Cancer Cell Detection Using a Hybrid Quantum and Classical

Machine Learning Model

Kalluru Hitesh and Pushpa P. V

Department of Electronics & Communications Engineering,Dayananda Sagar University, Bangalore, India

Keywords: Quantum Computing, Quantum Machine Learning, Feature Mapping, Support Vector Machine, Quantum

Kernel, Optimization.

Abstract: The early diagnosis of cancer using MRI is vital in medical diagnostics. Traditional machine learning

approaches struggle with the high dimensionality and complexity of medical image data. As quantum

computing technology progresses, such hybrid approaches are expected to become increasingly practical,

leading to significant advancements in the early detection and diagnosis of cancer. This research

investigates quantum machine learning for the classification task, utilizing a Support Vector Machine

(SVM) with a quantum kernel to detect cancer cells from MRI scans with improved accuracy and

efficiency. The quantum feature space is created through quantum feature mapping of classical data,

enhancing the SVM's ability to classify cancerous and non-cancerous cells. The proposed solution consists

of a quantum machine learning model, that utilizes the classical algorithm with quantum kernel, showing a

significant potential to revolutionize medical diagnostics. By integrating the strengths of quantum

computing with classical machine learning techniques, this approach provides a powerful and efficient tool

for medical image analysis. The proposed quantum machine learning model gives the accurate analysis of

cancer cells detection present in MRI scans of the brain.

1 INTRODUCTION

Detecting cancer is crucial in medical diagnosis,

with MRI and other imaging techniques playing a

key role. Traditional image analysis methods,

though effective, require significant computational

power and miss small but critical details that

distinguish cancerous cells from healthy ones

(Biamonte, Wittek, et al. , 2017). Quantum Machine

Learning (QML) offers a promising solution to

improve medical image analysis. By leveraging

quantum phenomena like superposition and

entanglement, QML algorithms can process complex

datasets and identify subtle patterns that

conventional methods overlook (Havlíček, Córcoles,

et al. , 2019). The proposed optimized solution

combines Classical Machine Learning and Quantum

Computing, utilizing a classical Support Vector

Machine (SVM) model with a quantum kernel

(Schuld, and, Petruccione, 2018). This hybrid

approach aims to enhance the accuracy and

reliability of cancer cell detection from MRI scans

of brain. The quantum kernel maps the input datasets

into a high-dimensional quantum feature space,

making data points more separable (Farhi and

Neven, 2020). This integration of classical and

quantum techniques can significantly improve

detection performance.

The core of this approach is the quantum feature

map, which transforms classical input data into

quantum states. This mapping enables the SVM

model to operate within a quantum-enhanced

framework. The quantum kernel computes the inner

product of these quantum states, providing a

similarity measure that feeds into the SVM. By

reformulating the problem in this manner, the SVM

provides a better and more expressive feature space,

improving its ability to distinguish between

cancerous and non-cancerous cells. QML's potential

advantages over traditional methods are numerous.

The higher dimensionality of the quantum feature

space can reveal intricate structures in the data,

enhancing pattern recognition capabilities.

Additionally, the inherent parallelism of quantum

computing allows for the simultaneous processing of

multiple states, potentially speeding up

computations and improving efficiency(Mohseni

and Lloyd, 2018).

Hitesh, K. and P. V, P.

Cancer Cell Detection Using a Hybrid Quantum and Classical Machine Learning Model.

DOI: 10.5220/0013589100004664

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 3rd International Conference on Futuristic Technology (INCOFT 2025) - Volume 2, pages 189-194

ISBN: 978-989-758-763-4

189

These benefits are particularly valuable in

medical imaging, where accurate and timely

diagnosis is critical. Implementing this hybrid

quantum-classical approach involves several key

steps. Initially, classical MRI data is pre-processed

and converted into a format suitable for quantum

processing. The quantum feature map then

transforms this data into quantum states. This

research work is expected to yield higher accuracy

in cancer detection compared to traditional machine

learning methods.

In this paper, we discuss the related work in

section II. The section III describes about the

process of the detection of cancer cells using the

quantum machine learning model. Simulation results

and discussions are presented in section IV,

followed by the conclusion in section V.

2 RELATED WORK

The following is related work performed in various

papers, journals, and books in the field of quantum

machine learning and medical image analysis. In the

work by Havlíček et al. (2019), the authors

introduced the concept of quantum-enhanced feature

spaces, demonstrating how quantum kernels can be

used to improve the performance of classical

machine learning algorithms like support vector

machines (SVM). Schuld and Petruccione (2018)

highlighted applications of quantum computing in

chemistry, with implications for medical imaging.

The work by Biamonte et al. (2017) provided an

overview of quantum machine learning algorithms

and their applications, including medical imaging.

