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Quantum machine learning (QML) is a promising early use case for quantum computing. There has been progress in the last five years from theoretical studies and numerical simulations to proof of concepts. Use cases demonstrated on…

Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…

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…

In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finite sequences of elementary quantum gates and establish their…

Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core…

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific…

Quantum Machine Learning (QML) has emerged as a promising framework for exploring how quantum dynamics may enhance data processing tasks. Here we investigate Quantum Extreme Learning Machines (QELMs), a quantum analogue of classical Extreme…

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…

This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has…

Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren…

This article presents a simplified version of the author's previous work. We first construct a causal growth process (CGP). We then form path Hilbert spaces using paths of varying lengths in the CGP. A sequence of positive operators on…

Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…

Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…

We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…

Quantum correlations are central to the foundations of quantum physics and form the basis of quantum technologies. Here, our goal is to connect quantum correlations and computation: using quantum correlations as a resource for computation -…

Quantum machine learning has the potential to enable advances in artificial intelligence, such as solving problems intractable on classical computers. Some fundamental ideas behind quantum machine learning are similar to kernel methods in…

Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…

Quantum neural networks (QNNs) play a pivotal role in addressing complex tasks within quantum machine learning, analogous to classical neural networks in deep learning. Ensuring consistent performance across diverse datasets is crucial for…

We compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the…