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Variational Quantum Circuits (VQC) lie at the forefront of quantum machine learning research. Still, the use of quantum networks for real data processing remains challenging as the number of available qubits cannot accommodate a large…

Quantum machine learning has demonstrated significant potential in solving practical problems, particularly in statistics-focused areas such as data science and finance. However, challenges remain in preparing and learning statistical…

Variational quantum machine learning algorithms have become the focus of recent research on how to utilize near-term quantum devices for machine learning tasks. They are considered suitable for this as the circuits that are run can be…

Large-scale quantum systems require optical coherence between distant quantum devices, necessitating spectral indistinguishability. Scalable solid-state platforms offer promising routes to this goal. However, environmental disorders,…

Recent work suggests that convolutional neural networks of different architectures learn to classify images in the same order. To understand this phenomenon, we revisit the over-parametrized deep linear network model. Our analysis reveals…

Parameterized Quantum Circuits (PQC) are drawing increasing research interest thanks to its potential to achieve quantum advantages on near-term Noisy Intermediate Scale Quantum (NISQ) hardware. In order to achieve scalable PQC learning,…

Variational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also…

Neural operators have emerged as powerful surrogates for modeling complex physical problems. However, they suffer from spectral bias making them oblivious to high-frequency modes, which are present in multiscale physical systems. Therefore,…

Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive…

Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently…

Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be…

Angle encoding has emerged as a popular feature map for embedding classical data into quantum models, naturally generating truncated Fourier series with universal function approximation capabilities. Despite this expressive capability,…

In this review, we survey the latest approaches and techniques developed to overcome the spectral bias towards low frequency of deep neural network learning methods in learning multiple-frequency solutions of partial differential equations.…

State space models (SSMs) leverage linear, time-invariant (LTI) systems to effectively learn sequences with long-range dependencies. By analyzing the transfer functions of LTI systems, we find that SSMs exhibit an implicit bias toward…

The ability to use quantum technology to achieve useful tasks, be they scientific or industry related, boils down to precise quantum control. In general it is difficult to assess a proposed solution due to the difficulties in characterising…

Deep convolutional neural networks have shown remarkable performance on various computer vision tasks, and yet, they are susceptible to picking up spurious correlations from the training signal. So called `shortcuts' can occur during…

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…

Over-parameterized deep neural networks (DNNs) with sufficient capacity to memorize random noise can achieve excellent generalization performance, challenging the bias-variance trade-off in classical learning theory. Recent studies claimed…

Adversarial training has been considered an imperative component for safely deploying neural network-based applications to the real world. To achieve stronger robustness, existing methods primarily focus on how to generate strong attacks by…

Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as…