Our code is available at https://github.com/martaskrt/qdeq.

The success of modern deep learning hinges on the ability to train neural networks at scale. Through clever reuse of intermediate information, backpropagation facilitates training through gradient computation at a total cost roughly proportional to running the function, rather than incurring an additional factor proportional to the number of parameters -- which can now be in the trillions. Naively, one expects that quantum measurement collapse entirely rules out the reuse of quantum information as in backpropagation. But recent developments in shadow tomography, which assumes access to multiple copies of a quantum state, have challenged that notion. Here, we investigate whether parameterized quantum models can train as efficiently as classical neural networks. We show that achieving backpropagation scaling is impossible without access to multiple copies of a state. With this added ability, we introduce an algorithm with foundations in shadow tomography that matches backpropagation scaling in quantum resources while reducing classical auxiliary computational costs to open problems in shadow tomography. These results highlight the nuance of reusing quantum information for practical purposes and clarify the unique difficulties in training large quantum models, which could alter the course of quantum machine learning.

Quantum federated learning (QFL) combines quantum computing and federated learning to enable decentralized model training while maintaining data privacy. QFL can improve computational efficiency and scalability by taking advantage of quantum properties such as superposition and entanglement. However, existing QFL frameworks largely focus on homogeneity among quantum \textcolor{black}{clients, and they do not account} for real-world variances in quantum data distributions, encoding techniques, hardware noise levels, and computational capacity. These differences can create instability during training, slow convergence, and reduce overall model performance. In this paper, we conduct an in-depth examination of heterogeneity in QFL, classifying it into two categories: data or system heterogeneity. Then we investigate the influence of heterogeneity on training convergence and model aggregation. We critically evaluate existing mitigation solutions, highlight their limitations, and give a case study that demonstrates the viability of tackling quantum heterogeneity. Finally, we discuss potential future research areas for constructing robust and scalable heterogeneous QFL frameworks.

This study explores the performance of Quantum Support Vector Classifiers (QSVCs) and Quantum Neural Networks (QNNs) in comparison to classical models for machine learning tasks. By evaluating these models on the Iris and MNIST-PCA datasets, we find that quantum models tend to outperform classical approaches as the problem complexity increases. While QSVCs generally provide more consistent results, QNNs exhibit superior performance in higher-complexity tasks due to their increased quantum load. Additionally, we analyze the impact of hyperparameter tuning, showing that feature maps and ansatz configurations significantly influence model accuracy. We also compare the PennyLane and Qiskit frameworks, concluding that Qiskit provides better optimization and efficiency for our implementation. These findings highlight the potential of Quantum Machine Learning (QML) for complex classification problems and provide insights into model selection and optimization strategies

Effective and accurate diagnosis of diseases such as cancer, diabetes, and heart failure is crucial for timely medical intervention and improving patient survival rates. Machine learning has revolutionized diagnostic methods in recent years by developing classification models that detect diseases based on selected features. However, these classification tasks are often highly imbalanced, limiting the performance of classical models. Quantum models offer a promising alternative, exploiting their ability to express complex patterns by operating in a higher-dimensional computational space through superposition and entanglement. These unique properties make quantum models potentially more effective in addressing the challenges of imbalanced datasets. This work evaluates the potential of quantum classifiers in healthcare, focusing on Quantum Neural Networks (QNNs) and Quantum Support Vector Machines (QSVMs), comparing them with popular classical models. The study is based on three well-known healthcare datasets -- Prostate Cancer, Heart Failure, and Diabetes. The results indicate that QSVMs outperform QNNs across all datasets due to their susceptibility to overfitting. Furthermore, quantum models prove the ability to overcome classical models in scenarios with high dataset imbalance. Although preliminary, these findings highlight the potential of quantum models in healthcare classification tasks and lead the way for further research in this domain.

--Accurate and reliable diagnosis of diseases is crucial in enabling timely medical treatment and enhancing patient survival rates. In recent years, Machine Learning has revolutionized diagnostic practices by creating classification models capable of identifying diseases. However, these classification problems often suffer from significant class imbalances, which can inhibit the effectiveness of traditional models. Therefore, the interest in Quantum models has arisen, driven by the captivating promise of overcoming the limitations of the classical counterpart thanks to their ability to express complex patterns by mapping data in a higher-dimensional computational space. This work proposes a novel approach for enhancing the classification performance of Quantum Neural Networks (QNN) consisting of multiple V ariational Quantum Circuits (VQCs) arranged sequentially. This strategy increases the nonlinearity of the model by exploiting the measurement operation and improving its ability to capture complex patterns.

We compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the employed quantum circuits compatible with near-term quantum devices and use two distinct methodologies: applying randomized NNs on dimensionality-reduced data and applying CNNs to full image data. We evaluate these approaches on three fully-classical data sets of increasing complexity: an artificial hypercube data set, MNIST handwritten digits and industrial images. Our central goal is to shed more light on how quantum and classical models perform for various binary classification tasks and on what defines a good quantum model. Our study involves a correlation analysis between classification accuracy and quantum model hyperparameters, and an analysis on the role of entanglement in quantum models, as well as on the impact of initial training parameters. We find classical and quantum-classical hybrid models achieve statistically-equivalent classification accuracies across most data sets with no approach consistently outperforming the other. Interestingly, we observe that quantum NNs show lower variance with respect to initial training parameters and that the role of entanglement is nuanced. While incorporating entangling gates seems advantageous, we also observe the (optimizable) entangling power not to be correlated with model performance. We also observe an inverse proportionality between the number of entangling gates and the average gate entangling power. Our study provides an industry perspective on quantum machine learning for binary image classification tasks, highlighting both limitations and potential avenues for further research in quantum circuit design, entanglement utilization, and model transferability across varied applications.

Early identification of abnormal physiological patterns is essential for the timely detection of cardiac disease . This work introduces a hybrid quantum - classical convolutional neural network (QCNN) designed to classify S3 and murmur abnormalities in heart sound signals. The approach transforms one - dimensional phonocardiogram (PCG) signals into compact two - dimensional images through a combination of wavelet feature extraction and adaptive threshold compression methods . We compress the cardiac sound patterns into an 8 - pixel image so that only 8 qubits are needed for the quantum stage. Preliminary results on the HLS - CMDS dataset demonstrate 93.3 3 % classification accuracy on the test set, and 97.14% on the train set, suggesting that quantum models can effi-cientl y capture temporal - spectral correlations in biomedical signals. To our knowledge, this is the first application of a QCNN algorithm for bio acoustic signal processing . The proposed method represents an early step toward quantum - enhanced diagnostic systems f or resource - constrained healthcare environments.

This study presents a comprehensive empirical comparison between quantum machine learning (QML) and classical machine learning (CML) approaches in Automated Market Makers (AMM) and Decentralized Finance (DeFi) trading strategies through extensive backtesting on 10 models across multiple cryptocurrency assets. Our analysis encompasses classical ML models (Random Forest, Gradient Boosting, Logistic Regression), pure quantum models (VQE Classifier, QNN, QSVM), hybrid quantum-classical models (QASA Hybrid, QASA Sequence, QuantumRWKV), and transformer models. The results demonstrate that hybrid quantum models achieve superior overall performance with 11.2\% average return and 1.42 average Sharpe ratio, while classical ML models show 9.8\% average return and 1.47 average Sharpe ratio. The QASA Sequence hybrid model achieves the highest individual return of 13.99\% with the best Sharpe ratio of 1.76, demonstrating the potential of quantum-classical hybrid approaches in AMM and DeFi trading strategies.

Quantum federated learning (QFL) has been recently introduced to enable a distributed privacy-preserving quantum machine learning (QML) model training across quantum processors (clients). Despite recent research efforts, existing QFL frameworks predominantly focus on unimodal systems, limiting their applicability to real-world tasks that often naturally involve multiple modalities. T o fill this significant gap, we present for the first time a novel multi-modal approach specifically tailored for the QFL setting with the intermediate fusion using quantum entanglement. Furthermore, to address a major bottleneck in multimodal QFL, where the absence of certain modalities during training can degrade model performance, we introduce a Missing Modality Agnostic (MMA) mechanism that isolates untrained quantum circuits, ensuring stable training without corrupted states. Simulation results demonstrate that the proposed multimodal QFL method with MMA yields an improvement in accuracy of 6.84% in independent and identically distributed (IID) and 7.25% in non-IID data distributions compared to the state-of-the-art methods.