Abstract Variational quantum algorithms are among the most widely studied approaches for applying near-term quantum devices to learning tasks. In this work we investigate a supervised quantum-autoencoder-style classifier that encodes images by amplitude encoding and predicts labels from a designated readout sub-register. Building on the quantum-autoencoder (QAE)-style classifier of Asaoka and Kudo, we make three contributions. First, we give a rigorous equivalence result showing that, for computational-basis label states, the original SWAP-test-based training objective can be estimated without ancilla and reference registers by directly measuring the readout subsystem. This simplification reduces circuit resources while preserving the same training signal. Second, we propose a lightweight hybrid extension: instead of using only the probability of the correct readout bitstring, we estimate the full readout distribution and apply a learnable temperature-and-bias post-processing followed by a softmax normalization. Across MNIST, KMNIST, and Fashion-MNIST (restricted to eight classes), this classical post-processing yields substantial and statistically significant improvements in evaluation accuracy, consistently across cross-entropy and mean-squared-error objectives. Finally, to interpret these gains we analyze Fisher-geometry summaries based on effective dimension and complementary Fisher-spectrum diagnostics for both the quantum models and the classical baselines. Empirically, the hybrid quantum model is associated with a more spectrally concentrated and anisotropic Fisher geometry, with Fisher mass concentrated in fewer dominant directions and with a substantially larger local Fisher scale after training.
Abstract Variational quantum algorithms are among the most widely studied approaches for applying near-term quantum devices to learning tasks. In this work we investigate a supervised quantum-autoencoder-style classifier that encodes images by amplitude encoding and predicts labels from a designated readout sub-register. Building on the quantum-autoencoder (QAE)-style classifier of Asaoka and Kudo, we make three contributions. First, we give a rigorous equivalence result showing that, for computational-basis label states, the original SWAP-test-based training objective can be estimated without ancilla and reference registers by directly measuring the readout subsystem. This simplification reduces circuit resources while preserving the same training signal. Second, we propose a lightweight hybrid extension: instead of using only the probability of the correct readout bitstring, we estimate the full readout distribution and apply a learnable temperature-and-bias post-processing followed by a softmax normalization. Across MNIST, KMNIST, and Fashion-MNIST (restricted to eight classes), this classical post-processing yields substantial and statistically significant improvements in evaluation accuracy, consistently across cross-entropy and mean-squared-error objectives. Finally, to interpret these gains we analyze Fisher-geometry summaries based on effective dimension and complementary Fisher-spectrum diagnostics for both the quantum models and the classical baselines. Empirically, the hybrid quantum model is associated with a more spectrally concentrated and anisotropic Fisher geometry, with Fisher mass concentrated in fewer dominant directions and with a substantially larger local Fisher scale after training.
Brain tumor image classification is an essential pre-processing task for tumor diagnosis and treatment planning. In medical imaging, quantum computing analyse medical imaging data, offering potential speedups and new representations compared to classical methods. The brain images are transformed through resizing and normalization to a uniform 32 × 32 × 3 resolution. Subsequently, these processed images are converted into vectors to enable encoding into quantum states. The feature set is reduced using Principal Component Analysis (PCA) to ensure compatibility with the restricted qubit count in the quantum circuits. Through amplitude encoding, these vectors are mapped to quantum states, allowing for a compact and efficient data representation within the quantum domain. A parameterized Variational Quantum Circuit(VQC), consisting of entangling gates and trainable rotations, processes the encoded quantum states to learn features that can effectively discriminate between classes. The loss is calculated from the measured expectation values of Pauli-Z observables and optimized using classical gradient descent, where the objective function is the mean squared error. The trained quantum model is designed for multi-class classification, specifically distinguishing between meningioma, glioma tumors, pituitary tumors, and the absence of a tumor. The outcome of this proposed work demonstrates the VQC’s advantage over classical baselines, including Random Forest, and Support Vector Machine (SVM) and Multi-Layer Perceptron (MLP). The VQC achieved the highest accuracy of 95% and the best robustness (Specificity 0.983). Crucially, the VQC accomplished this using only 24 trainable parameters, showcasing a significant increase in parameter efficiency compared to the classical models. The novelty of this work is the quantitative demonstration that a custom-designed, resource-efficient quantum model can outperform established classical deep learning methods in both performance and efficiency for complex medical image classification. The VQC provides a 3.5-fold gain in parameter efficiency, achieving the highest accuracy of 95% using only 24 trainable parameters. This efficiency is enabled by the novel application of amplitude encoding to the medical images, which compresses 16 features into just 4 qubits. The VQC demonstrates robustness vital for medical diagnostics, achieving a Specificity of 0.983. Its shallow architecture is also NISQ-friendly and remains stable by avoiding the Barren Plateau issue (Gradient Norm: 0.11), validating the path toward quantum advantage in diagnostic tools. The results of this approach highlight the potential amplitude encoding in quantum machine learning, as a feasible and effective method for classifying real-world medical images. This work also opens avenues for future hybrid quantum-classical diagnostic systems that could utilize richer quantum state encodings for significant gains in computational efficiency and accuracy.
