure, which includes multiple tensor nodes. The dimensions of these multiple tensor nodes are used to calculate the shrinkage of the input feature values ​​and weight parameters, and finally calculate the shrinkage vector with a dimension equal to the number of classes, which is used to calculate the predicted probability of each class instance. Step S3: Train the hybrid quantum neural network model using the training set data and the validation set data to obtain the trained hybrid quantum neural network model; Step S4: Classify the image data to be classified using the trained hybrid quantum neural network model; In steps S3 and S4, the hybrid quantum neural network model employs a parameterized quantum circuit, where the entangled layer Ub contains specified sample labels. This entangled layer extracts the primary features to obtain higher-level features for quantum convolution operations. After the module completes the measurement, its output serves as the input node tensor in the matrix multiplication state structure, followed by the forward computation of the matrix multiplication state network part, and finally, the model's performance is evaluated. The model evaluation has two criteria: the first is the convergence of the loss function, the corresponding mathematical form of which is as follows: ; in, Represents the number of categories, It is the index of the training set samples. It is a length of The one-hot encoded true label vector, The length after model prediction is The probability distribution vector, where each component represents the predicted data as a category. The probability; another evaluation criterion is the accuracy of the model's predictions, which has the following mathematical form: ; in, This indicates the number of samples in the test set. It is the index of the test set samples; Indicates the sample Perform a prediction and return the index corresponding to the maximum predicted value. Indicates sample The true label; therefore. When the result is true, it means that the model is effective for the sample. The prediction results are consistent with the actual labels.

2. The image classification method according to claim 1, characterized in that: Step S1 also includes a preprocessing method using pooling compression, which takes the original grayscale image with a shape of 28×28 and performs an average pooling operation with a kernel size of 6 to obtain a feature map containing the primary features, and the compressed size is 4×4.

3. The image classification method according to claim 1, characterized in that: Step S2 also includes the selection and design of the entanglement structure in the parameterized quantum circuit module, which involves the use of two entanglement structures. The first selection is the CX dual quantum gate, and its corresponding matrix form is as follows: ; The second structure is the entanglement structure Ub designed for selected sample labels, and its design process is as follows: Input: A 28x28 normalized pixel matrix Output: Entanglement module Ub Process steps: Step 1: Obtain a processing matrix U of size 4x4. % Perform pooling compression on the pixel matrix, reducing the dimension from 28x28 to 4x4. Step 2, construct the binary matrix B. By setting a threshold or applying a mask, matrix U is processed to obtain binary matrix B. Step 3: Calculate the symmetric matrix V and generate the undirected graph G: V = B * B^T % Calculate the autocorrelation matrix of V and map it to an undirected graph G. Step 4, Construct matrix Hb based on undirected graph G: ； % Dj represents the number of edges between node j and its neighboring nodes. Step 5, Construct matrix Ub based on matrix Hb: ; % The adjustment parameter in the experiment is set to 1. Return: Ub.

4. The image classification method according to claim 1, characterized in that: Step S2 also includes the parameter node update method in the classification module, which is the same as the parameter update method in the quantum circuit part. The Adam optimizer is used to calculate the gradient and iteratively update the parameters.

5. The image classification method according to claim 1, characterized in that: Step S3 also includes a step of verifying the hybrid quantum neural network model using the verification set data, including setting a given threshold or stopping the training iteration when the maximum number of iterations is met, thus completing the training of the hybrid quantum neural network model.

6. The image classification method according to claim 1, characterized in that: In steps S3 and S4, the hybrid quantum neural network model employs a parameterized quantum circuit with an entangled layer Ub containing specified sample labels, enabling the primary features to be extracted layer by layer to obtain higher-level features. For the same type of label sample input, the same quantum circuit structure is used for the network's forward propagation computation.

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