Page 1

Brain Tumor Diagnosis Using Quantum Convolutional Neural Networks

Muhammad Al-Zafar Khan ¶∥, Nouhaila Innan ‡∗, Abdullah Al Omar Galib§†, Mohamed Bennai ‡∗∗

∗

Quantum United Arab Emirates (QUAE), UAE

‡

Quantum Physics and Magnetism Team, LPMC, Faculty of Sciences Ben M’sick,

Hassan II University of Casablanca, Morocco

§

Independent Researcher

∥

m.khan@quae.ae,

∗

nouhaila.innan-etu@etu.univh2c.ma,

†

abdullahalomargalib@gmail.com,

∗∗

mohamed.bennai@univh2c.ma

Abstract—Integrating Quantum Convolutional Neural Net-

works (QCNNs) into medical diagnostics represents a trans-

formative advancement in the classification of brain tumors.

This research details a high-precision design and execution of

a QCNN model specifically tailored to identify and classify

brain cancer images. Our proposed QCNN architecture and

algorithm have achieved an exceptional classification accuracy

of 99.67%, demonstrating the model’s potential as a powerful

tool for clinical applications. The remarkable performance of our

model underscores its capability to facilitate rapid and reliable

brain tumor diagnoses, potentially streamlining the decision-

making process in treatment planning. These findings strongly

support the further investigation and application of quantum

computing and quantum machine learning methodologies in

medical imaging, suggesting a future where quantum-enhanced

diagnostics could significantly elevate the standard of patient care

and treatment outcomes.

Index Terms—Quantum Convolutional Neural Networks, Con-

volutional Neural Networks, Quantum Machine Learning, Quan-

tum Computing

I. INTRODUCTION

Brain tumors are neoplasms that represent abnormal cell

growth within the brain and its surrounding structure. Al-

though a relatively rare form of cancer – in comparison to

other cancers – analogous to other cancers, it can be benign

or malignant, and it is poorly diagnosed because neurological

symptoms cannot be detected easily, and specific tests like

biopsies and analysis of brain scans, needs to be conducted

by human experts. The process of diagnoses usually involves

three facets: Consideration of molecular features, analysis of

histological characteristics (microscopic analysis of cells and

tissues from the brain), and anatomical location (lobal regions

of the brain).

Holistically, these tumors are categorized as follows:

1) Meningiomas: Tumors originating from the meninges

surrounding the brain and the spinal cord.

2) Pituitary Adenomas: Tumors that originate in the pi-

tuitary gland at the base of the brain.

3) Gliomas: Tumors that originate from the glial cells

in the central nervous system. Gliomas are the most

common type of brain tumors that are developed, and

are therefore known as “primary brain tumors.”

4) Metastatic Lesions: Tumors that originate from cancer

cells in other parts of the body, and have spread via

metastatis to the brain. Therefore, they are known as

“secondary brain tumors”.

5) Medulloblastomas: Tumors that originate from the

cerebellum, and are most commonly found in children.

6) Acoustic Neuromas / Schwannomas: Tumors that orig-

inate from the Schwann cells insulting nerve fibers.

7) Pinealomas / Pineocytoma: Tumors that originate from

the pineal gland.

According to research published by the American Cancer

Society [1], in 2023 for the state of Ohio in the United States, it

was reported that 24 810 adults (with 14 280 being men, and

10 530 being women) in the United States were diagnosed

with a form of cancerous tumors of the brain and spinal

cord, and a 2020 survey found that globally 308 102 people

were diagnosed. Although a small percentage of the overall

population of the United States and the world, respectively,

these patients are eligible to receive the best care possible.

Usually, treatment paths are patient-specific, depending on

several factors, such as the patient’s current state of health, the

presence of other underlying diseases, and so on. As with other

cancers, treatment is very expensive, and requires the patient

to take significant steps to a complete lifestyle overhaul.

This multifarious approach encompasses, amongst others, a

change of diet, incorporation of exercise, radiation therapy,

immunotherapy, chemotherapy, and molecular therapy.

With the current Artificial Intelligence (AI) revolution in

all fields that the world is experiencing, the medical field is

no exception. Specifically, within the context of the analysis

of medical images for diagnosis and prognosis, Convolutional

Neural Networks (CNNs) are a type of NN architecture

designed for computer vision and image processing assign-

ments. Similar to how a perceptron is modeled after biological

neurons, the CNN is modeled after the cortical preprocessing

regions of the striate cortex (primary visual cortex – V1) and

the prostrate cortex (secondary visual cortex – V2), located

at the occipital lobe at the back of the brain. Analogous to

how computer vision tasks in the pre-Machine Learning (ML)

and pre-Deep Learning (DL) eras used to be concerned with

detecting edges, shapes, and textures, the neurons in this region

are sensitive to discerning these patterns. CNNs have proven

to be invaluable in the medical domain, and many healthcare

facilities are incorporating CNN-based classification systems

together with medical experts for early disease detection, and

recommended treatment plans [2]–[4].

Architecturally, the CNN is described as being composed

of two distinguishable layers:

1) Convolutional Layer: These contain adjustable fil-

arXiv:2401.15804v1 [eess.IV] 28 Jan 2024

ters/kernels/weights optimized for the task’s superlative

performance. The output from this layer is known as

feature maps. Given a two-dimensional input image X,

the kernel K is applied in order to get the feature map

Y at each spatial location

Y (i, j) =

∑

m

∑

n

X(i + m, j + n) · K(m, n),

(1)

where i and m are the x-coordinates of the image

and kernel locations respectively, and j and n are the

y-coordinates image and kernel locations respectively.