Quantum Machine Learning methods are becoming a key component for various types of tasks making predictions or decisions based on datasets. Recent efforts and researches on quantum computing point out the significance of quantum speedup advantage, especially for learning processes that require enormous amount of computational resources. Advances in both quantum hardware design and hybrid quantum-classical software frameworks accommodate a paradigm shift from classical to quantum. In consideration with this quantum leap notion, we investigate the capability of variational quantum algorithms (VQA) on a real world problem of user localization dealing with the binary classification task. This paper introduces a VQA with four variants that differ in the number of layers related to the variational quantum circuit (VQC) part of the VQA. The samples from a publicly available user localization dataset are first preprocessed through padding, scaling and normalization. Next, they are mapped into three qubit quantum states using amplitude encoding as a data embedding scheme. Unitary transformation of the mapped quantum data in the VQC is followed by a measurement in computational basis to produce predictions for the labels. The error between true and predicted labels is computed in a classical manner and a cost function minimization process is executed with the aid of gradient descent algorithm. The updated training parameters from the optimization stage are fed into the VQC and this process is repeated until the learnable parameters converge. The simulation results demonstrate that the designed VQA for binary classification achieves an accuracy value of 99% in the training phase. Moreover, the ratio of predicted labels to true labels approaches to 93% during the validation of actual user locations based on the signal strength received from the routers that are positioned at different places in a facility. Keywords—quantum machine learning, user localization, variational quantum algorithm, variational quantum circuit, amplitude encoding
This thesis presents a systematic empirical evaluation of quantum machine learning performance under noisy intermediate-scale quantum (NISQ) era constraints. Through 670 controlled experiments, it evaluated quantum kernel support vector machines and variational quantum classifiers against classical baselines on MNIST binary and multiclass classification tasks with systematic variation of problem difficulty, feature dimensionality (4, 8 qubits), and training set size (n ∈{100, 250, 400, 500, 2000, 4000}). Statistical rigor was ensured through five random seeds per condition and comprehensive significance testing. During the testing with binary datasets, classical methods (SVM, logistic regression, k-NN, neural networks) achieved 85.9% to 99.6% accuracy with training times under one second across all sample sizes. Quantum kernel methods utilizing ZZ feature maps yielded 70.5% to 96.0% accuracy, requiring 129 to 2,140 seconds training with quadratic sample size scaling. Larger scale quantum experiments (n = 4000 for both architectures, 8-qubit encoding with n = 2000 for quantum kernels) proved computationally impossible on available hardware leading to out of memory errors, highlighting practical NISQ-era scalability constraints. Variational quantum classifiers exhibited persistent performance stagnation, failing to exceed 66.5% accuracy despite increases in training data and feature dimensionality. Performance gaps ranged from 3.3 to 35.2 percentage points. All quantum classical differences achieved statistical significance (p< 0.05, with 13 of 14 comparisons meeting p< 0.01) and exhibited large to very large efect sizes (d> 1.0, with 13 of 14 comparisons exceeding d> 2.0). To further evaluate performance and scalability, a 4 class classification experiment was conducted following an identical experimental protocol, with training set sizes of n ∈{100, 250, 400}. Across 180 runs, classical baselines achieved mean accuracies between 87.2% and 95% across both 4 and 8 dimensional data. Quantum Kernel SVM struggled during runs with 4 dimensions, accuracy varying between 64.6% and 74%. Quantum Kernel SVM accuracy declined 16%-25% when the dimension and qubit count were increased to 8, showing findings of exponential kernel concentration. The Variational Quantum Classifier also performed poorly, with accuracy ranging from 43.4% to 44.6% across all runs, providing further evidence that it failed to leverage additional features or training data. Experiments employed noiseless statevector simulation, establishing that quantum underperformance stems from fundamental algorithmic limitations independent of hardware noise. A further extension to 8 class classification (digits 0–7) confirmed and amplified these findings: classical methods maintained 65–83% accuracy while Quantum Kernel SVM degraded to 34–47% and VQC collapsed to 21–23%, approaching the 12.5% random baseline. Supplementary appendix experiments further examined amplitude encoding on raw 784 dimensional pixel features and an alternative angle encoding scheme on the 8-class task; the latter demonstrated that replacing the ZZ Feature Map with simple per qubit rotations substantially recovered quantum kernel performance, suggesting feature map design as a more consequential variable than circuit depth or qubit count in near-term quantum classification.
