Related papers: Variational Quantum Solutions to the Advection-Dif…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…
Achieving high-performance computation on quantum systems presents a formidable challenge that necessitates bridging the capabilities between quantum hardware and classical computing resources. This study introduces an innovative…
Portfolio construction has been a long-standing topic of research in finance. The computational complexity and the time taken both increase rapidly with the number of investments in the portfolio. It becomes difficult, even impossible for…
Simulations of chemical dynamics are a powerful means for understanding chemistry. However, classical computers struggle to simulate many chemical processes, especially non-adiabatic ones, where the Born-Oppenheimer approximation breaks…
Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…
This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
Modeling electronic systems is an important application for quantum computers. In the context of materials science, an important open problem is the computational description of chemical reactions on surfaces. In this work, we outline a…
This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of…
Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship…
Modern Cloud/Edge architectures need to orchestrate multiple layers of heterogeneous computing nodes, including pervasive sensors/actuators, distributed Edge/Fog nodes, centralized data centers and quantum devices. The optimal assignment…
Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
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 introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
This work is a benchmark study for quantum-classical computing method with a real-world optimization problem from industry. The problem involves scheduling and balancing jobs on different machines, with a non-linear objective function. We…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…