Subsequently, a nonlinear activation function that serves

the network in order to introduce sparsity into the

network, mitigate small gradients so that the vanishing

gradients problem is avoided during backpropagation,

and speed up the convergence of the loss function.

Typically in a CNN, a ReLU(x) = max(0,x), or a

variant, is used.

2) Pooling Layer/Max Pooling/Subsampling: These re-

duce the spatial resolution of the feature maps by a

process called downsampling, which reduces the size of

the feature map, typically by half its original size. There

are several types of pooling operations, these include:

a) Max Pooling: Chooses the maximum value from

each subregion of the feature map.

Y (i, j) = max

m,n

X(i × s + m, j × s + n),

(2)

where s is the stride or number of pixel shifts over

the input matrix.

b) Average Pooling: Chooses the average value from

each subregion of the feature map.

Y (i, j) =

1

k

∑

m

∑

n

X(i × s + m, j × s + n). (3)

c) c2 Norm Pooling: Chooses the ℓ2 norm of each

subregion in the feature map.

Y (i, j) =

1

k

∑

m

∑

n

X2(i×s+m, j ×s+n). (4)

d) Global Pooling: Chooses the maximum or average

value across all the feature maps in a layer. This

produces a single scalar value for each feature map.

Subsequently, once a series of convolution and pooling

layers are applied (the number of each is an adjustable

hyperparameter decided to maximize accuracy, and minimize

time to convergence), the output is flattened, and fed to

the terminal layer, where by classification takes place. Gen-

erally, the sigmoid, σしぐま(x) = 1/ [1 + exp(−x)], function is

used for binary classification tasks, or the softmax, ˜σしぐま(x) =

exp(xi)/ ∑

|classes|

j=1

exp(xj), is used, where |classes| is the

number of classes.

Furthermore, the sub-operations within the network that take

place include:

Subsampling decreases the number of weights in the net-

work, thereby increasing the receptive field of the neurons in

order to capture more information about the input image on

a global scale, and improve the network’s ability to recognize

objects, no matter their location via translational invariance.

Convolution is the mathematical operation of sliding a filter

matrix, containing learnable weights that help infer different

features over the image and take the inner product of the

matrix with the pixel at each location to extract the feature.

The importance of convolution cannot be over-stressed as it is

fundamental for automatically discerning features, thus elimi-

nating the need for manual feature engineering. However, each

time a convolutional operator is applied, the dimensionality of

the image is reduced.

Padding is the process of adding pixels around the edge of

an image prior to applying the convolutional operator. This

process is vital because it ensures that the resulting feature

map has the same dimensions as the input image. In addition, if

images are not edge-pixelated, once the convolutional operator

is applied.

Batch normalization is a statistical technique used to nor-

malize the activations of the neurons in the CNN. This is

accomplished by adjusting and scaling the inputs to each layer.

However, classical CNNs have the drawback of being un-

able to learn global and remote semantic information well,

amongst others. Therefore, a natural consideration for ad-

vancement would be the incorporation of another thriving

technology; thus, our proposal of supplementation via Quan-

tum Machine Learning (QML). Below we summarize the

drawbacks of classical CNNs, and highlight how QCCNs may

conceivably address these challenges.

1) The Problem of Overfitting: CNNs are highly prone

to learning the probability distributions of the training

data “too well”, and therefore even learn erroneous noise

and outliers. Owing to larger feature spaces, QCNNs are

potentially less prone to overfitting.

2) Cost of Computation: Regular CNNs have quadratic

runtimes, O(Ni×N2

o ×S2

i ×S2

c ), where Ni is the number

of input feature maps, No is the number of output feature

maps, Si is the size of the input feature map, and Sc

is the size of the convolution filter. QCNNs have the

potential to be much lower due to the superposition of

qubits that create an exponential speedup.

3) Learning Mappings from Features to the Predictor:

As the image dataset gets more complicated, and more

expansive in size, CNNs limited in their expressivity.

QCNNs have the potential to be more expressive due

to exploiting the quantum mechanical properties of

superposition and entanglement.

Therefore, it is evident that considering QCNNs, and the

augmentation of classical CNNs with QML proves to be a

fruitful venture. Integrally, QML is a developing research

enterprise, that has myriad real-world applications in diverse

fields like drug discovery [5]–[9], materials science [10], [11],

condensed matter physics [12]–[15], optimization [16]–[20],

finance [21]–[25], logistics planning [26]–[29], cryptography

Image

Convolution + ReLU

Kernel

Pooling

Convolution + ReLU

Pooling

Flatten

Layer

Fully

Connected

Layer

Softmax

Input:

Output:

Label 1

Label 2

Label 3

Label 4

Label

Feature Extraction

Classification

Probability

Distribution

Feature Maps

Fig. 1: Architecture of a classical CNN.

and cybersecurity [30], [31], and many other innovative appli-

cations [32]–[35].

The augmentation of QML with CNNs leads to Quantum

Convolutional Neural Networks (QCNNs). In this study, we

use QCNNs to perform brain tumor classifications on an open-

source brain tumor image dataset. While this is not novel, this

study offers several contemporary advancements, and superior

performance for in-distribution classification, as well as out-

of-distribution generalizability.