Farhi and Neven (2020) investigated the use of

quantum neural networks for classification tasks. A

detailed review of advancements in quantum

machine learning and its potential applications,

including healthcare, is presented by Mohseni and

Lloyd (2018). Adcock et al. (2015) discussed

quantum information processing techniques relevant

to quantum machine learning. McArdle et al. (2020)

introduced foundational quantum algorithms for

machine learning, emphasizing the potential speed-

ups for data processing. Zhu et al. (2019) provided a

comprehensive review of quantum machine learning

algorithms and their potential for various

applications, including medical diagnostics. In the

paper by El Maouaki et al. (2024), a Quantum

Support Vector Machine (QVSM) was applied to

prostate cancer detection. Mari et al. (2020)

reviewed a high-dimensional QSVM framework and

its application to image classification. The paper by

Mishra et al. (2019) demonstrated quantum neural

networks on a quantum computer by detecting breast

cancer.

3 QUANTUM MACHINE

LEARNING ALGORITHM FOR

THE CANCER CELLS

DETECTION

Quantum Machine Learning is the integration of

machine learning programs with quantum

algorithms. In this research work, we developed a

quantum machine learning model for detecting the

cancer cells from the MRI scans of images.

There are two types of datasets taken for this

work, testing and training. Each dataset consists of

cancer and non-cancer MRI scans of brain. Fig. 1

shows one of the training MRI scans of the cancer

cells belonging to the tumor called glioma.

Figure 1: MRI scan of brain consistingglioma

Figure 2: MRI scan of benign cells

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The Fig. 2 shows one of the training MRI scans

of benign cells (non-cancer cells).

These datasets are then incorporated into the

quantum states. The study of Support Vector

Machine and Quantum Kernel is performed using

the following steps:

3.1 Data Encoding

A collection of 24 datasets comprising MRI scans of

both glioma (cancer) and benign (non-cancer) cells,

distinguishing between cancerous and non-

cancerous cell samples are considered in this work,

each described by D features. Each feature is

encoded into quantum states using qubits. Let |𝑥



⟩

represent the quantum state corresponding to the 𝑖



data point.This encoding transforms classical data

into quantum states, which can then be processed

using quantum feature maps.

Any text or material outside the aforementioned

margins will not be printed.

3.2 Feature Mapping

Quantum feature mapping is a step that allows

classical data to be encoded in quantum states so as

to leverage some intrinsic properties of quantum

mechanics in capturing the intricate patterns existing

in the data. By applying a feature map Φ, input data

points are mapped into a higher-dimensional

quantum feature space, enhancing the ability to

detect complex relationships within the data.

|𝑥



⟩ → |Φ(𝑥



)⟩

(1)

3.3 Quantum Kernal

A quantum kernel K(x, y) measures the

similarity between two quantum states |φ(x)⟩ and

|φ(y)⟩. This quantum kernel is fundamental in the

Support Vector Classifier (SVC) optimization

process. It helps find the optimal hyperplane that

separates data points into various classes. The

quantum kernel enables the SVC to operate in a

higher-dimensional space, thus improving its ability

to distinguish between cancerous and non-cancerous

cells. Following equation establishes the relation

between the quantum kernel and the quantum states.

K(𝑥



,𝑥



) = ⟨Φ(𝑥



)| Φ(𝑥



)⟩

(2)

3.4 Optimization

The Support Vector Classifier (SVC) optimization

using quantum kernel is used to find the optimal

hyperplane, which separates the data points into

various classes. High accuracy obtained proves the

effectiveness of the quantum-enhanced approach in

identifying cancerous cells from MRI scans of brain.

Consider 𝛼



, 𝛼



to be the Lagrange multipliers, then

𝑚𝑖



𝑛



(𝛴

,

𝛼



𝛼



𝑦



𝑦



K(𝑥



,𝑥



)) - 𝛴



𝛼



; 0 ≤

𝛼



≤ C &𝛴



𝛼



𝑦



= 0

(3)

In traditional Support Vector Machines (SVMs),

an optimal hyperplane is identified to distinguish

between different data classes. However, by

applying a quantum feature map like ZZFeatureMap,

classical image data can be elevated to a high-

dimensional Hilbert space. Our approach leverages

the FidelityQuantumKernel, which measures the

similarity between data point pairs by assessing the

fidelity of their corresponding quantum state

representations. This quantum kernel is then

seamlessly integrated into a classical SVM, enabling

the creation of a robust classifier. This classifier

excels at identifying complex, non-linear decision

boundaries within the quantum feature space,

enhancing its ability to accurately categorize data.

3.5 Execution

The implementation of the SVM algorithm utilizing

a quantum kernel involves a series of steps. First,

MRI scans of brain images are retrieved from the

datasets and resized to a uniform scale. The input

data is then categorized into testing and training sets,

with each set containing both cancerous and non-

cancerous images. To prevent feature imbalance,

standard scaling is applied to normalize the MRI

scan features. Following scaling, the data is divided

into training and testing sets to assess the model's

performance.

