Related papers: An end-to-end quantum algorithm for nonlinear flui…
We employ the principle of minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…
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…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
In this perspective, we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best…
Quantum computing promises revolutionary advances in modeling materials and molecules. However, the up-to-date runtime estimates for utility-scale applications on certain quantum hardware systems are in the order of years rendering quantum…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
We propose an end-to-end quantum algorithm to simulate rapidly distorted turbulence via linear combination of Hamiltonian (LCHS). The algorithm comprises three primary stages: the efficient preparation of an initial turbulent state with a…
Digital quantum computers promise exponential speedups in performing quantum time-evolution, providing an opportunity to simulate quantum dynamics of complex systems in physics and chemistry. However, the task of extracting desired quantum…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
We propose a quantum algorithm for the linear advection-diffusion equation (ADE) Lattice-Boltzmann method (LBM) that leverages dynamic circuits. Dynamic quantum circuits allow for an optimized collision-operator quantum algorithm,…
Quantum algorithms are gaining attention in Computational Fluid Dynamics (CFD) for their favorable scaling, as encoding physical fields into quantum probability amplitudes enables representation of two to the power of n spatial points with…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…
Computational fluid dynamics (CFD) has become a cornerstone of modern water engineering, providing quantitative tools for the analysis, prediction, and management of complex hydraulic systems across a wide range of spatial and temporal…
We present a non-iterative algorithm, FloatStepper, for coupling the motion of a rigid body and an incompressible fluid in computational fluid dynamics (CFD) simulations. The purpose of the algorithm is to remove the so-called added mass…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
One of the biggest challenges for simulating the Boltzmann equation is the evaluation of fivefold collision integral. Given the recent successes of deep learning and the availability of efficient tools, it is an obvious idea to try to…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
We apply Carleman linearization of the Lattice Boltzmann (CLB) representation of fluid flows to quantum emulate the dynamics of a 2D Kolmogorov-like flow. We assess the accuracy of the result and find a relative error of the order of…