The original contributions of this paper are: The integration

of an extremely large image dataset, which is significant

considering the computational power available in the NISQ

era; the development and implementation of a QCNN with

a classical component that achieves high accuracy; and a

modular and scalable framework for the QCNN that ensures

adaptability to various computational contexts.

The structure of this paper is organized in the following

manner:

In Sec. II, we provide a literature review of the most relevant

papers in the field.

In Sec. III, we delve into the methodologies and underlying

theories of QCNNs, providing a detailed theoretical back-

ground.

In Sec. IV, we describe the process and implementation of

the QCNN used in this study, detailing the adaptations and

enhancements made to the original model.

In Sec. V, we present the results of our experiments.

In Sec. VI, we summarize our research findings and provide

a reflective analysis of the results obtained.

II. LITERATURE REVIEW

Below, we present salient studies that have motivated our

research undertaking, that have applied QML to brain tumor

classification tasks, and briefly describe the results obtained.

In [36], the authors developed a hybrid quantum-classical

CNN (HQC-CNN) model for brain tumor classification. The

novelties of the proposed network were that it achieved a

high classification score (97.8%), it was easy to train, and

converged to a solution very quickly. The classification prob-

lem was posed as a quaternary model, i.e. having four output

class types: Meningioma, glioma, pituitary, and no tumor.

In addition, it was demonstrated that the proposed network

outperformed many well-known models.

In [37], the authors use deep features extracted from the

famous Inception V3 model, combined with a parametric

quantum circuit on a predictor variable with four classes,

similar to the classification task in [36]. Using three datasets

as benchmarks (from Kaggle, the 2020-BRATS dataset, and

locally-collected dataset), it was shown that the hybrid ap-

proach proposed here should have superior performance com-

pared to traditional CNNs, with more than 90% accuracy.

The research in [38] sets out to address the ever-growing

size of image datasets in medical diagnoses, whilst maintaining

patient privacy, with a specific emphasis on brain tumor im-

ages. Further, a secure encryption-decryption framework is de-

signed to work on MRI data, and a 2-qubit tumor classification

model is implemented. The Dice Similarity Coefficient (DSC)

was used as a validation metric, and the model was found

to have a value of 98%. This research not only considered

designing a high-accuracy brain tumor classification model,

but also addressed the issue of cryptographic concerns.

In [39], the authors aim to address concerns around tu-

mor imaging and prediction using traditional ML techniques

amongst children and teenagers. Using India as a study group,

it is found that the data lacks variability, and does not account

for abnormalities within these specific groups. To address

this, a QCNN model is proposed that integrates techniques

from image processing to mitigate noise. It is found that the

proposed quantum network achieves an 88.7% accuracy.

In [40], the authors use MRI-radiomatic data to implement a

brain tumor model using a Quantum Neural Network (QNN).

The workflow involved the usage of a mutual information

feature selection (MIFS) technique, and the problem was

converted into a combinatorial optimization task, which was

subsequently solved using a quantum annealer on a D-Wave

machine. While specifically not a CNN-based model, or aug-

mentation thereof, the technique proved versatile and achieved

on-par accuracies with classical methods.

In [41], the authors design an automatic MRI segmentation

model based on qutrits (quantum states of the form |ψぷさい⟩ =

αあるふぁ |0⟩+βべーた |1⟩+γがんま |2⟩ with |αあるふぁ|2+|βべーた|2+|γがんま|2 = 1), called quantum

fully self-supervised neural networks (QFS-Net) It is shown

that this approach increases segmentation accuracy (model

predictability) – outperforming classical networks – and con-

vergence. Besides using a qutrit framework for which the

model is based, the other novel contributions of this research

were the implementation of parametrized Hadamard gates,

the neighborhood-based topological interconnectivity amongst

network layers, and the usage of nonlinear transformations. It

was demonstrated that QFS-Net demonstrated favorable results

on the Berkeley gray-scale images.

Various other literature pieces are contained within the

pieces discussed above, and it will be an exercise in futility

simply to repeat the findings. However, what is evident is

that the hybrid approach, via augmentation of the QCNN

with salient features of the classical CNN, emphasized in

the literature, serves as motivation for adopting a hybridized

approach to the network in this paper.

III. METHODOLOGY

In this section, we present the mathematical formalism of

QCNNs.

Comparably similar to CNNs, QNNs use a network of

quantum convolution layers and quantum activation functions

to perform feature extraction from images. Operationally, as

presented in Fig. 2, we can describe the operation of a QCNN

as follows:

1) Data Encoding: Classical data Di ∈ D is converted to

a single-qubit quantum state |ψぷさいi⟩∈H,

Di

encoding

−→ |ψぷさいi⟩ = αあるふぁ |0⟩ + βべーた |1⟩ ,

(5)

where αあるふぁ, βべーた ∈ C are complex probability amplitudes.

2) Quantum Convolution: This is achieved by applying

a series of quantum gates to the encoded state |ψぷさい⟩. We

cumulatively represent these gates as U∗,

U∗ |ψぷさい⟩ = U∗

∆

= combination(H⊗n1 ,R

⊗n2

θしーた

,

X⊗n3 ,Y ⊗n4 ,Z⊗n5 ,...),

(6)

where the function combination represents taking

amalgamations of the single-qubit gates for ni, and

i = 1, 2,..., number of times.