A quantum circuit comprising 8 qubits is

developed using the PauliFeatureMap, mirroring the

feature dimension. Subsequently, a quantum kernel

fidelity object is created using the feature map and

quantum simulator backend. The backend operation

is performed using QASM Simulator. With the

precomputed kernel, an SVC classifier is initialized

using the quantum kernel. The SVM model is then

trained using the quantum kernel matrix computed

on the training data. The model's performance is

evaluated on the testing data by calculating accuracy

and fine-tuning parameters such as the C value and

(

Cancer Cell Detection Using a Hybrid Quantum and Classical Machine Learning Model

191

number of repetitions. This iterative process enables

optimization of the model's performance.

Throughout this process, the quantum kernel

facilitates the exploration of complex relationships

within the data, enhancing the model's ability to

accurately distinguish between cancerous and non-

cancerous images. By leveraging quantum

computing's capabilities, this approach offers a

promising avenue for improving medical diagnosis

and treatment.

The pseudo code for the implementation of

support vector machine using quantum kernel for the

cancer cells detection is given below.

LOAD & PREPROCESS MRI scans (resize,

normalize, flatten)

SPLIT DATA into training and test sets

SCALE FEATURES using StandardScaler

INITIALIZE ZZFeatureMap with input

feature dimension

CREATE FidelityQuantumKernel using the

feature map

SETUP SVC with precomputed kernel

PIPELINE with scaler and SVC

COMPUTE training kernel matrix with

quantum kernel on training data

TRAIN SVM model with training kernel

matrix

𝐾



= [K (𝑥



,𝑥



)] ∀𝑥



,𝑥



∈𝑋



COMPUTE test kernel matrix with quantum

kernel on test data

PREDICT with SVM model on test kernel

matrix

𝐾



= [K (𝑥



,𝑥



)] ∀𝑥



∈𝑋



,𝑥



∈𝑋



CALCULATE & DISPLAY accuracy with test

labels and

redictions

4 SIMULATION RESULTS AND

DISCUSSIONS

The simulation is performed using qiskit. Fig.3

illustrates the quantum circuit architecture,

accompanied by a cross-validation accuracy of 0.88

± 0.24. The model's accuracy reaches 1.00 when

rounded-off to two digits. The specific values inside

the PauliFeatureMap define the transformations

applied to each qubit within the feature map. These

parameters are essential as they determine the

encoding of classical data into quantum states,

directly impacting the effectiveness of the quantum

machine learning model.

The maximum accuracy is achieved by altering

C-Value, randomness, repetitions of the circuit’s

execution. In quantum machine learning, the

concepts of the `C value`, randomness, and

repetition are pivotal. The `C value`, used in Support

Vector Machines (SVM), balances model

complexity and training accuracy, with higher values

focusing on minimizing training errors and lower

values promoting generalization. Randomness in

machine learning and quantum computing appears in

random initialization of model parameters, data

sampling, and the inherent probabilistic nature of

quantum states and measurements. Repetition is

essential for obtaining reliable results, whether

through averaging outcomes of multiple quantum

measurements or cross-validation in classical

machine learning to ensure stability and

generalization of models. These elements interplay

in quantum kernels and SVMs, where the quantum

instance executes numerous trials to average out the

inherent randomness and stabilize the model’s

predictions, all while carefully tuning the `C value`

to achieve an optimal balance between overfitting

and underfitting.

Figure 3: Output of the SVM model using Quantum

Kernel

The graph in Fig.4 represents support vector

machine using quantum kernel.The contour lines of

red and blue colours indicate the probability of

finding cancer and non-cancer cells respectively.

The black-coloured contour lines indicate the

difficulty in classification of cancer and non-cancer

cells, due to the similarities within the training and

testing datasets.

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Figure 4: Graph of Support Vector Machine using

Quantum Kernel

Fig.5 shows the graph of number of Repetitions

vs C Value vs Accuracy, keeping Randomness

constant. The accuracy increases as the number of

repetitions and the C value increases.

Figure 5: Graph of Repetitions vs C Value vs Accuracy

5 CONCLUSION

The proposed work illustrates the potential of

Quantum Machine Learning in the medical field. By

using Support Vector Machine (SVM) with

Quantum Kernel, cancer detection from MRI scans

is achieved with a higher accuracy. The pre-

processing of classical MRI data using quantum

feature mapping, and with the quantum kernel to

calculate similarity measures, the hybrid model

accurately classifies cancerous and non-cancerous

cells. This model combines the strengths of both

quantum and classical computing, providing a

powerful and efficient tool for medical image

analysis. As quantum computing technology

progresses, such hybrid approaches are expected to

become more feasible, leading to significant

advancements in early cancer detection and

diagnosis. The proposed model gives accurate

detection of cancer cells using quantum machine

learning, thereby enhancing the analysis of medical

image diagnostics.

ACKNOWLEDGEMENTS

Kalluru Hiteshand Pushpa P.V acknowledge funding

support for Chanakya – UGfellowship from the

National Mission on Interdisciplinary Cyber

Physical Systems, of the Department of Science and

Technology, Govt. of India through the I-HUB

Quantum Technology Foundation.

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