=Paper=
{{Paper
|id=Vol-3392/paper15
|storemode=property
|title=Multiclass Image Classification Based on Quantum-Inspired Convolutional Neural Network
|pdfUrl=https://ceur-ws.org/Vol-3392/paper15.pdf
|volume=Vol-3392
|authors=Hamza Kamel Ahmed,Baraa Tantawi,Gehad Ismail Sayed
|dblpUrl=https://dblp.org/rec/conf/cmis/AhmedTS23
}}
==Multiclass Image Classification Based on Quantum-Inspired Convolutional Neural Network==
https://ceur-ws.org/Vol-3392/paper15.pdf
Multiclass Image Classification Based on Quantum‐Inspired
Convolutional Neural Network
Hamza Kamel Ahmeda,b, Baraa Tantawia and Gehad Ismail Sayed a
a
School of Computer Science, Canadian International College (CIC), New Cairo, Egypt
b
Computer Science Department, School of Science and Technology, Troy University, USA
Abstract
Multiclass image classification is considered a challenging task in computer vision that
requires correctly classifying an image into one of the multiple distinct groups. In recent
years, quantum machine learning has emerged as a topic of significant interest among
researchers. Using quantum concepts such as superposition and entanglement, quantum
machine learning algorithms provide a more efficient method of processing and classifying
high-dimensional image data. This paper proposes a new image classification model using
quantum-inspired convolutional neural network architecture or, shortly, QCNN. The
proposed model consists of two main phases; pre-processing and classification based on the
QCNN phase. Seven benchmark datasets with different characteristics are adopted to
evaluate the performance of the proposed model. The experimental results revealed that the
proposed QCNN outperformed its classical version. Additionally, the results demonstrated
the effectiveness of the proposed model compared with the state-of-the-art models.
Keywords 1
Quantum Computing, Convolutional Neural Networks, Image Classification, Quantum
Machine Learning
1. Introduction
Convolutional neural networks (CNNs) have experienced rapid expansion in the image
classification and multiclass image classification fields. Which computer vision task requires
categorizing an image into one of many categories? As the number of classes increases, the task's
difficulty increases, and it requires identifying fine-grained details that differentiate between distinct
objects or classes. In recent years, convolutional neural networks (CNNs) have become a popular
solution to this issue. The CNN architecture is designed to mimic the structure of the visual cortex in
humans and animals. It consists of multiple layers of interconnected nodes trained to extract and
identify various image features. The input image is fed to the CNN's first layer, and each successive
layer extracts increasingly complex features. The class with the highest probability is selected as the
predicted class based on the probabilities generated by CNN's output layer.
Although CNNs have been demonstrated to be an effective tool for image classification and
other computer vision tasks, they may not always perform at their best with small datasets [12].
Quantum computing comes into play at this point. Using quantum concepts such as superposition and
entanglement, quantum computing can potentially improve traditional machine-learning techniques
[13]. Notably, it has been demonstrated that quantum machine learning algorithms provide superior
feature selection capabilities than classical methods, enabling more efficient processing and
classification of high-dimensional data [14]. Consequently, a growing interest has been in developing
machine-learning models inspired by quantum mechanics, such as quantum-inspired CNNs [15].
1
The Sixth International Workshop on Computer Modeling and Intelligent Systems (CMIS-2023), May 3, 2023, Zaporizhzhia, Ukraine
EMAIL: hamzakamel.a@gmail.com (H. Ahmed); baraa.tantawi@gmail.com (B. Tantawi); gehad_sayed@cic-cairo.com (G. Sayed)
ORCID: 0000-0003-0895-8873 (H. Ahmed); 0000-0003-1045-579X (B. Tantawi); 0000-0001-9007-916X (G. Sayed)
© 2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org) Proceedings
These models aim to combine the power of convolutional neural networks (CNNs) with the benefits
of quantum computing to improve performance on complex image classification tasks [16]. This
paper proposes a new image classification model based on quantum computing principles, including
entanglement and superposition, in conjunction with the CNN layer. The proposed model comprises
two principal phases: pre-processing and the classification-based quantum convolutional neural
network phase. The original image undergoes image resizing and data normalization during the pre-
processing phase. The processed images are then used as input for the proposed QCNN architecture.