3) Quantum Pooling: The operation is carried out by

performing the quantum SWAP test: Given two quantum

states |ψぷさいi⟩ , |ψぷさいj⟩ and an ancillary qubit |0⟩,

3.1. Apply the Hadamard gate to the ancillary qubit in

order to create a superposition

H |0⟩ =

1

√

2

(|0⟩ + |1⟩) = |+⟩ .

(7)

3.2. Apply the controlled-SWAP gate with |0⟩ as the

control, and |ψぷさいi⟩ and |ψぷさいj⟩ as the the targets,

CSWAP(|0⟩ ; |ψぷさいi⟩ , |ψぷさいj⟩) = |0⟩⟨0|⊗|ψぷさいi⟩⟨ψぷさいi|

+ |1⟩⟨1|⊗|ψぷさいj⟩⟨ψぷさいi| .

(8)

3.3 Apply the Hadamard transformation,

H |0⟩ = |+⟩ .

4) Fully-Connected Layer: This layer is composed of

neurons that are oriented in a feed-forward arrangement

whereby previous neurons are connected to all subse-

quent neurons.

5) Measurement: Perform measurement to ascertain the

end state.

In Algorithm 1, we provide a general procedure for applying

the QCNNs model to any dataset.

Algorithm 1 QCNN(D)

procedure QCNN(D)

Input: a dataset D = {D1,D2,...,Dp} consisting of

p n × m-dimensional images

Initialize the number of repeats q for the quantum

convolutional and quantum pooling layers

for each image Di in D do

Encode Di into quantum state |ψぷさいi⟩

repeat

Apply U∗,

Measure

Apply quantum SWAP test

until q times

end for

Apply a fully connected NN to transform the output into

a 1D vector of class scores

Measure to obtain classifications

Return classified image with associated probability

end procedure

IV. PROCESS AND IMPLEMENTATION

In this section, we detail the practical steps taken to opera-

tionalize our QCNN model by discussing the workflow. We be-

gin by delineating the composition and sourcing of our dataset,

followed by the procedures employed in data preprocessing to

ensure optimal model input quality. Subsequently, we elucidate

our innovative approach to quantum image processing, which

sets the stage for the subsequent CNN training. This phase

Data

Encoding

Quantum Convolution:

Quantum

Pooling

Measurement

Output

Fully-Connected Layer

Results

Fig. 2: Hypothetical architecture of QCNNs model.

is critical as it underpins the model’s ability to learn from

the quantum-enhanced feature space. Each step is crafted to

build incrementally towards a robust and practical QCNN

application.

A. Dataset

The dataset used in this research [42] comprises 3 064

T1-weighted contrast-enhanced images extracted from 233

patients, encompassing three distinct brain tumor types, as

shown in Fig. 3: meningioma (708 slices), glioma (1 426

slices), and pituitary tumor (930 slices). The data is organized

in MATLAB format (.mat files), each containing a structure

that encapsulates various fields detailing the image and tumor-

specific information. Each MATLAB (.mat) file in the dataset

encompasses the following key fields:

a. cjdata.label: An integer indicating the tumor type,

coded as follows:

1) Meningioma

2) Glioma

3) Pituitary Tumor

Fig. 3: Distribution of sample sizes across tumor categories in

the dataset.

b. cjdata.PID: Patient ID, serving as a unique identi-

fier for each patient.

c. cjdata.image: Image data representing the T1-

weighted contrast-enhanced brain scan.

d. cjdata.tumorBorder: A vector storing the coor-

dinates of discrete points delineating the tumor border.

The vector format is as follows:

• [x1,y1,x2,y2,...]

• These coordinate pairs represent planar positions

on the tumor border and were generated through

manual delineation, offering the potential to create

a binary image of the tumor mask.

e. cjdata.tumorMask: A binary image where pixels

with a value of 1 signify the tumor region. This mask is

a crucial resource for further segmentation and analysis.

This dataset provides a diverse set of brain scans, as shown

in Fig. 4, and includes manual annotations of tumor borders,

fostering the development and evaluation of robust image

processing and ML models for brain cancer classification [43],

[44].

B. Data Preprocessing

This step loads the MATLAB data files and extracts image

data, tumor labels, and relevant information, and then it

converts the T1-weighted images to a format suitable for

quantum circuit processing.

C. Quantum Image Processing

In this step, the QCNN circuit stands as a pivotal com-

ponent, and the circuit comprises several essential elements.

Initially, a quantum device with 4 qubits initializes using

PennyLane’s default qubit simulator [45], as presented in

Fig. 5. A significant step in this process is setting the parameter

θしーた to πぱい/2. This parameter finds its application in Controlled-

Rotation-Z (CRZ) and Controlled-Rotation-X (CRX) gates.

The circuit employs Rotation-X (RX) gates applied to each

qubit. These gates rotate the qubit around the X-axis of the

Bloch sphere. The rotation angle is proportional to the pixel

value times πぱい. This operation is mathematically expressed as

|ψぷさい′⟩ =

3

⊗

i=0

RX(ϕiπぱい) |ψぷさい⟩ ,

(9)

with

RX (ϕiπぱい) =

(

cos ϕiπぱい/2

−ı sin ϕiπぱい/2

−ı sin ϕiπぱい/2)

cos ϕiπぱい/2

)

,

(10)

Fig. 4: Diagnostic imaging examples: Brain tumor types from the dataset.

