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Variational quantum algorithms (VQAs) represent a promising pathway toward achieving practical quantum advantage on near-term hardware. Despite this promise, for generic, expressive ans\"atze, their scalability is critically hindered by…
Quantum computing is an important developing technology with the potential to revolutionise the landscape of scientific and business problems that can be practically addressed. The widespread excitement derives from the potential for a…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…
Classical-quantum hybrid algorithms have recently garnered significant attention, which are characterized by combining quantum and classical computing protocols to obtain readout from quantum circuits of interest. Recent progress due to…
Great efforts have been dedicated in recent years to explore practical applications for noisy intermediate-scale quantum (NISQ) computers, which is a fundamental and challenging problem in quantum computing. As one of the most promising…
Variational quantum algorithms (VQAs) are widely applied in the noisy intermediate-scale quantum era and are expected to demonstrate quantum advantage. However, training VQAs faces difficulties, one of which is the so-called barren plateaus…
We investigate two unconditionally energy stable invariant energy quadratization (IEQ) finite element methods (FEMs) [Chen et al. Numerical Algorithms, DOI: 10.1007/s11075-024-01910-z, 2024] for solving the Cahn-Hilliard-Navier-Stokes…
While numerical simulations are presented in most papers introducing new methods to enhance the VQE performance, comprehensive, comparative, and applied studies remain relatively rare. We present a comprehensive, yet concise guide for the…
The recent developments of quantum computing present potential novel pathways for quantum chemistry, as the increased computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems.…
To arrive at some viable product design, product development processes frequently use numerical simulations and mathematical programming techniques. Topology optimization, in particular, is one of the most promising techniques for…
Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We…
Quantum computing is an emerging field on the multidisciplinary interface between physics, engineering, and computer science with the potential to make a large impact on computational intelligence (CI). The aim of this paper is to introduce…
Parameterized quantum circuits (PQCs) are pivotal components of variational quantum algorithms (VQAs), which represent a promising pathway to quantum advantage in noisy intermediate-scale quantum (NISQ) devices. PQCs enable flexible…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
Parameterized quantum circuits (PQCs) play an essential role in the application of variational quantum algorithms (VQAs) in noisy intermediate-scale quantum (NISQ) devices. The PQCs are a leading candidate to achieve a quantum advantage in…
Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest…
In this paper, a novel paradigm of mobile edge-quantum computing (MEQC) is proposed, which brings quantum computing capacities to mobile edge networks that are closer to mobile users (i.e., edge devices). First, we propose an MEQC system…