This paper's primary contribution is summarized in the following points:
1. A new QCNN architecture is proposed.
2. The proposed QCNN is applied to the multiclass image classification problem.
3. Seven benchmark datasets are used to evaluate the proposed model.
4. A comparative analysis between the proposed model and state-of-the-art models is considered.
The remainder of the paper's format is as follows: Section 2 presents the related work; Section 3
introduces the overall proposed image classification model based on QCNN in detail; and Section 4
presents and discusses the results of experiments conducted on various datasets using the proposed
QCNN architecture. Section 5 concludes with a summary of the paper's key findings, a discussion of
the limitations of the proposed model, and suggestions for future research directions.
2. Literature review
CNNs have demonstrated efficacy in multi-class image classification by extracting higher-level
image information and outperforming conventional image processing [1]. CNNs' ability to capture
complex image characteristics has led to significant advances in computer vision tasks such as object
recognition [4], semantic segmentation [6], and target detection [8]. Recent studies have proposed
altering CNN's architecture to enhance its performance in multi-class image classification tasks [2].
These alterations are intended to improve the network's precision, reduce computational complexity,
and accelerate the training procedure. These modifications include the addition of skip connections
[3], the use of various activation functions [4], and the incorporation of attention mechanisms [5]. In
numerous studies involving computer vision, CNNs have produced outstanding results. For instance,
some papers [5, 6] focused on target detection. The authors of [5] created a CNN-based infrared dim
small target detection algorithm that proved effective and precise for detecting small targets in
infrared images with low SCR and complex scenes. They incorporated spatially finer, target-oriented
shallow features and semantically more robust deep features.
In contrast, the authors of [6] presented a depth recognition algorithm for robot vision systems
used for apple picking. Using deep learning techniques, the algorithm achieved greater recognition
accuracy and robustness than conventional methods, demonstrating the potential of deep learning in
agricultural robot applications. Other studies [7, 8] have investigated semantic segmentation. The
authors of [7] proposed a multi-receptive-field convolutional neural network (MRFNet) to extract rich
and useful context information from complex and dynamic medical images. On three public medical
image datasets, including SISS, 3DIRCADb, and SPES, the MRFNet demonstrated exceptional
performance. In the study [8], the authors introduced a novel network architecture for thermal image
semantic segmentation called edge-conditioned convolutional neural network (EC-CNN). The end-to-
end-trained EC-CNN generated high-quality segmentation results by incorporating prior edge
knowledge. In addition, they presented a new benchmark dataset, Segmenting Objects in Day and
Night (SODA), to facilitate exhaustive evaluations in thermal image semantic segmentation. In
addition, CNN architectures have demonstrated their effectiveness in image classification, as
demonstrated in [9, 10–11]. Regarding image classification, the authors of [9] proposed the dilated
CNN and the HDC models, demonstrating improved training efficiency and accuracy on the MNIST
dataset and a wide-band remote sensing image dataset. The research in [10] centered on classifying
biological images using inverted residual blocks to replace some CNN modules to address the
increased computational time. The method demonstrated promising performance online on five
benchmark datasets, including two biological IM performances. Lastly, [11] sought to identify an
appropriate architecture for transfer learning and identified Inception-v3 as such. The retrained
Inception-v3 model performed significantly better than previous state-of-the-art works on the CIFAR-
10 dataset. This study's findings demonstrated the utility of transfer learning and paved the way for
future developments in deep neural networks.
Researchers are investigating the potential benefits of combining CNNs with quantum computing
techniques in light of the development of quantum computing. The training and application of
quantum CNNs (QCNNs) have the potential to accelerate significantly. Quantum mechanics enables
QCNNs to perform specific calculations significantly faster than their classical counterparts. As full-
fledged quantum computation is still a distant prospect, the research in [13] discusses the potential of
quantum-inspired (QI) algorithms implemented on classical computers to improve existing machine-
learning techniques. Based on the theory of Quantum State Discrimination (QSD), they developed a
QI algorithm for direct multi-class classification that provides a systematic method for locating sub-
optimal solutions. This strategy enabled them to extend the capabilities of previous QI classifiers,
which were restricted to binary classification, and address general multi-class datasets. In [14], the
authors proposed a novel algorithm for feature selection based on a generalized embedding of
Quadratic Unconstrained Binary Optimization (QUBO), which is executable on both classical and
quantum hardware. They used mutual information as the basis for measures of importance and
redundancy, with an interpolation factor serving as a counterbalance. Experiments comparing
standard feature selection methods and their performance on various machine learning models
demonstrated the effectiveness of the researchers' framework. In addition, they successfully executed
one of their experiments on actual quantum hardware, demonstrating the algorithm's viability and
compatibility with NISQ. Although their experiments were conducted on low-dimensional problems
due to hardware constraints, the authors anticipate that the algorithm will scale with future quantum
computing advancements.