Fig. 5: QCNN circuit.

where |ψぷさい⟩ = |0⟩

⊗4

represents the initial state of the quantum

system, and ϕi are the elements of the pixel value array passed

to the quantum circuit.

Following this, the circuit incorporates controlled rotation

gates, specifically CRZ and CRX gates. These gates are

applied between each pair of adjacent qubits and between the

last and first qubits. These gates introduce interactions between

the qubits. Mathematically, this is represented as

|ψぷさい′′⟩ = (CRZ(θしーた)0,1 · CRX(θしーた)0,1)

× (CRZ(θしーた)1,2 · CRX(θしーた)1,2)

× (CRZ(θしーた)2,3 · CRX(θしーた)2,3) |ψぷさい′⟩

(11)

with

CRZ(θしーた) =











1 0

0

0

0 1

0

0

0 0 exp(−ıθしーた/2)

0

0 0

0

exp(ıθしーた/2)











,

(12)

and

CRX(θしーた) =











1 0

0

0

0 1

0

0

0 0

cos θしーた/2

−ı sin θしーた/2

0 0 −ı sin θしーた/2

cos θしーた/2











,

(13)

where CRZ(θしーた) and CRX(θしーた) are the phase-parameterized CRZ

and CRX gates, respectively. Moreover, the circuit incor-

porates CZ gates that are applied between each pair of

adjacent qubits and between the last and first qubits. we

add an additional layer of entanglement between the qubits,

Mathematically, this is represented as

|ψぷさい′′′⟩ = CZ0,1 · CZ1,2 · CZ2,3 · CZ3,0 |ψぷさい′′⟩

(14)

with

CZ =











1 0 0

0

0 1 0

0

0 0 1

0

0 0 0 −1











,

(15)

Finally, the measurement phase occurs. In this phase, the

expectation value of the Pauli-Z operator is measured on the

first qubit. This step provides the average result of numerous

measurements, mathematically encapsulated as

M = ⟨ϕ′′′′′ |Z| ϕ′′′′′⟩ ,

(16)

where |ϕ′′′′′⟩ is the state after the CZ gates, indicating the

output of the quantum convolution operation on the 2 × 2

patch as a complex function of the pixel values, reflective of

the quantum nature of the operation.

The quantum convolution function plays a crucial role in

the process of quantum image processing. This function is

designed to perform a quantum convolution operation on an

input image. The function requires two arguments: Firstly, an

image represented as a 2D NumPy array, where each element

corresponds to a pixel value. Secondly, the step size, which

divides the image into patches, is set to 2 by default, thus the

image is divided into 2 × 2 patches.

In terms of processing, the function begins by initializing

a new 2D array of zeros. The dimensions of this array are

determined by the height and width of the image divided

by the step size, and this array serves to store the output of

the quantum convolution operation. Subsequently, the function

divides the image into 2×2 patches by looping over the image

with the specified step size. For each 2×2 patch, the function

flattens the patch into a 1D array and then applies the quantum

convolution operation, as performed by the QCNN circuit.

The measurement result of this operation is then stored in

the corresponding position in the output array.

In the output layer, the function returns a new 2D array.

Each element in the array represents the result of the quantum

convolution operation on the corresponding 2 × 2 patch in

the original image. This resulting array can be perceived

as a transformed version of the original image, where the

transformation is a complex function of the pixel values

stemming from the quantum nature of the operation.

The core component of the implementation is a loop de-

signed for image processing, which iterates through every

file in a designated folder, provided that the current file has

been processed during each iteration. If it has not, it loads

the image and its associated label from the file. Following

this, it resizes and normalizes the image. Subsequently, a

quantum convolution function is applied to the image. Finally,

the processed image and its label are saved into a new file.

D. CNN Training

This approach involves training the CNN on quantum-

processed image data. The model architecture comprises vari-

ous layers, each with specific functions. The first is a Conv2D

layer with 32 filters, a 3×3 kernel size, and ReLU activation,

designed to detect low-level features like edges and corners in

the input image. This is followed by a MaxPooling2D layer

with a 2×2 pool size, which reduces the spatial dimensions of

the input by taking the maximum value in each 2×2 window,

aiding in translation invariance and reducing computational

complexity. Another Conv2D layer is then applied, with 64

filters, and once again with ReLU activation, to detect more

complex features from the previous layer’s output. A second

MaxPooling2D layer further reduces the input’s spatial

dimensions. The flatten layer then converts the 2D output into

a 1D array for processing in the dense layers. Subsequently,

a dense layer with 128 units and ReLU activation learns to

represent the input in a 128-dimensional space, detecting high-

level features. To prevent overfitting, a dropout layer with

a 0.5 dropout rate is included, randomly setting half of the

input units to 0 during training. Finally, another dense layer

with 4 units and softmax activation outputs the probabilities

of the input image belonging to each of the four classes.

This comprehensive architecture enables the classical CNN

to effectively learn from the quantum-processed data.

V. RESULTS AND DISCUSSION

This study thoroughly examined the application of a type

QCNN for classifying brain tumor images for the purpose of

having a more expressive model that can be used in diagnostic

medicine. The performance metrics from our findings highlight

the model’s exceptional accuracy and potential application for

commercialization and usage in a real-world setting.

