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.

Security of quantum key distribution (QKD) relies on certifying that observed correlations arise from genuine quantum entanglement rather than eavesdropper manipulation. Theoretical security proofs assume idealized conditions, practical certification must contend with adaptive adversaries who optimize their attack strategies against detection systems. Established fundamental adversarial limits for quantum certification using Eve GAN, a generative adversarial network trained to produce classical correlations indistinguishable from quantum. Our central finding: when Eve interpolates her classical correlations with quantum data at mixing parameter, all tested detection methods achieve ROC AUC = 0.50, equivalent to random guessing. This means an eavesdropper needs only 5% classical admixture to completely evade detection. Critically, we discover that same distribution calibration a common practice in prior certification studies inflates detection performance by 44 percentage points compared to proper cross distribution evaluation, revealing a systematic flaw that may have led to overestimated security claims. Analysis of Popescu Rohrlich (PR Box) regime identifies a sharp phase transition at CHSH S = 2.05: below this value, no statistical method distinguishes classical from quantum correlations; above it, detection probability increases monotonically. Hardware validation on IBM Quantum demonstrates that Eve-GAN achieves CHSH = 2.736, remarkably exceeding real quantum hardware performance (CHSH = 2.691), illustrating that classical adversaries can outperform noisy quantum systems on standard certification metrics. These results have immediate implications for QKD security: adversaries maintaining 95% quantum fidelity evade all tested detection methods. We provide corrected methodology using cross-distribution calibration and recommend mandatory adversarial testing for quantum security claims.

Quantum key distribution (QKD) security fundamentally relies on the ability to distinguish genuine quantum correlations from classical eavesdropper simulations, yet existing certification methods lack rigorous statistical guarantees under finite-sample conditions and adversarial scenarios. We introduce TARA (Test by Adaptive Ranks), a novel framework combining conformal prediction with sequential martingale testing for quantum anomaly detection that provides distribution-free validity guarantees. TARA offers two complementary approaches. TARA k, based on Kolmogorov Smirnov calibration against local hidden variable (LHV) null distributions, achieving ROC AUC = 0.96 for quantum-classical discrimination. And TARA-m, employing betting martingales for streaming detection with anytime valid type I error control that enables real time monitoring of quantum channels. We establish theoretical guarantees proving that under (context conditional) exchangeability, conformal p-values remain uniformly distributed even for strongly contextual quantum data, confirming that quantum contextuality does not break conformal prediction validity a result with implications beyond quantum certification to any application of distribution-free methods to nonclassical data. Extensive validation on both IBM Torino (superconducting, CHSH = 2.725) and IonQ Forte Enterprise (trapped ion, CHSH = 2.716) quantum processors demonstrates cross-platform robustness, achieving 36% security margins above the classical CHSH bound of 2. Critically, our framework reveals a methodological concern affecting quantum certification more broadly: same-distribution calibration can inflate detection performance by up to 44 percentage points compared to proper cross-distribution calibration, suggesting that prior quantum certification studies using standard train test splits may have systematically overestimated adversarial robustness.

Quantum machine learning (QML) seeks to harness quantum computation to enhance machine learning tasks [1, 2, 3, 4, 5]. Quantum computers can perform certain linear algebra subroutines faster than classical machines under state preparation assumptions [6, 7, 8]. Motivated by such potential quantum speedups, a variety of QML models have been explored--from quantum kernel methods to variational quantum circuits--all aiming to outperform their classical counterparts [9, 10, 11, 12, 13, 14, 15, 16]. A key component of any QML model is how data are encoded into and processed by quantum circuits [17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. For classical input data, one common approach is to embed the data into a quantum state through parameterized gate operations. Recent work has shown that repeatedly encoding data within a circuit-- a technique known as data re-uploading--enhances a model's expressive power, and in particular, that even a single qubit can serve as a universal quantum classifier [27, 28, 18, 29].

Quantum Laboratory, Fujitsu Research, Fujitsu Limited, 4-1-1 Kawasaki, Kanagawa 211-8588, Japan (Dated: September 18, 2025) Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments. This approach can efficiently solve certain quantum problems that are classically intractable, suggesting potential advantages of harnessing quantum data. However, addressing large-scale problems still requires significant amounts of data beyond the limited computational resources of near-term quantum devices. We propose a scalable ML framework called Geometrically Local Quantum Kernel (GLQK), designed to efficiently learn quantum many-body experimental data by leveraging the exponential decay of correlations, a phenomenon prevalent in noncritical systems. In the task of learning an unknown polynomial of quantum expectation values, we rigorously prove that GLQK substantially improves polynomial sample complexity in the number of qubits n, compared to the existing shadow kernel, by constructing a feature space from local quantum information at the correlation length scale. This improvement is particularly notable when each term of the target polynomial involves few local subsystems. Remarkably, for translationally symmetric data, GLQK achieves constant sample complexity, independent of n. We numerically demonstrate its high scalability in two learning tasks on quantum many-body phenomena. These results establish new avenues for utilizing experimental data to advance the understanding of quantum many-body physics. Understanding complex quantum many-body phenomena is a pivotal challenge across various fields, including physics, chemistry, and biology. Classical computational approaches often struggle to capture the intricate interplay of interactions in these systems due to the exponential dimensionality of the Hilbert space. Recent advances in experimental control over quantum systems offer a promising avenue for probing these phenomena.

