For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.
For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.
Surrogate models are ubiquitously used in industry and academia to efficiently approximate given black box functions. As state-of-the-art methods from classical machine learning frequently struggle to solve this problem accurately for the often scarce and noisy data sets in practical applications, investigating novel approaches is of great interest. Motivated by recent theoretical results indicating that quantum neural networks (QNNs) have the potential to outperform their classical analogs in the presence of scarce and noisy data, we benchmark their qualitative performance for this scenario empirically. Our contribution displays the first application-centered approach of using QNNs as surrogate models on higher dimensional, real world data. When compared to a classical artificial neural network with a similar number of parameters, our QNN demonstrates significantly better results for noisy and scarce data, and thus motivates future work to explore this potential quantum advantage in surrogate modelling. Finally, we demonstrate the performance of current NISQ hardware experimentally and estimate the gate fidelities necessary to replicate our simulation results.
The rapid advancement of artificial intelligence (AI) and deep learning (DL) has catalyzed the emergence of several optimization-driven subfields, notably neuromorphic computing and quantum machine learning. Leveraging the differentiable nature of hybrid models, researchers have explored their potential to address complex problems through unified optimization strategies. One such development is the Spiking Quantum Neural Network (SQNN), which combines principles from spiking neural networks (SNNs) and quantum computing. However, existing SQNN implementations often depend on pretrained SNNs due to the non-differentiable nature of spiking activity and the limited scalability of current SNN encoders. In this work, we propose a novel architecture—Spiking-Quantum Data Re-upload Convolutional Neural Network (SQDR-CNN)—that enables joint training of convolutional SNNs and quantum circuits within a single backpropagation framework. Unlike its predecessor, SQDR-CNN allow convergence to reasonable performance without the reliance of pretrained spiking encoder and subsetting datasets. We also clarified some theoretical foundations, testing new design using quantum data-reupload with different training algorithm-initialization and evaluate the performance of the proposed model under noisy simulated quantum environments. As a result, we were able to achieve 86% of the mean top-performing accuracy of the state of the art (SOTA) SNN baselines, yet uses only 0.5% of the smallest spiking model’s parameters. Through this integration of neuromorphic and quantum paradigms, we aim to open new research directions and foster technological progress in multi-modal, learnable systems.
The rapid advancement of artificial intelligence (AI) and deep learning (DL) has catalyzed the emergence of several optimization-driven subfields, notably neuromorphic computing and quantum machine learning. Leveraging the differentiable nature of hybrid models, researchers have explored their potential to address complex problems through unified optimization strategies. One such development is the Spiking Quantum Neural Network (SQNN), which combines principles from spiking neural networks (SNNs) and quantum computing. However, existing SQNN implementations often depend on pretrained SNNs due to the non-differentiable nature of spiking activity and the limited scalability of current SNN encoders. In this work, we propose a novel architecture, Spiking-Quantum Data Re-upload Convolutional Neural Network (SQDR-CNN), that enables joint training of convolutional SNNs and quantum circuits within a single backpropagation framework. Unlike its predecessor, SQDR-CNN allow convergence to reasonable performance without the reliance of pretrained spiking encoder and subsetting datasets. We also clarified some theoretical foundations, testing new design using quantum data-reupload with different training algorithm-initialization and evaluate the performance of the proposed model under noisy simulated quantum environments. As a result, we were able to achieve 86% of the mean top-performing accuracy of the SOTA SNN baselines, yet uses only 0.5% of the smallest spiking model's parameters. Through this integration of neuromorphic and quantum paradigms, we aim to open new research directions and foster technological progress in multi-modal, learnable systems.
Quantum and classical machine learning have been naturally connected through kernel methods, which have also served as proof-of-concept for quantum advantage. Quantum embeddings encode classical data into quantum feature states, enabling the construction of embedding quantum kernels (EQKs) by measuring vector similarities and projected quantum kernels (PQKs) through projections of these states. However, in both approaches, the model is influenced by the choice of the embedding. In this work, we propose using the training of a quantum neural network (QNN) to construct neural quantum kernels, specifically neural EQKs and neural PQKs—problem-inspired kernel functions. Unlike previous approaches, our method requires the kernel matrix to be constructed only once, significantly reducing computational overhead. To achieve this, we introduce a scalable training method for an n -qubit data reuploading QNN. Furthermore, we demonstrate neural quantum kernels can alleviate exponential concentration and enhance generalization capabilities compared to problem-agnostic kernels, positioning them as a scalable and robust solution for quantum machine learning applications.
Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains less understood. In this paper, we formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks that consist of interleaved encoding circuit blocks and trainable circuit blocks. First, we prove that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series. We in particular establish the exact correlations between the parameters of the trainable gates and the Fourier coefficients, resolving an open problem on the universal approximation property of QNN. Second, we discuss the limitations of single-qubit native QNNs on approximating multivariate functions by analyzing the frequency spectrum and the flexibility of Fourier coefficients. We further demonstrate the expressivity and limitations of single-qubit native QNNs via numerical experiments. We believe these results would improve our understanding of QNNs and provide a helpful guideline for designing powerful QNNs for machine learning tasks.
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.