Quantum Neural Networks (QNNs) have gained significant attention due to their strong expressibility and potential learning. The effectiveness of QNNs is impacted by the choice of input embedding when training samples are limited. Numerous QNN architectures have been reported in the literature; however, the effects of input embedding and entanglement strategies have yet to be examined. In this study, a comprehensive investigation of different embedding techniques, such as θ = x . π / Δ and θ = a r c t a n ( x ) + π / Δ , has been used in a QNN to predict the melting point of the metal oxide, where the dataset is limited to only 70 samples. Further, multiple scaling factors ( Δ ) for each embedding with linear and circular entanglements, along with variational circuit depths, have been examined. The robustness of each embedding has been evaluated using 21 independent random parameter initialisations, while prediction performance has been statistically evaluated using R 2 and RMSE with a generalisation gap. From the results, it is observed that the embeddings such as θ = a r c t a n ( x ) + π / 4 and θ = a r c t a n ( x ) + π / 5 have been performed invariably across random initialisation and achieved superior results compared with other embeddings. Finally, the performance of the QNN has been compared with traditional machine learning algorithms, and the results show that it outperforms the others.
Quantum Neural Networks (QNNs) have gained significant attention due to their strong expressibility and potential learning. The effectiveness of QNNs is impacted by the choice of input embedding when training samples are limited. Numerous QNN architectures have been reported in the literature; however, the effects of input embedding and entanglement strategies have yet to be examined. In this study, a comprehensive investigation of different embedding techniques, such as θ = x . π / Δ and θ = a r c t a n ( x ) + π / Δ , has been used in a QNN to predict the melting point of the metal oxide, where the dataset is limited to only 70 samples. Further, multiple scaling factors ( Δ ) for each embedding with linear and circular entanglements, along with variational circuit depths, have been examined. The robustness of each embedding has been evaluated using 21 independent random parameter initialisations, while prediction performance has been statistically evaluated using R 2 and RMSE with a generalisation gap. From the results, it is observed that the embeddings such as θ = a r c t a n ( x ) + π / 4 and θ = a r c t a n ( x ) + π / 5 have been performed invariably across random initialisation and achieved superior results compared with other embeddings. Finally, the performance of the QNN has been compared with traditional machine learning algorithms, and the results show that it outperforms the others.
Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of QNNs. However, in almost all literature, QNNs' expressive power is numerically validated using only simple univariate functions. We surprisingly discover that state-of-the-art QNNs with strong expressive power can have poor performance in approximating even just a simple sinusoidal function. To fill the gap, we propose four expressibility-enhancing strategies for QNNs: Sinusoidal-friendly embedding, redundant measurement, post-measurement function, and random training data. We analyze the effectiveness of these strategies via mathematical analysis and/or numerical studies including learning complex sinusoidal-based functions. Our results from comparative experiments validate that the four strategies can significantly increase the QNNs' performance in approximating complex multivariable functions and reduce the quantum circuit depth and qubits required.
Quantum neural network (QNN) models have received increasing attention owing to their strong expressibility and resistance to overfitting. It is particularly useful when the size of the training data is small, making it a good fit for materials informatics (MI) problems. However, there are only a few examples of the application of QNN to multivariate regression models, and little is known about how these models are constructed. This study aims to construct a QNN model to predict the melting points of metal oxides as an example of a multivariate regression task for the MI problem. Different architectures (encoding methods and entangler arrangements) are explored to create an effective QNN model. Shallow-depth ansatzs could achieve sufficient expressibility using sufficiently entangled circuits. The "linear" entangler was adequate for providing the necessary entanglement. The expressibility of the QNN model could be further improved by increasing the circuit width. The generalization performance could also be improved, outperforming the classical NN model. No overfitting was observed in the QNN models with a well-designed encoder. These findings suggest that QNN can be a useful tool for MI.