Vectorized quantum block encoding provides a way to embed classical data into Hilbert space, offering a pathway for quantum models, such as Quantum Transformers (QT), that replace classical self-attention with quantum circuit simulations to operate more efficiently. Current QTs rely on deep parameterized quantum circuits (PQCs), rendering them vulnerable to QPU noise, and thus hindering their practical performance. In this paper, we propose the Vectorized Quantum Transformer (VQT), a model that supports ideal masked attention matrix computation through quantum approximation simulation and efficient training via vectorized nonlinear quantum encoder, yielding shot-efficient and gradient-free quantum circuit simulation (QCS) and reduced classical sampling overhead. In addition, we demonstrate an accuracy comparison for IBM and IonQ in quantum circuit simulation and competitive results in benchmarking natural language processing tasks on IBM state-of-the-art and high-fidelity Kingston QPU. Our noise intermediate-scale quantum friendly VQT approach unlocks a novel architecture for end-to-end machine learning in quantum computing.

Quantum Machine Learning (QML) represents a promising frontier at the intersection of quantum computing and artificial intelligence, aiming to leverage quantum computational advantages to enhance data-driven tasks. This review explores the potential of QML to address the computational bottlenecks of classical machine learning, particularly in processing complex datasets. We introduce the theoretical foundations of QML, including quantum data encoding, quantum learning theory and optimization techniques, while categorizing QML approaches based on data type and computational architecture. It is well-established that quantum computational advantages are problem-dependent, and so potentially useful directions for QML need to be systematically identified. Key developments, such as Quantum Principal Component Analysis, quantum-enhanced sensing and applications in material science, are critically evaluated for their theoretical speed-ups and practical limitations. The challenges posed by Noisy Intermediate-Scale Quantum (NISQ) devices, including hardware noise, scalability constraints and data encoding overheads, are discussed in detail. We also outline future directions, emphasizing the need for quantum-native algorithms, improved error correction, and realistic benchmarks to bridge the gap between theoretical promise and practical deployment. This comprehensive analysis underscores that while QML has significant potential for specific applications such as quantum chemistry and sensing, its broader utility in real-world scenarios remains contingent on overcoming technological and methodological hurdles.

Quantum machine learning models that leverage quantum circuits as quantum feature maps (QFMs) are recognized for their enhanced expressive power in learning tasks. Such models have demonstrated rigorous end-to-end quantum speedups for specific families of classification problems. However, deploying deep QFMs on real quantum hardware remains challenging due to circuit noise and hardware constraints. Additionally, variational quantum algorithms often suffer from computational bottlenecks, particularly in accurate gradient estimation, which significantly increases quantum resource demands during training. We propose Iterative Quantum Feature Maps (IQFMs), a hybrid quantum-classical framework that constructs a deep architecture by iteratively connecting shallow QFMs with classically computed augmentation weights. By incorporating contrastive learning and a layer-wise training mechanism, IQFMs effectively reduces quantum runtime and mitigates noise-induced degradation. In tasks involving noisy quantum data, numerical experiments show that IQFMs outperforms quantum convolutional neural networks, without requiring the optimization of variational quantum parameters. Even for a typical classical image classification benchmark, a carefully designed IQFMs achieves performance comparable to that of classical neural networks. This framework presents a promising path to address current limitations and harness the full potential of quantum-enhanced machine learning.

This study explores the intersection of continuous-variable quantum computing (CVQC) and classical machine learning, focusing on CVQC data encoding techniques, including Displacement encoding and squeezing encoding, alongside Instantaneous Quantum Polynomial (IQP) encoding from discrete quantum computing. We perform an extensive empirical analysis to assess the impact of these encoding methods on classical machine learning models, such as Logistic Regression, Support Vector Machines, K-Nearest Neighbors, and ensemble methods like Random Forest and LightGBM. Our findings indicate that CVQC-based encoding methods significantly enhance feature expressivity, resulting in improved classification accuracy and F1 scores, especially in high-dimensional and complex datasets. However, these improvements come with varying computational costs, which depend on the complexity of the encoding and the architecture of the machine learning models. Additionally, we examine the trade-off between quantum expressibility and classical learnability, offering valuable insights into the practical feasibility of incorporating these quantum encodings into real-world applications. This study contributes to the growing body of research on quantum-classical hybrid learning, emphasizing the role of CVQC in advancing quantum data representation and its integration into classical machine learning workflows.