Pre-trained quantum convolutional neural network for COVID-19 disease classification using computed tomography images

VGG16

The well-known CNN architecture VGG16 (Simonyan & Zisserman, 2014) achieved 92.7% top-5 test accuracy in the ILSVRC 2014 challenge on the ImageNet dataset. It is composed of convolutional, dense, and pooling layers, with 3 × 3 filters for convolutional and 2 × 2 for max pooling, respectively. The model takes in 224 × 224 input images and uses two convolution layers with 64 filters and a max pooling to reduce the output height and width to 112 × 112 × 64. Additionally, two convolutional layers with 128 filters are used, followed by a max pooling layer that lowers the activation size to 56 × 56 × 128. Similarly, a pooling layer that lowers the output activation to 28 × 28 × 256 comes after three convolutional layers with 256 filters. After pooling layers, there are two stacks of three convolutional layers with 512 filters. Next, the output of the last pooling layer, which is 7 × 7 × 512, is accepted by dense layers with 4,096 nodes. One further dense layer with 4,096 nodes comes after the first dense layer. The model’s 1,000-node softmax layer is the last component (Choudhary et al., 2022).

Quantum neural networks

Quantum neural network is a useful tool which has seen more development over the years mainly after twentieth century. Similar to ANNs, QNNs are a new, practical, and usable idea. The quantum computation paradigm, which is superior to the standard ANN, was combined with the fundamentals of ANN to create QNN, which is now superior. QNN is utilized in huge data management, computer gaming, and function approximation, among other applications. QNN algorithms find use in the modeling of social networks, automated control systems, and associative memory devices, among other domains (Jeswal & Chakraverty, 2019b).

Quantum computing has been demonstrated to be useful for enhanced state approximation and feature representation in quantum machine learning. Quantum computing is expected to play a major role in numerous sectors and has the potential to surpass traditional computers (Watabe et al., 2021). Quantum bits, or qubits, are used in quantum computing, which is inspired by particles in quantum states. Superposition is the capacity of a particle in a quantum state to exist in two states at once (Gultom, 2017). The strategy to tackle this phenomenon is translated into computations with 0,1 or both qubits (Kaye, Laflamme & Mosca, 2006).

Qubit

The essential building units of information utilized in quantum computing are qubits, which are represented by a state vector (Gado & Younes, 2021). Paul Dirac is the creator of the Dirac notation, which is one of the notations used in quantum mechanics. The sign used to identify a vector in Dirac notation is written as follows: (1)${\displaystyle |a〉=ket}$ (2)${\displaystyle 〈a|=bra.}$

Furthermore, these notations will be operated by quantum logic gates. The essential component of quantum information is a quantum bit, or qubit. There are two possible states for this two-level system to exist in.

Gates and operations

Unitary operators, or unitary matrices with respect to a basis, are what quantum gates are known as. In the context of quantum computing, and more specifically the quantum circuit model of computation, a simple quantum circuit that operates on a limited number of qubits is called a quantum logic gate, or simply a quantum gate. The fundamental components of quantum circuits are classical logic gates, just as they are the fundamental components of conventional digital circuits. A group of qubits (i.e., objects having a Qid) can be subjected to an effect called a gate. Qubits can have gates applied to them by either calling the gate on the qubits themselves or by calling the gate on their method. An operation is the object that is produced by these calls.

Circuit

A Circuit is made up of many Moments. A Moment is a collection of Operations that occur inside the same imaginary time interval. An operation is an effect that modifies a certain subset of qubits; gate operations are the most prevalent kind of operations. The structure of the circuit is shown in Fig. 1.

CNN vs QCNN architecture

Classical neural networks are mathematical models that may be taught to identify patterns in data and figure out complicated problems. They are inspired by the human brain. Their foundation is made up of a network of linked nodes, or neurons, arranged in layers and having parameters that may be taught through the use of deep learning or machine learning training techniques.

The goal of quantum machine learning (QML) is to create new and improved learning schemes by fusing ideas from conventional machine learning with quantum computing. By fusing parametrized quantum circuits with conventional neural networks, QNNs implement this general idea. QNNs are observed from two perspectives since they are located at the intersection of two fields:

• From a machine learning perspective, QNNs are analogous to their classical counterparts in that they are algorithmic models that can be trained to uncover hidden patterns in data. With the use of quantum gates that are trained using weights that can be adjusted, these models are able to load classical data (inputs) into a quantum state. The procedures for importing and processing data are depicted in a generic QNN example in Fig. 1. To train the weights using backpropagation, the output obtained from monitoring this state can thereafter be fed into a loss function.

