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Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
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…
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
Interacting spin systems in solids underpin a wide range of quantum technologies, from quantum sensors and single-photon sources to spin-defect-based quantum registers and processors. We develop a quantum-computer-aided framework for…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many…
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 define some of the programming and system-level challenges facing the application of quantum processing to high-performance computing. Alongside barriers to physical integration, prominent differences in the execution of quantum and…
We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping…
Quantum computational chemistry holds great promise for simulating molecular systems more efficiently than classical methods by leveraging quantum bits to represent molecular wavefunctions. However, current implementations face significant…
In light of recent exciting progress in building up quantum computing facilities based on both optical and cold-atom techniques, the algorithms for quantum simulations of particle-physics systems are in rapid progress. In this paper, we…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing…
Computational fluid dynamics (CFD) is a specialised branch of fluid mechanics that utilises numerical methods and algorithms to solve and analyze fluid-flow problems. One promising avenue to enhance CFD is the use of quantum computing,…
Machine learning and quantum computing are two technologies that are causing a paradigm shift in the performance and behavior of certain algorithms, achieving previously unattainable results. Machine learning (kernel classification) has…
The potential of Quantum Machine Learning (QML) in data-intensive science is strictly bottlenecked the difficulty of interfacing high-dimensional, chaotic classical data into resource-limited, noisy quantum processors. To bridge this gap,…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…
People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…