We implement a hybrid quantum-classical model for image classification that compresses MNIST digit images into a low-dimensional feature space and then maps these features onto a 5-qubit quantum state. First, an autoencoder compresses each 28×28 image (784 pixels) into a 64-dimensional latent vector, preserving salient features of the digit with minimal reconstruction error. We further reduce the latent representation to 5 principal components using Principal Component Analysis (PCA), to match the 5 available qubits. These 5 features are encoded as rotation angles in a quantum circuit with 5 qubits. The quantum feature map applies single-qubit rotations (Ry gates) proportional to the feature values, followed by a Hadamard gate and a cascade of entangling CNOT gates to produce a non-product entangled state. Measuring the 5-qubit state yields a 32-dimensional probability distribution over basis outcomes, which serves as a quantum-enhanced feature vector for classification. A classical neural network with a softmax output is then trained on these 32-dimensional quantum feature vectors to predict the digit class. We evaluate the hybrid model on the MNIST dataset and compare it to a purely classical baseline that uses the 64-dimensional autoencoder latent features for classification. The results show that the hybrid model can successfully classify digits, demonstrating the feasibility of integrating quantum computing in the classification pipeline, although its accuracy (about 75\% on test data) currently falls below the classical baseline (about 98\% on the same compressed data).
Abstract One-class classification (OCC) is a fundamental problem in pattern recognition with a wide range of applications. This work presents a semi-supervised quantum machine learning algorithm for such a problem, which we call a variational quantum one-class classifier (VQOCC). The algorithm is suitable for noisy intermediate-scale quantum computing because the VQOCC trains a fully-parameterized quantum autoencoder with a normal dataset and does not require decoding. The performance of the VQOCC is compared with that of the one-class support vector machine (OC-SVM), the kernel principal component analysis (PCA), and the deep convolutional autoencoder (DCAE) using handwritten digit and Fashion-MNIST datasets. The numerical experiment examined various structures of VQOCC by varying data encoding, the number of parameterized quantum circuit layers, and the size of the latent feature space. The benchmark shows that the classification performance of VQOCC is comparable to that of OC-SVM and PCA, although the number of model parameters grows only logarithmically with the data size. The quantum algorithm outperformed DCAE in most cases under similar training conditions. Therefore, our algorithm constitutes an extremely compact and effective machine learning model for OCC.
The expressivity and scalability of fixed feature embeddings and shallow quantum circuits for Quantum Support Vector Machines (QSVMs) are restricted due to the limitations of near-term hardware. In this work, we propose a novel QSVM framework consisting of Low-Rank Adaptation (LoRA)-modified VisionTransformer embeddings as well as trainable variational quantum circuits. The architecture enhances the representational power by the joint optimization of embedding and circuit parameters. Empirical evaluation on distilled benchmark datasets shows significant performance gains, with up to 38.7% absolute accuracy improvement on MNIST (61.3% to 100.0%). The model also achieves 91% to 100% test accuracies on Fashion-MNIST, KMNIST and CIFAR-10 datasets with only 200 training samples for each dataset. The results show that the performance improvements are due to the joint design between the feature embeddings and the quantum circuits, rather than just the quantum kernels. Cross-dataset evaluations and circuit-depth analyses provide experimental evidence that the approach is suitable for scalable quantum machine learning in image classification tasks.