Recent advances in quantum computing and machine learning have brought about a promising intersection of these two fields, leading to the emergence of quantum machine learning (QML). However, the integration of quantum computing and machine learning poses several challenges. One of the prominent challenges lies in the presence of barren plateaus (BP) in QML algorithms, particularly in quantum neural networks (QNNs). Recent studies have successfully identified the fundamental causes underlying the existence of BP in QNNs. This paper presents a framework designed to explore the interplay of multiple factors contributing to the BP problem in quantum neural networks (QNNs), which poses a critical challenge for the practical applications of QML. We focus on the combined influence of data encoding, qubit entanglement, and ansatz expressibility in hybrid quantum neural networks (HQNNs) for multi-class classification tasks. Our framework aims to empirically analyze the joint impact of these factors on the training landscape of HQNNs. Our results show that the occurrence of the BP problem in HQNNs is contingent upon the expressibility of the underlying ansatz and the type of the adopted data encoding technique. Additionally, we observe that qubit entanglement also plays a role in exacerbating the BP problem. Leveraging various evaluation metrics for classification tasks, we systematically evaluate the performance of HQNNs and provide recommendations tailored to different constraint scenarios. Our findings emphasize the significance of our framework in addressing the practical success of QNNs.
Recent advances in quantum computing and machine learning have brought about a promising intersection of these two fields, leading to the emergence of quantum machine learning (QML). However, the integration of quantum computing and machine learning poses several challenges. One of the prominent challenges lies in the presence of barren plateaus (BP) in QML algorithms, particularly in quantum neural networks (QNNs). Recent studies have successfully identified the fundamental causes underlying the existence of BP in QNNs. This paper presents a framework designed to explore the interplay of multiple factors contributing to the BP problem in quantum neural networks (QNNs), which poses a critical challenge for the practical applications of QML. We focus on the combined influence of data encoding, qubit entanglement, and ansatz expressibility in hybrid quantum neural networks (HQNNs) for multi-class classification tasks. Our framework aims to empirically analyze the joint impact of these factors on the training landscape of HQNNs. Our results show that the occurrence of the BP problem in HQNNs is contingent upon the expressibility of the underlying ansatz and the type of the adopted data encoding technique. Additionally, we observe that qubit entanglement also plays a role in exacerbating the BP problem. Leveraging various evaluation metrics for classification tasks, we systematically evaluate the performance of HQNNs and provide recommendations tailored to different constraint scenarios. Our findings emphasize the significance of our framework in addressing the practical success of QNNs.
The field of machine learning has experienced rapid development over the last decades and has found numerous applications across diverse domains ranging from industrial to personal settings. Quantum computing, on the other hand, is an emerging field offering a fundamentally different computational paradigm that can potentially surpass traditional computational approaches in certain domains.In this thesis, we explore the intersection between these two fields, commonly referred to as quantum machine learning (QML). In particular, we focus on Quantum neural networks (QNNs), which have gained attention in the field of QML due to the unparalleled success of their classical counterparts. However, the limitations of the current quantum computers have led to hybrid approaches combining classical and quantum devices. We, therefore, use hybrid quantum neural networks (HQNNs) to explore the potential advantages of QNNs in various practical applications.First, we explore the design space of HQNNs as there is no standardized methodology for designing quantum layers in HQNNs. Various quantum layer designs with different data encoding techniques are investigated, identifying the optimal set of quantum gates for different encoding strategies.We also investigate the impact of cost function globality and locality on the performance of HQNNs for real-world applications, namely: binary and multi-class classification. We exploit a single parameterized quantum circuit (PQC) structure with both single (local) and all-qubit (global) measurements. Our results show that the global cost function significantly outperforms the local cost function on multi-class classification. In contrast, both global and local cost functions have comparable performance on binary classification problems.Moreover, we propose a framework for analyzing the impact of various components of HQNNs with respect to each other on multi-class classification tasks, specifically focusing on the data encoding and quantum layers (expressibility and entanglement between qubits). Two ansatz structures, entangled and unentangled, are used to investigate the existence of the barren plateau (BP) in HQNNs. We further evaluate the impact of entanglement on trainability and provide recommendations for different constraint scenarios. The results show that the overall expressibility of the quantum layers impacts the presence of the BP phenomenon and that entanglement plays a role in the training landscapes of HQNNs, depending on the data encoding technique. Finally, we propose a new architecture for quantum neural networks (QNNs) called residual quantum neural networks (ResQNets), inspired by the classical residual neural networks (ResNets), to address the issue of BP in QNNs. ResQNets split the conventional QNN architecture into multiple quantum nodes (QNs), each with its own PQC, allowing residual connections between QNs. The results show that incorporating residual connections results in improved training performance, making ResQNets a promising solution for overcoming the problem of BP in QNNs.