3. The Proposed image classification based on QCNN model
The two primary phases of the proposed image classification model are the pre-processing phase
and the classification based on the QCNN phase. The overall design of the proposed image
classification model is depicted in Figure 1. From this figure, it can be seen that the original images
are first normalized, after which the normalized images are fed into the quantum convolutional layer,
after which a series of classical convolutional layers are applied, followed by a fully connected layer
to obtain the final class. The following sections will go over each part's full description.
Figure 1: The architecture of the proposed image classification model
3.1. Pre‐processing phase
Preparing and transforming the raw dataset into a more acceptable format for subsequent analysis
and modeling is the primary goal of the pre-processing phase. The original images in this study are
downsized to 28x28, and after that, data normalization is applied to all of the images in the dataset.
Data normalization is crucial to improve the effectiveness and interpretability of machine learning
algorithms. Normalization is a method that rescales the input features to a uniform range, usually
between 0 and 1. This standardized range aids in reducing the influence of data distribution and scale
differences, which could otherwise result in biased and less-than-ideal model performance. Each pixel
in the image is normalized in this study by multiplying it by the highest number, 255. Each data point
in the image is effectively scaled down to a value between 0 and 1 when this procedure is done to the
entire dataset's image. The model is made to be less sensitive to the input characteristics' absolute
values and more focused on the underlying patterns and relationships in the data by doing this
normalization.
3.2. Classification based on QCNN phase
This phase feeds the processed image into the quantum convolutional neural network (QCNN).
The quantum and classical components of the proposed QCNN make up its two main components.
The proposed creates a powerful and effective classification system by combining the advantages of
both quantum and conventional methodologies. Next, a detailed description of each part is presented.
3.2.1. Quantum part
The quantum part transforms the input data using the capabilities of quantum computing as a pre-
processing layer. Quantum encoding, convolution, and measurement comprise its three main
components. The block diagram for the quantum part of the proposed QCNN architecture is shown in
Figure 2.
Figure 2: The block diagram of the quantum part of the proposed QCNN
The input data is first embedded into a quantum state during the quantum encoding stage. Nine
qubits total are used in this study. The following equation is commonly used to represent a quantum
state.
|ψ⟩ 1 0 (1)
α|0⟩ β|1⟩ α β
0 1
where |ψ⟩ is the quantum state, α and β are complex coefficients or amplitudes, and |0⟩ and |1⟩
represent the basis states. In quantum computation, the amplitude contains the probability information
of finding qubits in a specific state, and the normalized |𝛼|² |𝛽|² 1 expresses this probability.
The input data can be embedded using various methods, depending on the embedding method.
These embeddings each have unique traits and use cases. For instance, one method prepares a
quantum state using binary data, another utilizes that data to encode data into the amplitudes of a
quantum state, and yet another encodes data into the rotation angles of quantum gates. An essential
step in quantum encoding is to embed the input data into a quantum state, enabling the model to use
quantum computing. The type of data being used and the problem being solved determine the
embedding approach to be used; each method has unique properties and applications.
The embedding approach used in this paper is called AngleEmbedding. AngleEmbedding modifies
the behavior of quantum gates based on the input data values by encoding classical information into
the rotation angles of the gates. In our case, the rotation gate employed is the gate denoted by the
equation below.
𝜃 𝜃
cos 𝑖 sin
𝑅 𝜃 2 2 (2)
𝜃 𝜃
𝑖 sin cos
2 2
This method is especially effective for continuous or real-valued data since it enables a concise
representation of the input data within the quantum system. AngleEmbedding allows the model to
benefit from the unique features of quantum computing, which may improve speed and make it
possible to identify intricate patterns in the data that conventional methods could miss. The
application of a random quantum circuit comes after the input data has been integrated into a quantum
state. Many single-qubit gates, including the RX and controlled-NOT gates with the same angle, were
randomly selected to make up this circuit. The random circuit operates as a non-linear transformation
of the input data, which might aid in revealing intricate patterns in the data that traditional methods
might find challenging to identify.