The loss and accuracy were calculated for 20 epochs for

the training and validation data. As presented in Fig. 6a, the

progressive decline in loss indicates the model’s robust error

minimization capabilities. This steady reduction in training and

validation loss signifies that the QCNN model is effectively

learning from the training data while also generalizing well

to new, unseen data. Such a trend strongly indicates the

model’s ability to avoid overfitting, a common challenge in

deep learning models applied to medical image analysis.

Similarly, the consistent increase in accuracy shown in Fig.

6b confirms the model’s competence in correctly classifying

brain tumors. The high accuracy rate, especially with a peak

validation accuracy of 99.67% is particularly noteworthy given

the complexity and variability inherent in medical imaging

data. This suggests that the QCNN can capture intricate

patterns and features in the images, which are crucial for

accurate diagnosis. However, it is crucial to note that per-

formance may vary with changes in image complexity and

dataset diversity. The confusion matrix, shown in Fig. 7,

offers additional insights into the model’s performance, par-

ticularly in its class-wise accuracy. The perfect classification

of “pituitary tumor” cases is a testament to the model’s

precision. However, the challenges observed in differentiating

between the meningioma and glioma classes. This highlights

areas for further refinement. These misclassifications may stem

from the inherent similarities in the imaging characteristics

of these tumor types, suggesting a need for more nuanced

feature extraction techniques or additional training data to

enhance differentiation. The practical utility of the QCNN

model is further validated through the real-world test cases

showcased in Fig. 8, which displays 10 randomly selected

test images, each annotated with its actual label and the

model’s prediction. The accurate predictions in these cases

demonstrate the model’s readiness for deployment in clinical

settings, where it can aid in the rapid and reliable diagnosis

of brain tumors.

In summary, the QCNN model’s outstanding performance in

this study demonstrates its capability as a powerful analytical

tool in medical imaging and highlights its transformative

potential in clinical diagnostics. The model’s high accuracy,

achieved in the challenging task of brain tumor image clas-

sification, underscores its precision and reliability. Moreover,

the robustness of the QCNN in processing and interpreting

complex image data attests to its sophisticated design and

adaptability. This robustness is particularly crucial in medical

imaging, where image variability and accuracy are paramount.

The QCNN model’s ability to consistently improve over

training epochs, as evidenced by decreasing loss and in-

(a)

(b)

Fig. 6: Training and validation performance plots: (a) Loss and (b) Accuracy.

Fig. 7: Confusion matrix displaying class-wise performance.

creasing accuracy, indicates a strong learning capability and

a practical approach to generalizing from training data to

unseen data. This aspect is vital for clinical applications where

models must perform reliably on diverse and novel datasets.

Furthermore, despite some challenges, the model’s nuanced

handling of different tumor types opens avenues for further

optimization and rarefaction. These qualities collectively posi-

tion the QCNN model as a promising candidate for real-world

clinical applications, potentially revolutionizing how medical

imaging is analyzed and interpreted.

VI. CONCLUSION

This paper presents a comprehensive exploration of QCNNs

in the context of medical imaging, particularly for brain

tumor classification. A theoretical overview of QCNNs and

conventional CNNs was provided, followed by a detailed

literature review of various approaches in this domain. This

theoretical groundwork laid the foundation for our practical

implementation, which introduced innovative modifications

while adhering to general QCNN principles.

Our implementation strategy involved integrating a conven-

tional CNN within the QCNN framework, essentially creating

a hybrid model that leverages both technologies’ strengths.

This approach deviates from standard QCNN designs and

represents an experimental foray into uncharted territories of

neural network architectures.

Additionally, using a quantum simulator to execute the

model and generate results is a significant step in practical

QML applications. The outcomes achieved in this study high-

light that a quantum approach provides uplift over classical

approaches as evidenced by the accuracy rates in classifying

complex medical images. This provides a compelling case for

the QCNN model’s efficacy.

The findings of this research contribute to the growing

body of knowledge on the applicability of QML in solving

real-world problems, particularly in medical diagnostics. In

addition, this opens up new possibilities for future research,

including the potential to explore other complex tasks.

In conclusion, this study advances our understanding of

QCNNs and demonstrates their practical application in a

critical field. The promising results pave the way for further

exploration and development of QML solutions in medical

imaging, potentially significantly enhancing diagnostic accu-

racy and patient outcomes.

DECLARATIONS

Conflicts of Interest

The authors declare no competing interests.

Authors’ contributions

All authors have contributed equally.

Fig. 8: Sample predictions with true and predicted labels.

Availability of Data and Materials

The datasets and numerical details necessary to replicate

this work are available from the corresponding author upon

reasonable request.

REFERENCES

1 Siegel, R. L., Giaquinto, A. N., & Jemal, A. (2024). “Cancer statistics,

2024”. CA: A Cancer Journal for Clinicians, https://doi.org/10.3322/caac.

21820.

2 Ullah, U., & Garcia-Zapirain, B. (2024). “Quantum Machine Learning

Revolution in Healthcare: A Systematic Review of Emerging Perspectives

and Applications”. IEEE Access, https://doi.org/10.1109/ACCESS.2024.

3353461.

3 Vatandoost, M., & Litkouhi, S. (2019). “The future of healthcare facilities:

how technology and medical advances may shape hospitals of the future”.