• QNNs are quantum algorithms that are built on parametrized quantum circuits and may be trained variationally using classical optimizers, according to the theory of quantum computing. As shown in Fig. 2, these circuits include an ansatz (with trainable weights) and a feature map (with input parameters).

• Fig. 2: Generic quantum neural network structure (Treinish, 2023), showing three stages: (1) Data Loading (Feature Map), (2) Data Processing (Ansatz), and (3) Measurement (Treinish, 2023)

Based on quantum computing, the QCNN is an advancement of the CNN. The primary characteristics and architectures of CNNs are extended into quantum systems by QCNN (Oh, Choi & Kim, 2020).

The integration of the QNN component with the classical neural network architecture is facilitated by the Qiskit framework, a comprehensive open-source quantum computing development platform developed by IBM. Qiskit provides a robust set of tools for quantum circuit design, simulation, and execution on quantum hardware. Utilizing the Qiskit framework and EstimatorQNN, it incorporates quantum circuit-based operations for enhanced data processing. The feature map and ansatz circuits define the quantum layer’s structure, facilitating data encoding and processing in a quantum format. These circuits are composed into a single quantum circuit object, which is then configured within the EstimatorQNN class. This class enables gradient computation with respect to input data and parameters, crucial for model training. Integrated seamlessly into the classical neural network architecture via the TorchConnector wrapper, the QNN enhances the model’s computational capabilities, potentially improving its ability to capture complex patterns in image data.

Dataset

In this study, we make use of the SARS-CoV-2 dataset of COVID-19 CT-scan images, which Soares et al. (2020) made available. This dataset includes 2,482 CT-scan images taken from hospitals in Sao Paulo, Brazil. Out of the 2,482 images, 1,252 images belong to the COVID-19 positive class, and 1,230 images belong to the COVID-19 negative class. Both COVID-19 positive and COVID-19 negative images are randomly shown in Fig. 3. The dimension of the images in the dataset is 224 × 224. As shown in Table 1, the dataset was divided into two parts as 80% training and 20% validation. The dataset can be downloaded from this online location (https://www.kaggle.com/plameneduardo/sarscov2-ctscan-dataset).

Data transformation

In order to optimize chest CT-scan pictures for later analysis and classification tasks, the paper’s technique involves a comprehensive data preprocessing phase. This crucial first step guarantees that the dataset is suitably formatted and standardized for use by machine learning algorithms. Critical parameters like the root directory holding the dataset and transformation settings are supplied when the custom dataset is first created. This stage offers a framework that is required for the next preprocessing steps.

Firstly, the images are resized to a uniform size of (256, 256) pixels, ensuring consistency in dimensions across the dataset. This resizing operation is crucial for mitigating discrepancies in image sizes, which can adversely affect model performance during training and inference. The photos are then converted to grayscale while maintaining three channels, which is done in order to minimize computing complexity without sacrificing important image information.

In order to make the preprocessed pictures compatible with PyTorch-based machine learning frameworks, they must finally be transformed into PyTorch tensor format. This conversion makes it possible to handle and manipulate data inside the computational network in an effective manner, which makes it easier to integrate machine learning algorithms. Finally, DataLoader objects are created for both the training and testing datasets with a batch size of 64 and enabling shuffling.

A data loader is a crucial component in machine learning workflows, efficiently managing the loading of large datasets during model training and testing phases. It facilitates batch processing, essential for stochastic gradient descent optimization, by feeding data in manageable portions to the model, leading to faster convergence and better generalization. data loader also seamlessly integrates data augmentation techniques, shuffling, and sampling of the dataset to prevent overfitting and enhance diversity in training examples. Its support for parallelism enables faster loading of batches, leveraging multi-core processors. Moreover, data loader offers flexibility for customizing data loading pipelines, including preprocessing steps and handling different data formats, making it an indispensable tool for streamlining the data pipeline in machine learning tasks. After all data preprocessing, data loader objects are created for both the training and testing datasets with a batch size of 64 and shuffling of inputs.