The image is then processed by a quantum convolutional step, which works similarly to a
conventional convolutional layer but uses quantum circuits. This step entails processing the image
through many quantum filters, each of which is a quantum circuit that only processes a small portion
of the image. The output tensor, which depends on the quantum kernel size and the type of padding
employed, will take a particular shape depending on the stride and padding used. After that, a selected
activation function, such as ReLU, sigmoid, or tanh, is applied to the output tensor to create
nonlinearity. The Pauli-Z operator is then used for each qubit to measure it on a computational basis.
The expectation values are employed as features and fed into the traditional CNN layers in the
classical part.
3.2.2. Classical part
Convolutional and fully connected blocks are combined to create a deep learning architecture in
the classical part. The primary classifier for the processed dataset is represented by this architecture,
which uses the predictive capabilities of traditional deep learning architectures. Max-pooling layers
are put first, then convolutional layers, to create convolutional blocks. To lessen overfitting, they also
have dropout layers. These blocks are in charge of identifying regional patterns and features in the
input data, assisting the model in recognizing crucial data details for the classification task.
On the other hand, fully connected blocks act as the model's final steps, merging the information
that the convolutional blocks have learned and deciding how to interpret the data. The final dense
layer, which has a SoftMax activation function, comes after the fully connected layers and generates
the class probabilities for each potential class. Classical architecture may learn intricate patterns in the
data and produce precise predictions based on the cleaned dataset by combining these building blocks
with information derived from the quantum layer.
4. Experimental results and discussion
Four main experiments are conducted to evaluate the general effectiveness of the proposed image
classification model based on QCNN. Seven benchmark datasets are used to assess how well the
proposed model based on QCNN performs. These datasets include BreastMNIST, OrganMNIST,
ChestMNIST, PneumoniaMNIST, FashionMNIST, CIFAR-10, and Brain MRI Images. The adopted
datasets are described in Table 1 according to the number of samples and classes. The adopted
benchmark datasets have a varying number of classes, as can be shown.
It should be noted that the proposed model was evaluated on 200 training samples and 50 testing
samples due to the existing constraints of quantum hardware. These samples were chosen at random.
The first experiment aims to identify the best kernel size by experimenting with different kernel sizes.
The model's performance in the second experiment is contrasted before and after adding the Quantum
convolutional layer. The third experiment evaluates the proposed model using several benchmark
datasets. The fourth experiment examines the proposed model with state-of-the-art models. These
experiments used accuracy, sensitivity, precision, and f1-score as evaluation criteria. The CoLab
notebook platform and the Pennylane Quantum Library were used for all experiments.
Table 1
Datasets description
Number of Number of
Samples Classes
Brain MRI 253 2
PneumoniaMNIST 5,856 2
BreastMNIST 780 2
OrganMNIST 23,660 11
FashionMNIST 70,000 10
CIFAR-10 60,000 10
ChestMNIST 112,120 2
Finding the ideal kernel size for the proposed model is the goal of the first experiment in Figure 3.
It should be noted that the Brain MRI Images dataset, one of the adopted datasets, is used to test the
ideal kernel size. As can be seen, the accuracy for the kernel with a size of 1x1 is 73.75%; for the
kernel with a size of 5x5 it is 77.50%; for the kernel with a size of 10x10 it is 97.95%; and finally, for
the kernel with a size of 20x20, it is 98.65%. From this chart figure, it can be demonstrated that a
20x20 kernel size is the most efficient kernel size. The following experiments will continue to use this
kernel size in the upcoming experiments. Also, 700 epochs will be used as well.
Figure 3: Comparison of using different kernel sizes in terms of accuracy
Results are obtained before and after applying the quantum convolutional layer to the dataset of
Brain MRI images to demonstrate the significance of using the layer in the proposed QCNN. The
experiment makes use of some evaluation metrics. Accuracy, precision, recall, and f1-score are the
measures used for evaluation. Using the quantum convolutional layer increased the proposed model's
accuracy to 98.65%, while doing without it reduced it to 92.68%, as shown in Table 2. Thus, it can be
seen that applying the fundamentals of quantum computing to one of the convolutional layers can
considerably boost the functionality of CNN architecture.