Hybrid quantum neural networks (HQNNs) integrate parameterized quantum circuits (PQCs) within classical networks, where the behavior of the underlying PQCs is often the primary focus of analysis. In this context, expressibility and trainability are widely used to characterize PQC's performance and are commonly assumed to exhibit a trade-off, where highly expressive circuits are more susceptible to barren plateaus. However, the validity of this relationship in HQNNs remains unclear. In this paper, we systematically analyze the expressibility--trainability relationship in HQNNs across varying circuit depths, qubit counts, entanglement topologies. We consider different training configurations, including pure PQCs, quantum-only training in hybrid setting, and full end-to-end training of hybrid models. Our results show that pure PQCs exhibit only a weak and regime-dependent trade-off, while hybrid architectures increasingly disrupt and can eliminate this relationship under full hybrid training. This indicates that classical components reshape the optimization landscape, decoupling trainability from PQC expressibility. We further propose a multi-objective neural architecture search (NAS) framework that jointly optimizes expressibility, trainability, and task performance over a combined classical--quantum design space, revealing different Pareto-optimal solutions under full end-to-end and quantum only training in hybrid setting. different trainability definitions. Our results suggest that hybridization is not just an implementation detail, but a defining factor in the performance of quantum machine learning models.
Abstract Hybrid quantum-classical neural networks (HQNNs) are a promising paradigm in quantum enhaced machine learning, yet their evaluation remains an open challenge constrained by two key issues: reliance on single metrics (e.g., loss or gradients) and synthetic benchmarks that fail to reflect real-world complexities. This work introduces a multi-metric diagnostic framework, that offers a holistic view of HQNN behavior by analyzing primary axes: quantum trainability (gradient norms), model convergence (loss curves), and quantum utility (via the Quantum Contribution Score, QCS). And secondary axes: expressivity, gradient efficiency and entanglement entropy. Across 16 models over real-world and synthetic data with a classical artificial neural network as baseline. Through this framework empirical phenomena in practical evaluations are developed, including gradient recovery after barren plateaus, data and expressivity dependent QCS trends, relation between gradient behaviour and qubit to layer ratio and model convergence despite barren plateaus.
Quantum Neural Networks (QNNs) offer a promising framework for integrating quantum computing principles into machine learning, yet their practical capabilities and limitations remain insufficiently studied. In this work, we systematically investigate the trainability and approximation properties of QNNs by benchmarking diverse circuit architectures and encoding strategies across synthetic and real-world datasets. We analyze several ansätze, including Hamming, binary, exponential, ternary, turnpike and Golomb, by evaluating their ability to learn synthetic data modeled as random finite Fourier series. To assess real-world applicability, we further evaluate QNNs on two time-series classification tasks: a Fischertechnik pneumatic leak detection dataset and the publicly available NASA bearing fault dataset. Our experiments show that while broader frequency spectra can theoretically enhance expressivity, practical trainability is strongly influenced by architectural factors such as qubit count and circuit depth. Notably, we find that QNNs perform best when the frequency spectrum is tailored to the target function's complexity but remains as compact as possible. Moreover, architectures with identical frequency spectra can differ in trainability, with configurations using more qubits and fewer layers generally performing better, except in the single-layer case. These findings provide guidelines for selecting QNN ansätze and offer new insights into the interplay between expressivity and trainability in quantum machine learning.
Quantum machine learning (QML) is an emerging research area that combines quantum computation with classical machine learning (ML). The primary objective of QML is to enhance the performance of traditional ML algorithms by harnessing quantum phenomena. Inspired by the success of classical neural networks (NNs), their quantum analog, commonly known as quantum neural networks (QNNs), are widely being investigated. Despite the significant interest, the literature still lacks some concrete evidence about QNN's superiority over their classical counterparts, especially in practical applications. This paper empirically demonstrates a greater capacity in hybrid quantum neural networks (HQNNs) for a practical application, namely multi-class classification. In particular, we train both the HQNNs and their equivalent classical counterparts on the same data. We then benchmark the models' accuracy for quantifying model's capacity, where greater accuracy typically implies greater capacity. The results demonstrate a clear quantum advantage, i.e., greater capacity of HQNNs over their classical counterparts, where the HQNN models constantly achieve better accuracy. This superiority in performance by HQNNs serves as a foundational study for further investigation to magnify the quantum advantage in real-world applications of HQNNs.
Quantum machine learning has emerged as a promising application domain for near-term quantum hardware, particularly through hybrid quantum-classical models that leverage both classical and quantum processing. Although numerous hybrid architectures have been proposed and demonstrated successfully on benchmark tasks, a significant open question remains regarding the specific contribution of quantum components to the overall performance of these models. In this work, we aim to shed light on the impact of quantum processing within hybrid quantum-classical neural network architectures through a rigorous statistical study under ideal, noise-free simulation. We systematically assess a selection of commonly used HQNN architectures on three binary medical classification tasks covering medical signal data as well as planar and volumetric images. In doing so, we examine the influence attributable to classical and quantum aspects such as encoding schemes, entanglement, and circuit size. Within this experimental setting, we find that in best-case scenarios, hybrid models show performance comparable to their classical counterparts. However, in most cases, performance metrics deteriorate when the investigated QNN components replace matched classical processing layers. Our multi-modal analysis provides empirical insights into the contributions of the tested quantum components and advocates for cautious claims and design choices for hybrid models in near-term applications.