Variational Quantum Circuit Classifies Brain Tumors Using Compact Amplitude Encoding Architecture

Researchers have demonstrated a specialized hybrid quantum-classical computing methodology that successfully classifies brain tumor magnetic resonance imaging scans with high diagnostic accuracy and remarkable parameter efficiency. Utilizing a compact four-qubit Variational Quantum Classifier driven by an amplitude encoding technique, the proposed system achieved an overall classification accuracy of 95 percent and an exceptional specificity of 0.983. The experimental investigation evaluated multi-class discrimination across four distinct clinical categories: glioma, meningioma, pituitary tumors, and normal magnetic resonance scans representing the absence of a tumor. When evaluated against established classical machine learning baselines—specifically Support Vector Machines, Random Forests, and Multi-Layer Perceptrons—the quantum model demonstrated clear quantitative superiority in diagnostic precision. Crucially, the variational quantum circuit attained this top performance using only 24 trainable parameters, representing a 3.5-fold reduction in parameter count compared to the optimal classical Multi-Layer Perceptron baseline. This substantial parameter efficiency demonstrates that a custom-designed, resource-efficient quantum architecture can surpass conventional classical machine learning models in medical image classification, establishing an empirical validation of quantum advantage within diagnostic imaging pipelines.

Brain tumors represent one of the deadliest medical conditions worldwide, where timely identification of specific tumor types is essential for establishing clinical treatment planning and extending patient survival. Within oncology, primary brain tumors are classified by cellular origin: gliomas arise from glial cells in the brain or spinal cord, meningiomas develop from the protective meninges membranes, and pituitary tumors originate from the pituitary gland. Magnetic resonance imaging provides a powerful non-invasive diagnostic modality, generating axial, coronal, and sagittal views across T1-weighted, T2-weighted, and fluid-attenuated inversion recovery sequences. In densely populated countries like India, manual radiological detection poses a time-consuming and error-prone challenge dependent on image quality and practitioner expertise. Although deep learning addresses medical problems effectively, complex architectures like convolutional networks and transformers face significant computational hurdles, requiring excessive memory, storage, energy, and prolonged training when handling high-dimensional medical data.

To address these classical computing bottlenecks and accommodate restricted qubit counts on quantum circuits, the research team established a systematic preprocessing and dimensionality reduction pipeline. The investigation utilized magnetic resonance images from the Brain Tumor MRI Dataset in the Kaggle BraTS repository, comprising 1,612 glioma cases, 1,645 meningioma cases, 1,757 pituitary tumor cases, and 2,000 cases with no tumor. Each image was preprocessed by resizing to a uniform 32 by 32 pixel resolution, flattened into a one-dimensional array, and normalized by dividing pixel values by 255. Even after resizing and flattening, an image contains 1,024 features, which would require an excessive number of physical qubits if encoded directly, as required qubit counts grow logarithmically with feature dimension. To ensure compatibility with quantum circuits, Principal Component Analysis was implemented across 3,000 flattened grayscale images, successfully reducing the 1,024 image features to a compact set of 16 principal components.

The statistical assessment of the Principal Component Analysis confirmed that this dimensional reduction preserved the necessary information while enabling lossless quantum state loading. Analysis of the scree plot across the principal components showed that the first four components alone retained 90.08 percent of the dataset variance, achieving an optimal trade-off between dimensionality reduction and information preservation. This minimal information loss resulted in a calculated quantum state fidelity of exactly 1.0, directly validating the success of the amplitude encoding process. The perfect fidelity confirmed that the resulting quantum state accurately mirrored the intended target state derived from the normalized principal components. This lossless mapping of classical data into quantum amplitudes validated both the data normalization procedure, which ensured unit norm vectors where the sum of squared amplitudes equals one, and the reliable performance of the amplitude embedding implementation prior to variational quantum processing.

To bridge classical image features and quantum computing architectures, the researchers employed amplitude encoding, which maps classical information directly into the probability amplitudes of a quantum state. In quantum theory, superposition allows qubits to exist in combinations of computational basis states simultaneously, while entanglement links multiple qubits such that the state of one cannot be described independently of the others. In contrast to angle encoding, which rotates qubit angles, or basis encoding, which transforms classical bits into basis states, amplitude encoding maps a normalized classical vector of length sixteen across the sixteen computational basis states of a four-qubit register. Because four qubits yield sixteen quantum state amplitudes (two to the fourth power equals sixteen), this mathematical formulation compresses sixteen classical features into four qubits. This exponential data representation capacity provides a dramatic compression advantage over linear classical methods, enabling compact, efficient embedding of medical imaging features within quantum circuits.

