We present substantially generalized and improved quantum algorithms over prior work for
inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we …

We present a full quantum algorithm for the lattice Boltzmann method for simulating fluid
flows, the only such algorithm to implement both the streaming and collision substeps as …

How well can quantum computers simulate classical dynamical systems? There is
increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond …

An approximate quantum state preparation method is introduced, called the Walsh series
loader (WSL). The WSL approximates quantum states defined by real-value functions of …

Loading functions into quantum computers represents an essential step in several quantum
algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency …

This is a review of recent research exploring and extending present-day quantum computing
capabilities for fusion energy science applications. We begin with a brief tutorial on both …

As we progress towards physical implementation of quantum algorithms it is vital to
determine the explicit resource costs needed to run them. Solving linear systems of …

We investigate the limitations of quantum computers for solving nonlinear dynamical
systems. In particular, we tighten the worst-case bounds of the quantum Carleman …

We propose an explicit algorithm based on the Linear Combination of Hamiltonian
Simulations technique to simulate both the advection-diffusion equation and a nonunitary …

The solution of large systems of nonlinear differential equations is needed for many
applications in science and engineering. In this study, we present three main improvements …