Related papers: Variational Quantum Solutions to the Advection-Dif…
Vortex interactions are commonly observed in atmospheric turbulence, plasma dynamics, and collective behaviors in biological systems. However, accurately simulating these complex interactions is highly challenging due to the need to capture…
Quantum solutions to differential equations represent quantum data -- states that contain relevant information about the system's behavior, yet are difficult to analyze. We propose a toolbox for reading out information from such data, where…
The Vlasov-Maxwell equations provide kinetic simulations of collisionless plasmas, but numerically solving them on classical computers is often impractical. This is due to the computational resource constraints imposed by the time evolution…
Although the foundations of the hydrodynamical formulation of quantum mechanics were laid over 50 years ago, it has only been within the past few years that viable computational implementations have been developed. One approach to solving…
Particle advection is the approach for extraction of integral curves from vector fields. Efficient parallelization of particle advection is a challenging task due to the problem of load imbalance, in which processes are assigned unequal…
The simulation of ion-atom collisions remains a formidable challenge due to the complex interplay between electronic and nuclear degrees of freedom. We present a hybrid quantum-classical computing framework for simulating time-dependent…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently…
A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum…
This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…
Quantum computing has attracted considerable attention in recent years because it promises speed-ups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers are, in most cases, still…
This paper aims to implement and evaluate the performance of quantum computing on solving combinatorial optimization problems arising from the operations of the power grid. To this end, we construct a novel mixed integer conic programming…
Liouvillian dynamics describes the evolution of a density operator in closed quantum systems. One extension towards open quantum systems is provided by the Lindblad equation. It is applied to various systems and energy regimes in solid…
Current technologies in quantum-based communications bring a new integration of quantum data with classical data for hybrid processing. However, the frameworks of these technologies are restricted to a single classical or quantum task,…
Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable…
In this paper, we propose a new methodology to design quantum hybrid diffusion models, derived from classical U-Nets with ResNet and Attention layers. Specifically, we propose two possible different hybridization schemes combining quantum…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
We demonstrate the feasibility of quantum computing for large-scale, realistic chemical systems through the development of a new interface using a quantum circuit simulator and CP2K, a highly efficient first-principles calculation software.…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, along with their potential merits and liabilities, are discussed and commented on.