We improved and normalized the raw picture data so that our neural network model could use it. This was accomplished by implementing several data transformations. Prioritizing the input data in a way that makes learning and inference easier is a critical part of preprocessing, and it will eventually increase the performance of the model in image classification tasks.

The proposed pre-trained QCNN architecture

First, the model uses weights from a large-scale image dataset (ImageNet) to incorporate a pre-trained VGG16 model. Using the generalizable features that VGG16 captures requires completing this step. The feature extractor is created by removing the last two layers of the VGG16 model. These layers typically consist of fully connected layers responsible for making predictions across multiple classes. By removing them, the feature extractor retains the ability to extract high-level features from the input images. Following the feature extractor, the model includes convolutional layers. These layers serve to further process the features extracted by the pre-trained VGG16 model. Each convolutional layer applies filters to the input data, capturing different aspects of the image and progressively extracting more abstract features. After first convolution layer, max pooling is applied. Max pooling reduces the spatial dimensions of the feature maps, retaining only the most important information. This helps in reducing computational complexity and extracting robust features invariant to small translations in the input images. Dropout regularization is applied after the second and fourth convolution layer. Dropout randomly sets a fraction of the input units to zero during training, which helps prevent overfitting by reducing the reliance on any individual neuron. This encourages the model to learn more robust features that generalize better to unseen data. These components enable the model to learn intricate patterns and representations from the input data. Then the output of these layers is flattened and passed through fully connected layers.

One feature that sets the model apart is the incorporation of a QNN. The architecture of the model incorporates quantum computing concepts with the application of this QNN after the second fully connected layer. Flexible tools for encoding classical data and applying quantum operations within the ansatz circuit are provided by Qiskit’s ZZFeatureMap and RealAmplitudes classes. ZZFeatureMap is a quantum feature map that converts classical data to quantum data. The reason for choosing a quantum feature map is to get the quantum advantage. The ZZFeatureMap is a second-order Pauli-Z evolution circuit. Pauli-Z is one of the three Pauli matrices (along with Pauli-X and Pauli-Y). It acts on a single qubit, flipping the sign of the qubit’s state if it is in the $|1〉$ state and leaving it unchanged if it is in the $|0〉$ state. A second-order Pauli-Z evolution circuit is a structured sequence of quantum gates that approximates the evolution of a quantum system under a Hamiltonian consisting of Pauli-Z terms (Havlíček et al., 2019).

The RealAmplitudes circuit is a heuristic trial wave function used as “ansatz” in chemistry applications or classification circuits in machine learning. In quantum computing, the term “ansatz” refers to a trial wave function or trial state used as a starting point for approximations or optimizations. In quantum computing, an “ansatz” is a specific form or structure for a quantum state or circuit, often used in variational algorithms. The RealAmplitudes class in Qiskit is a common ansatz used in variational quantum algorithms, such as the Variational Quantum Eigensolver (VQE) or Quantum Approximate Optimization Algorithm (QAOA) (Aleksandrowicz et al., 2019; Qin, 2023).

Gradient-based training is made easier with Qiskit’s EstimatorQNN class, which contains the entire QNN. The Estimator QNN (Gonaygunta et al., 2024) is a neural network that takes in a parametrized quantum circuit with designated parameters for input data and weights and outputs their expectation values. Quite often, a combined quantum circuit is used. Such a circuit is built from two circuits: a feature map (ZZFeatureMap), which provides input parameters for the network, and an ansatz (RealAmplitudes). This QNN component applies quantum operations to the output of the fully connected layers and makes predictions.

A final linear layer that produces the binary classification output completes the architecture. The model produces two values that represent the probability that each input belongs to a class. A concatenation operation is then used to combine the results.

The flowchart shown in Fig. 4 outlines pipeline for classifying CT-scan images as either COVID or non-COVID for our proposed model. The first step in the procedure is the acquisition of CT scan pictures, which are then preprocessed by resizing and formatting them appropriately. After that, the dataset is loaded using a DataLoader and split into training and testing sets. Then this data is fed to our model which includes the mentioned layers such as feature extraction by VGG16, basic CNN model and a QNN. Finally, our model generates the output.