The Variational Quantum Circuit was constructed using the PennyLane library across four qubit lines indexed zero, one, two, and three, receiving the amplitude-encoded features following classical dimensionality reduction. The circuit architecture is structured around two repeating variational layers, or ansatz units, designed to process the encoded quantum states. Within each layer, single-qubit operations are performed using four rotational gates with trainable parameters, followed by three Controlled-NOT gates that establish a linear, nearest-neighbor form of entanglement between adjacent qubits. Across the two layers, the circuit utilizes a total of 24 rotational gates and 6 Controlled-NOT gates, deliberately placed to maximize expressive power. The entire architecture maintains a shallow circuit depth of 14, representing the length of the longest sequential gate path. This shallow depth was deliberately chosen to minimize the accumulation of decoherence noise, ensuring the architecture remains lightweight, conducive to stable training, and compatible with near-term Noisy Intermediate-Scale Quantum hardware constraints.

Training of the Variational Quantum Classifier was conducted using the PennyLane default.qubit simulator in Google Colab alongside scikit-learn and OpenCV, establishing an ideal, noiseless performance benchmark. To ensure stable measurement statistics for classification, the experimental setup utilized a high shot count of 1,024 shots. The dataset was partitioned into an 80 percent training set and a 20 percent test set to assess model generalization. The circuit’s 24 trainable parameters were optimized over 100 epochs using a classical Stochastic Gradient Descent optimizer configured with a learning rate of 0.1. Mean Squared Error served as the cost function, evaluated by comparing measured expectation values against one-hot encoded diagnostic labels. During training, the quantum circuit parameters converged smoothly without erratic fluctuations, confirming a stable optimization process. Furthermore, the model maintained a steady gradient norm of 0.11, demonstrating reliable convergence and confirming that the low-depth ansatz successfully avoided the barren plateau issue.

The classification output of the quantum circuit is obtained from measured expectation values of single-qubit Pauli-Z observables, which exhibit a direct sinusoidal dependence on qubit rotation angles. In the experimental analysis of rotation angles ranging from 0 to 180 degrees, the Pauli-Z expectation value follows a cosine function. Applying a rotation around the Y-axis transforms the initial zero state into a superposition state governed by half-angle cosine and sine amplitudes. Evaluating the Pauli-Z operator expectation value for this transformed state yields a cosine dependency, starting at positive one for zero degrees where the qubit occupies the plus one eigenstate. As rotation proceeds, the expectation value decreases smoothly to zero at ninety degrees, reflecting an equal superposition of zero and one states with equal measurement probabilities, before reaching negative one at 180 degrees. This association between qubit rotations and Pauli-Z expectation values provides the foundational mechanism for producing classical predictions from the quantum circuit.

The development of this quantum diagnostic framework connects with a growing progression of research in quantum machine learning. Early theoretical foundations established that quantum algorithms could provide potential speedups in clustering and data classification, while subsequent work formulated circuit design and explored amplitude encoding feasibility on small datasets. Later studies applied variational quantum circuits to standard image collections like MNIST, while medical imaging investigations examined amplitude encoding in hybrid models for mammogram tumor detection and brain MRI classification. In classical brain tumor analysis, convolutional architectures and Capsule Networks achieved high robustness with fewer parameters, yet classical deep models continue to suffer from high computational costs and limited interpretability. Meanwhile, emerging quantum frameworks have introduced generative learning models combining Principal Component Analysis with variational circuits, fully quantum neural networks, and hybrid convolutional-quantum architectures. Extending this trajectory, the present study evaluated fully amplitude-encoded quantum circuits on brain MRI data, incorporating quantum-native metrics such as entanglement entropy, circuit depth, and parameter-to-qubit scaling.

In direct comparative benchmarks evaluated on the test dataset, the four-qubit Variational Quantum Classifier outperformed established classical baselines, including Random Forest, Support Vector Machine, and Multi-Layer Perceptron models. The quantum classifier registered the highest accuracy of 95 percent and demonstrated superior robustness with a specificity of 0.983, confirming effective multi-class discrimination across glioma, meningioma, pituitary, and non-tumor cases. Confusion matrix and receiver operating characteristic curve analyses validated that amplitude encoding successfully mapped the 16 classical features into quantum states, enabling the shallow circuit to capture non-linear decision boundaries more effectively than classical architectures. Crucially, the model accomplished this using only 24 trainable parameters, achieving a 3.5-fold gain in parameter efficiency compared to the classical Multi-Layer Perceptron. The authors concluded that amplitude encoding provides a feasible, NISQ-compatible mechanism to drastically reduce computational complexity, positioning quantum machine learning as a robust solution for medical image analysis while opening avenues for future hybrid diagnostic systems on larger quantum hardware.

Subject of Research: Brain tumor MRI classification using a variational quantum circuit and amplitude encoding

Article Title: A quantum computing approach for brain tumor image classification using amplitude encoding technique

Article References: K.P., M., Thiruvenkadam, K., & Pathmanaban, S. (2026). A quantum computing approach for brain tumor image classification using amplitude encoding technique. Discover Quantum Science, 2(1), Article 8. https://doi.org/10.1007/s44464-026-00005-z

Image Credits: AI Generated

DOI: 10.1007/s44464-026-00005-z

Keywords: Quantum Computing, Variational Quantum Circuits, Brain Tumor Classification, Amplitude Encoding, Medical Imaging, PennyLane, Machine Learning, Principal Component Analysis, quantum, computing, approach, brain