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The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure…
On the example of the Poynting-Thomson-Zener rheological model for solids, which exhibits both dissipation and wave propagation - with nonlinear dispersion relation -, we introduce and investigate a finite difference numerical scheme. Our…
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multiscale hyperbolic heat system with quantum algorithms (hence…
In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…
This document explores the potential of quantum computing in Thermal Science. Conceived as a living document, it will be continuously updated with experimental findings and insights for the research community in Thermal Science. By…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Developing scalable quantum algorithms to study finite-temperature physics of quantum many-body systems has attracted considerable interest due to recent advancements in quantum hardware. However, such algorithms in their present form…
Thermal properties of quantum fields at finite temperature are crucial to understanding strongly interacting matter and recent development in quantum computing has provided an alternative and promising avenue of study. In this work, we…
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…
We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations using a direct-forcing immersed boundary method to account for the dispersed phase. A volume of fluid approach is…
The thermal characteristics of silicon between 15 and 300 deg K are investigated by applying a computer program on the solution of the differential heat diffusion equation. The computer model is linked to high-purity silicon through a set…
Quantum computing holds great promise for solving classically intractable problems such as linear systems and partial differential equations (PDEs). While fully fault-tolerant quantum computers remain out of reach, current noisy…
We investigate variational problems in quantum thermodynamics at positive temperature, in which admissible states are constrained by prescribed outcomes of a finite set of measurements. We solve a problem raised by the recent work [Liu,…
We present results of interface-resolved simulations of heat transfer in suspensions of finite-size neutrally-buoyant spherical particles for solid volume fractions up to 35% and bulk Reynolds numbers from 500 to 5600. An Immersed…
In this paper, I discuss the challenges in porting hydrodynamic codes to futuristic exascale HPC systems. In particular, we describe the computational complexities of finite difference method, pseudo-spectral method, and Fast Fourier…
This study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behaviour within lattices at high temperatures in condensed…