Table 2
The results before and after applying the quantum convolutional layer
Accuracy (%) Precision (%) Recall (%) F-score (%)
Before 0.92 0.80 0.76 0.76
After 0.98 0.98 0.98 0.98
The proposed model was subsequently assessed and tested on seven benchmark datasets in the
third experiment in Table 3, including the Brain MRI dataset and six other benchmark datasets:
PneumoniaMNIST, BreastMNIST, OrganMNIST, FashionMNIST, CIFAR-10, and ChestMNIST.
Table 3 compares the proposed model's performance on several datasets, presenting the findings
regarding accuracy, precision, recall, and f-score. As demonstrated, the proposed model exhibits
superior learning and picture classification abilities across all datasets. Furthermore, the proposed
model performs well in multi-class and binary classification issues, demonstrating its adaptability and
versatility in handling different classification tasks. This emphasizes the proposed model's
adaptability and robustness in various image classification cases. The training and validation
accuracies are presented for 700 epochs in Figure 4 to assess the proposed model's performance
further. The proposed model is up-and-coming, as this graph shows. Both the validation and training
datasets showed high classification accuracy. These outcomes match those of the experiments shown
in Table 3.
Table 3
The performance of the proposed model using seven benchmark datasets in terms of accuracy,
precision, recall, and an f‐score.
Accuracy (%) Precision (%) Recall (%) F-score (%)
Brain MRI 0.98 0.98 0.98 0.98
PneumoniaMNIST 0.99 0.99 0.98 0.98
BreastMNIST 0.96 0.96 0.96 0.95
OrganMNIST 0.98 0.98 0.97 0.97
FashionMNIST 0.98 0.98 0.98 0.98
CIFAR-10 0.90 0.90 0.89 0.87
ChestMNIST 0.99 0.99 0.91 0.95
The performance of the proposed model in comparison to the state-of-the-art models, namely
hybrid quantum-classical convolutional neural network (HQC-CNN) [17], attentive octave
convolutional capsule network (AOC-Caps) [18], Feature Pyramid Vision Transformer (FPViT) [19],
cross-stitch Affine Network (CANet) [20], and convolution neural networks with 3x3 filter size
(ConvNet) [21] is shown in Table 4 for further assessment of the robustness of the model. This table
demonstrates how competitive the proposed model is. On most of the adopted datasets, it achieves the
highest accuracy.
Table 4
The performance of the proposed model vs. the state‐of‐the‐art models in terms of accuracy
The HQC-
CNN
AOC-Caps FPViT CANet ConvNet
Proposed
[17] [18] [19] [20] [21]
Model
Brain MRI 98.69 97.8 - - - -
PneumoniaMNIST 99.56 - 93.1 - - -
BreastMNIST 96.00 - - 88.46 - -
OrganMNIST 98.22 - 93.1 - - -
ChestMNIST 99.59 - - - 98.8 -
FashionMNIST 98.00 - - - - 93.68
CIFAR-10 90.00 - - - - 73.04
(a) (b)
(c) (d)
Figure 4: Training and validation accuracy through 700 epochs, (a) Brain MRI Images, (b)
OrganMNIST, (c) ChestMNIST, and (d) BreastMNIST
5. Conclusion
This study proposed a new quantum convolutional neural network architecture. The proposed
QCNN is applied to the image classification task. PneumoniaMNIST, FashionMNIST, CIFAR-10,
BreastMNIST, OrganMNIST, ChestMNIST, and Brain MRI Images benchmark datasets are adopted.
The experimental results revealed that exploiting quantum principles such as superposition and
entanglement in the classical CNN can positively boost its performance. The results showed that
increasing the kernel size of the quantum layer can significantly boost the performance of the
proposed QCNN. Moreover, the results revealed that the proposed QCNN obtained the best results
compared to several well-known landmark models. The overall proposed image classification model
achieves an accuracy of 98% for Brain MRI Images, 99% for ChestMNIST, 98% for OrganMNIST,
96% for BreastMNIST, 90% for CIFAR-10, 98% for FashionMNIST, and 99% for
PneumoniaMNIST. The main challenge in implementing the proposed QCNNs to large-scale image
classification tasks is the restricted capacity of quantum hardware, which limits the size of input
images and the number of layers employed in the network. As a result, in the future, the proposed
QCNN may be implemented using simple quantum circuits.
6. Acknowledgements
We extend our sincere gratitude to Artivay.INC's Quantum R&D department for their generous
sponsorship and invaluable support. Their contribution has been instrumental in the success of our
project, and we are truly grateful for their partnership.
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