The overarching goal of this unique architecture, which is shown in Fig. 5, is to capitalize on the strengths of both classical deep learning and quantum computing. Combining these methods should improve the model’s capacity to identify COVID-19-like patterns in medical images, potentially improving the accuracy and efficiency of COVID-19 detection models.

Performance metrics

The models’ performance was verified using the common assessment measures. The experiments used accuracy, precision, recall, specificity and F1-score as assessment measures. The following equations establish the various assessment metrics: FN stands for false negatives, TN for true negatives, TP for true positives, and FP for false positives. (3)${\displaystyle Accuracy=\frac{TP+TN}{TP+TN+FP+FN}.}$

Accuracy: Accuracy in classification is a metric that quantifies the proportion of correctly classified instances out of the total number of instances in the dataset. It is the most extensively used assessment metric to evaluate the classification performance and it is provided by this formula:

Precision: Precision in classification is a measure that quantifies the accuracy of positive predictions made by a classifier. It represents the ratio of true positive predictions to the total number of positive predictions made by the classifier, regardless of the actual class of the instances. Precision is calculated using this formula: (4)${\displaystyle Precision=\frac{TP}{TP+FP}.}$ Recall: Recall in classification, also known as sensitivity or true positive rate, measures the ability of a classifier to correctly identify all relevant instances, or the proportion of true positive instances that were correctly identified by the classifier. It is calculated using this formula: (5)${\displaystyle Recall=\frac{TP}{TP+FN}.}$

Specificity: Specificity in classification, also known as true negative rate, measures the ability of a classifier to correctly identify all negative instances. It quantifies the proportion of true negative instances that were correctly identified by the classifier out of all actual negative instances. Specificity is calculated using this formula: (6)${\displaystyle Specificity=\frac{TN}{TN+FP}.}$

F1-score: The F1-score is a metric that combines precision and recall into a single value, providing a balance between the two measures. It is calculated using the harmonic mean of precision and recall, giving equal weight to both metrics. The formula for calculating the F1-score is: (7)${\displaystyle F1-Score=2\times \frac{Precision\times Recall}{Precision+Recall}.}$

Confusion matrix: A confusion matrix is a table that summarizes the performance of a classification model by displaying the counts of true positive (TP), true negative (TN), false positive (FP), and false negative (FN) predictions made by the model on a dataset. It is a square matrix where rows represent the actual classes and columns represent the predicted classes. The main diagonal of the matrix contains the counts of correct predictions (TP and TN), while off-diagonal elements represent incorrect predictions (FP and FN). The confusion matrix provides insights into the classification performance, helping to evaluate the model’s accuracy, precision, recall, and other metrics.

Loss function: A crucial part of machine learning models is the loss function, which measures the difference between expected and actual values to determine how well the model performed during training. It is essential for directing the optimization process in the direction of reducing this difference and raising the accuracy of the model. In this study we used Cross-entropy loss function. Cross-entropy loss, also known as log loss, is a widely used loss function in classification tasks, particularly in scenarios involving multiple classes. It quantifies the difference between the predicted probability distribution and the actual distribution of class labels. Mathematically, for a classification problem with N samples and K classes, where y_ik denotes the true label (1 if sample i belongs to class k, 0 otherwise) and p_ik denotes the predicted probability of sample i belonging to class k, the cross-entropy loss is given by: (8)${\displaystyle Cross-EntropyLoss=-\frac{1}{N}\sum _{i=1}^N\sum _{k=1}^K{y}_{ik}log\left(p_{ik}\right).}$

The loss penalizes incorrect predictions more heavily, especially when the predicted probability diverges significantly from the true label. This property encourages the model to assign high probabilities to the correct class labels.

Accuracy per epoch graph: This graph displays the accuracy of a machine learning model on both the training and validation data over multiple epochs during the training process. Each epoch represents one complete pass through the entire training data. The accuracy per epoch graph typically has the number of epochs on the x-axis and the accuracy on the y-axis. It consists of two lines or curves: one representing the accuracy on the training data and the other representing the accuracy on the validation data. Monitoring accuracy per epoch helps assess how well the model is learning from the training data and generalizing to unseen data.