Quantum neural network (QNN) models have received increasing attention owing to their strong expressibility and resistance to overfitting. It is particularly useful when the size of the training data is small, making it a good fit for materials informatics (MI) problems. However, there are only a few examples of the application of QNN to multivariate regression models, and little is known about how these models are constructed. This study aims to construct a QNN model to predict the melting points of metal oxides as an example of a multivariate regression task for the MI problem. Different architectures (encoding methods and entangler arrangements) are explored to create an effective QNN model. Shallow-depth ansatzs could achieve sufficient expressibility using sufficiently entangled circuits. The "linear" entangler was adequate for providing the necessary entanglement. The expressibility of the QNN model could be further improved by increasing the circuit width. The generalization performance could also be improved, outperforming the classical NN model. No overfitting was observed in the QNN models with a well-designed encoder. These findings suggest that QNN can be a useful tool for MI.
Quantum Machine Learning (QML) has recently emerged as a highly promising research frontier. Within this domain, Quantum Neural Networks (QNNs),characterized by Variational Quantum Circuits (VQCs) at their core and featuring layers of quantum gates optimized by classical algorithms, have garnered significant attention. However, a rigorous and exhaustive evaluation of their practical performance remains largely incomplete. In this study, we conduct a comprehensive comparative analysis of three prominent hybrid classical-quantum architectures: Quantum Convolutional Neural Networks (QCNN), Quantum Recurrent Neural Networks (QRNN), and Quantum Vision Transformers (QViT), focusing on the critical dimensions of generalization, accuracy, and robustness. Our findings provide novel insights that address previous evaluative gaps. Notably, while these models exhibit exceptional performance on low-feature datasets such as MNIST, their learning efficacy degrades significantly when transitioned to high-feature datasets. Furthermore, convolutional-based models like QCNN appear less effective on high-dimensional data than other machine learning architectures. Additionally, while all models are susceptible to adversarial noise, traditional architectures, such as recurrent and convolutional networks, demonstrate superior resilience. Conversely, in the presence of quantum noise, the transformer-based architecture proves its strength by maintaining high robustness against measurement noise, channel noise, and finite-shot effects, whereas other architectures suffer marked performance declines. These results provide a granular perspective on the current state of the field and underscore the critical importance of tailoring model selection to the constraints of contemporary Noisy Intermediate-Scale Quantum (NISQ) environments.
Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the expressivity and inductive bias of QNNs by exploiting an exact mapping from QNNs with inputs x to classical perceptrons acting on x⊗x (generalised to complex inputs). The simplicity of the perceptron architecture allows us to provide clear examples of the shortcomings of current QNN models, and the many barriers they face to becoming useful general-purpose learning algorithms. For example, a QNN with amplitude encoding cannot express the Boolean parity function for n≥3, which is but one of an exponential number of data structures that such a QNN is unable to express. Mapping a QNN to a classical perceptron simplifies training, allowing us to systematically study the inductive biases of other, more expressive embeddings on Boolean data. Several popular embeddings primarily produce an inductive bias towards functions with low class balance, reducing their generalisation performance compared to deep neural network architectures which exhibit much richer inductive biases. We explore two alternate strategies that move beyond standard QNNs. In the first, we use a QNN to help generate a classical DNN-inspired kernel. In the second we draw an analogy to the hierarchical structure of deep neural networks and construct a layered non-linear QNN that is provably fully expressive on Boolean data, while also exhibiting a richer inductive bias than simple QNNs. Finally, we discuss characteristics of the QNN literature that may obscure how hard it is to achieve quantum advantage over deep learning algorithms on classical data.
Machine learning holds fundamental computational significance due to the increasing demand for efficient solutions to complex tasks in data analysis, pattern recognition, and optimization, which are essential for addressing the multifaceted challenges of modern society. As the volume of data proliferates at an unprecedented rate, the need for more powerful machine learning strategies becomes increasingly evident. Quantum neural networks (QNNs) represent an emerging and transformative research field that seeks to harness the unique principles of quantum mechanics to enhance the capabilities of machine learning algorithms. This survey examines various QNN approaches, including fully connected QNNs, quantum convolutional neural networks, equivariant QNNs, quantum Hopfield networks, quantum Boltzmann machines, quantum reservoir computing, and composite networks for quantum reinforcement learning, quantum generative learning, and quantum transfer learning. We summarize the relevant investigations on their performance, including learning accuracy, training time, and resource requirements, etc. Each QNN type has unique strengths and weaknesses, offering diverse solutions for different applications.