Hospital Practices and Research, 4(1), https://doi.org/10.15171/hpr.2019.

01.

4 Menegatti, D., et al. (2023). “CADUCEO: A Platform to Support Federated

Healthcare Facilities through Artificial Intelligence”. Healthcare, 11(15),

https://doi.org/10.3390/healthcare11152199.

5 Cao, Y., Romero, J., & Aspuru-Guzik, A. (2018). “Potential of quantum

computing for drug discovery”. IBM Journal of Research and Development,

62(6), https://doi.org/10.1147/JRD.2018.2888987.

6 Blunt, N. S., et al. (2022). “Perspective on the current state-of-the-art of

quantum computing for drug discovery applications”. Journal of Chemical

Theory and Computation, 18(12), https://doi.org/10.1021/acs.jctc.2c00574.

7 Zinner, M., Dahlhausen, F., Boehme, P., Ehlers, J., Bieske, L., & Fehring,

L. (2021). “Quantum computing’s potential for drug discovery: Early stage

industry dynamics.” Drug Discovery Today, 26(7), https://doi.org/10.1016/

j.drudis.2021.06.003.

8 Wang, P. H., Chen, J. H., Yang, Y. Y., Lee, C., & Tseng, Y. J. (2023). “Re-

cent Advances in Quantum Computing for Drug Discovery and Develop-

ment”, IEEE Nanotechnology Magazine, https://doi.org/10.1109/MNANO.

2023.3249499.

9 Batra, K., Zorn, K. M., Foil, D. H., Minerali, E., Gawriljuk, V. O., Lane,

T. R., & Ekins, S. (2021). “Quantum machine learning algorithms for drug

discovery applications”. Journal of Chemical Information and Modeling,

61(6), https://doi.org/10.1021/acs.jcim.1c00166.

10 Bauer, B., Bravyi, S., Motta, M., & Chan, G. K. L. (2020). “Quantum al-

gorithms for quantum chemistry and quantum materials science”. Chemical

Reviews, 120(22), https://doi.org/10.1021/acs.chemrev.9b00829.

11 Liu, H., Low, G. H., Steiger, D. S., Häner, T., Reiher, M., & Troyer,

M. (2022). “Prospects of quantum computing for molecular sciences”.

Materials Theory, 6(1), https://doi.org/10.1186/s41313-021-00039-z.

12 Smith, A., Kim, M. S., Pollmann, F., & Knolle, J. (2019). “Simulating

quantum many-body dynamics on a current digital quantum computer”. npj

Quantum Information, 5(1), https://doi.org/10.1038/s41534-019-0217-0.

13 Micheletti, C., Hauke, P., & Faccioli, P. (2021). “Polymer physics by

quantum computing”. Physical Review Letters, 127(8), https://link.aps.org/

doi/10.1103/PhysRevLett.127.080501.

14 Innan, N., Khan, M. A. Z., & Bennai, M. (2024). “Quantum computing for

electronic structure analysis: Ground state energy and molecular properties

calculations”. Materials Today Communications, 38(107760), https://doi.

org/10.1016/j.mtcomm.2023.107760.

15 Vorwerk, C., Sheng, N., Govoni, M., Huang, B., & Galli, G. (2022).

“Quantum embedding theories to simulate condensed systems on quantum

computers”. Nature Computational Science, 2(7), https://doi.org/10.1038/

s43588-022-00279-0.

16 Ajagekar, A., & You, F. (2019). “Quantum computing for energy systems

optimization: Challenges and opportunities”. Energy, 179, https://doi.org/

10.1016/j.energy.2019.04.186.

17 Ajagekar, A., Humble, T., & You, F. (2020). “Quantum computing based

hybrid solution strategies for large-scale discrete-continuous optimization

problems.” Computers & Chemical Engineering, 132, https://doi.org/10.

1016/j.compchemeng.2019.106630.

18 Wang, L., Tang, F.,& Wu, H. (2005). “Hybrid genetic algorithm based on

quantum computing for numerical optimization and parameter estimation”.

Applied Mathematics and Computation, 171(2), https://doi.org/10.1016/j.

amc.2005.01.115.

19 Shukla, A., & Vedula, P. (2019). “Trajectory optimization using quantum

computing”. Journal of Global Optimization, 75, https://doi.org/10.1007/

s10898-019-00754-5.

20 Li, Y., Tian, M., Liu, G., Peng, C., & Jiao, L. (2020). “Quantum

optimization and quantum learning: A survey”. Ieee Access, 8, https:

//doi.org/10.1109/ACCE.

21 Orús, R., Mugel, S., & Lizaso, E. (2019). “Quantum computing for

finance: Overview and prospects”. Reviews in Physics, 4, https://doi.org/

10.1016/j.revip.2019.100028.

22 Innan, N., Khan, M. A. Z., & Bennai, M. (2023). “Financial fraud

detection: a comparative study of quantum machine learning models”.

International Journal of Quantum Information, https://doi.org/10.1142/

S0219749923500442.

23 Emmanoulopoulos, D., & Dimoska, S. (2022). “Quantum machine learn-

ing in finance: Time series forecasting.” arXiv preprint arXiv:2202.00599.

24 Herman, D., et al. (2022). “A survey of quantum computing for finance”.

arXiv preprint arXiv:2201.02773.

25 Innan, N. et al. (2023). “Financial fraud detection using quantum graph

neural networks”. arXiv preprint arXiv:2309.01127.