Loss per epoch graph: This graph illustrates the loss, also known as the error or cost, of a machine learning model on both the training and validation data across multiple epochs during training. The loss per epoch graph usually has the number of epochs on the x-axis and the loss value on the y-axis. Similar to the accuracy per epoch graph, it comprises two lines or curves: one representing the loss on the training data and the other representing the loss on the validation data. The loss per epoch graph provides insights into the convergence and performance of the model during training, with lower loss values indicating better model fit.

Experimental results

The performance of the proposed model evaluated on SARS-CoV-2 CT dataset is discussed in this section. In this study, first we trained the dataset on pretrained models including ResNet50, ResNet18, VGG16, VGG19 and EfficientNetV2L and then the QCNN model was combined with these models for comparison. Table 3 provides a comparative analysis of various evaluation metrics across the mentioned models, offering insights into their respective performance and effectiveness. Out of all the models that were examined, the VGG16 model performed the best and showed remarkable results. The proposed model achieved 96.78% accuracy, 0.9837 precision, 0.9528 recall, 0.9835 specificity, 0.9678 F1-Score and 0.1373 loss. Figure 6 illustrates the accuracy per epoch graph, loss per epoch graph and confusion matrix, respectively.

The graphs collectively demonstrate the high performance and reliability of the model. The accuracy per epoch graph shows a rapid increase in training accuracy, with the validation accuracy closely following, indicating effective learning and minimal overfitting. The loss per epoch graph reveals a steady decrease in both training and validation loss, which signifies good generalization. The confusion matrix further highlights the model’s efficacy, showcasing its high accuracy and reliability in classifying the data correctly.

Table 4 is a comparison between different approaches of QCNN models across different studies, providing an overall insight about their approach, dataset used and results gained.

As mentioned earlier feature extraction is a crucial step in the process of capturing high level features of images. Figure 7 illustrates the feature extraction process of the VGG16 model applied to CT scan samples from both COVID-19 and non-COVID patients. In Fig. 7A, the COVID samples display various stages of convolutional layers, progressively highlighting distinctive patterns and textures within the chest images, essential for identifying COVID-19 related anomalies. Similarly, Fig. 7B shows the feature extraction for non-COVID samples, where different convolutional layers capture unique structural and textural features of healthy or non-COVID-affected lungs. The comparison between the two sets reveals how the VGG16 model distinguishes between COVID-19 and non-COVID cases by extracting and emphasizing different sets of features at each convolutional layer, enabling accurate classification based on the learned representations of the lung tissues.

These extracted features fed to the QCNN model to classify the image. Figure 8 demonstrates the model’s prediction ability in recognizing COVID-19 from chest CT scan images. Predictions are labeled above each image, and the model distinguishes between COVID-19 and non-COVID cases accurately. While the second and fifth images are correctly categorized as non-COVID, the first, third, and fourth images are correctly identified as COVID. This demonstrates the model’s effectiveness and reliability in assisting medical professionals with accurate diagnosis of COVID-19 based on chest CT scans.

We evaluated the model on multiple datasets to enable a more thorough investigation of the performance of our suggested model. Details of each dataset, including the total number of photos, the number of covid and non-covid images, and the accuracy of our model tested on each dataset, including SARS-CoV-2, are shown in Table 5. COVID-19 Lung CT Scans dataset (https://www.kaggle.com/datasets/luisblanche/covidct) contains 746 CT-scan images, which are collected from COVID-19-related papers from medRxiv, bioRxiv, NEJM, JAMA, Lancet, etc. The COVID-19 Lung CT Scans dataset (Aria et al., 2021) includes 8439 images gathered from actual patients in teaching hospitals’ radiology departments in Tehran, Iran. The COVID-19 X-ray and CT Scan Image (https://www.kaggle.com/datasets/ssarkar445/covid-19-xray-and-ct-scan-image-dataset) is a large dataset that includes both CT and X-ray images. We analyzed the CT images because our model was trained on them, and the multisource dataset contains 8055 CT-scan images and 9544 X-ray images. The Covid 19 CT Scan Dataset (https://www.kaggle.com/datasets/drsurabhithorat/covid-19-ct-scan-dataset) is a collection of 7621 CT images. In comparison to previous datasets, the SARS-CoV-2 dataset (https://www.kaggle.com/plameneduardo/sarscov2-ctscan-dataset) has demonstrated superior performance and data balancing. Overall, the model shows good results on tested dataset too.