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Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…

Quantum Physics · Physics 2009-11-13 Kenneth R. Brown , Robert J. Clark , Isaac L. Chuang

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…

The potential analysis of the capabilities of quantum computing, especially before fault tolerance at scale, is difficult due to the variety of existing hardware technologies with a wide spread of maturity. Not only the result of…

Quantum Physics · Physics 2025-07-23 Amine Bentellis , Benedikt Poggel , Jeanette Miriam Lorenz

This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…

Quantum Physics · Physics 2026-05-29 Uditnarayan Kouskiya , Caglar Oskay

The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…

Quantum Physics · Physics 2024-06-18 Valeria Cimini , Emanuele Polino , Mauro Valeri , Nicolò Spagnolo , Fabio Sciarrino

Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this…

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…

Quantum Physics · Physics 2007-05-23 O. Giraud , B. Georgeot

We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…

Numerical Analysis · Mathematics 2018-09-28 M. Holst , M. Licht

Quantum computing has demonstrated the potential to solve computationally intensive problems more efficiently than classical methods. Many software engineering tasks, such as test case selection, static analysis, code clone detection, and…

Software Engineering · Computer Science 2025-06-10 Jianjun Zhao

We present a mixed reality application (HoloFEM) for the Microsoft HoloLens. The application lets a user define and solve a physical problem governed by Poisson's equation with the surrounding real world geometry as input data. Holograms…

Graphics · Computer Science 2017-11-22 Anders Logg , Carl Lundholm , Magne Nordaas

The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…

Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum…

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…

The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview…

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…

Quantum Physics · Physics 2025-04-11 Niclas Schillo , Andreas Sturm

Classical simulation of real-space quantum dynamics is challenging due to the exponential scaling of computational cost with system dimensions. Quantum computer offers the potential to simulate quantum dynamics with polynomial complexity;…

Quantum Physics · Physics 2021-10-13 Chee-Kong Lee , Chang-Yu Hsieh , Shengyu Zhang , Liang Shi

As quantum computers advance, the complexity of the software they can execute increases as well. To ensure this software is efficient, maintainable, reusable, and cost-effective -key qualities of any industry-grade software-mature software…

Quantum computing is presently undergoing rapid development to achieve a significant speedup promised in certain applications. Nonetheless, scaling quantum computers remains a formidable engineering challenge, prompting exploration of…

We present a variational quantum algorithm for structural mechanical problems, specifically addressing crack opening simulations that traditionally require extensive computational resources. Our approach provides an alternative solution for…

Quantum computing provides computational advantages in various domains. To benefit from these advantages complex hybrid quantum applications must be built, which comprise both quantum and classical programs. Engineering these applications…