26 Correll, R., Weinberg, S. J., Sanches, F., Ide, T., & Suzuki, T. (2023).

“Quantum Neural Networks for a Supply Chain Logistics Applica-

tion”. Advanced Quantum Technologies, 6(7), https://doi.org/10.1002/qute.

202200183.

27 Weinberg, S. J., Sanches, F., Ide, T., Kamiya, K., & Correll, R. (2023).

“Supply chain logistics with quantum and classical annealing algorithms”.

Scientific Reports, 13(1), https://doi.org/10.1038/s41598-023-31765-8.

28 Azzaoui, A. E., Kim, T. W., Pan, Y., & Park, J. H. (2021). “A quantum

approximate optimization algorithm based on blockchain heuristic approach

for scalable and secure smart logistics systems”. Human-centric Computing

and Information Sciences, 11(46).

29 Gachnang, P., Ehrenthal, J., Hanne, T., & Dornberger, R. (2022). “Quan-

tum Computing in Supply Chain Management State of the Art and Research

Directions”. Asian Journal of Logistics Management, 1(1), https://doi.org/

10.14710/ajlm.2022.14325.

30 Dixit, V., et al. (2021). “Training a quantum annealing based restricted

boltzmann machine on cybersecurity data”. IEEE Transactions on Emerg-

ing Topics in Computational Intelligence, 6(3), https://doi.org/10.1109/

TETCI.2021.3074916.

31 Suryotrisongko, H., & Musashi, Y. (2022). “Evaluating hybrid quantum-

classical deep learning for cybersecurity botnet DGA detection”. Procedia

Computer Science, 197, https://doi.org/10.1016/j.procs.2021.12.135.

32 Innan, N., et al.(2023). “Quantum State Tomography using Quantum

Machine Learning”. arXiv preprint, arXiv:2308.10327.

33 Innan, N., & Khan, M. A. Z. (2023). “Classical-to-Quantum Sequence

Encoding in Genomics”. arXiv preprint, arXiv:2304.10786.

34 Innan, N., & Bennai, M. (2023). “Simulation of a Variational Quantum

Perceptron using Grover’s Algorithm”. arXiv preprint, arXiv:2305.11040.

35 Innan, N., Khan M. A. Z., & Bennai, M. (2023). “Enhancing quantum sup-

port vector machines through variational kernel training”. Quantum Infor-

mation Processing, 22(374), https://doi.org/10.1007/s11128-023-04138-3.

36 Dong, Y., Fu, Y., Liu, H., Che, X., Sun, L., & Luo, Y. (2023). “An

improved hybrid quantum-classical convolutional neural network for multi-

class brain tumor MRI classification”. Journal of Applied Physics, 133(6),

https://doi.org/10.1063/5.0138021.

37 Amin, J., Anjum, M. A., Sharif, M., Jabeen, S., Kadry, S., & Moreno Ger,

P. (2022). “A new model for brain tumor detection using ensemble transfer

learning and quantum variational classifier”. Computational Intelligence

and Neuroscience, https://doi.org/10.1155/2022/3236305.

38 Amin, J., Anjum, M. A., Gul, N., & Sharif, M. (2022). “A secure two-qubit

quantum model for segmentation and classification of brain tumor using

MRI images based on blockchain.” Neural Computing and Applications,

34(20), https://doi.org/10.1007/s00521-022-07388-x.

39 Chandra, S., Saxena, S., Kumar, S., Chaube, M. K., & Bodhey, N. K.

(2022, December). “A Novel Framework For Brain Disease Classification

Using Quantum Convolutional Neural Network.” 2022 IEEE International

Women in Engineering (WIE) Conference on Electrical and Computer En-

gineering (WIECON-ECE), https://doi.org/10.1109/WIECON-ECE57977.

2022.10150851.

40 Felefly, T. et al. (2023). “An Explainable MRI-Radiomic Quantum Neural

Network to Differentiate Between Large Brain Metastases and High-Grade

Glioma Using Quantum Annealing for Feature Selection.” Journal of

Digital Imaging, 36(6), https://doi.org/10.1007/s10278-023-00886-x.

41 Konar, D., Bhattacharyya, S., Panigrahi, B. K., & Behrman, E. C.

(2022). “Qutrit-Inspired Fully Self-Supervised Shallow Quantum Learning

Network for Brain Tumor Segmentation.” IEEE Transactions on Neural

Networks and Learning Systems, 33(11), https://doi.org/10.1109/TNNLS.

2021.3077188.

42 Cheng, Jun. “Brain Tumor Dataset”. Figshare. Dataset. (2017), https://

doi.org/10.6084/m9.figshare.1512427.v5.

43 Cheng, Jun, et al. “Enhanced Performance of Brain Tumor Classification

via Tumor Region Augmentation and Partition”. PLOS One. pp. 10.10

(2015), https://doi.org/10.1371/journal.pone.0140381.

44 Cheng, Jun, et al. “Retrieval of Brain Tumors by Adaptive Spatial Pooling

and Fisher Vector Representation.” PLOS One. pp. 11.6 (2016), https://doi.

org/10.1371/journal.pone.0157112.

45 Bergholm, Ville, et al. “Pennylane: Automatic differentiation of hybrid

quantum-classical computations.” arXiv, (2018), https://arxiv.org/abs/1811.

04968.