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We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…

Modern deep neural networks are highly over-parameterized compared to the data on which they are trained, yet they often generalize remarkably well. A flurry of recent work has asked: why do deep networks not overfit to their training data?…

Recently, there is interest in coincident 'sharpening' and 'learnability' transitions in monitored quantum systems. In the latter, an outside observer's ability to infer properties of a quantum system from measurements undergoes a phase…

Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine…

We present a set of methods to generate less complex error channels by quantum circuit parallelisation. The resulting errors are simplified as a consequence of their symmetrisation and randomisation. Initially, the case of a single error…

Parameterized quantum circuits (PQCs) have emerged as a foundational element in the development and applications of quantum algorithms. However, when initialized with random parameter values, PQCs often exhibit barren plateaus (BP). These…

Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit…

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…

Neural networks (NNs) are known to exhibit simplicity bias where they tend to prefer learning 'simple' features over more 'complex' ones, even when the latter may be more informative. Simplicity bias can lead to the model making biased…

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…

We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. We consider three random circuit families, namely, Haar random, $p=1$ QAOA, and random IQP circuits. Our results are as…

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes…

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

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…

Recent studies have noted an intriguing phenomenon termed Neural Collapse, that is, when the neural networks establish the right correlation between feature spaces and the training targets, their last-layer features, together with the…

We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement…

We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…

The overparameterization of variational quantum circuits, as a model of Quantum Neural Networks (QNN), not only improves their trainability but also serves as a method for evaluating the property of a given ansatz by investigating their…

Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…