Quantum Computing for nonlinear differential equations and turbulence

TL;DR

This paper explores the potential of quantum computing to simulate nonlinear differential equations and turbulence, addressing current challenges and proposing new algorithm-hardware pairings for advanced simulations.

Contribution

It reviews recent progress in quantum algorithms and hardware for nonlinear dynamics and suggests innovative pairings to enable future turbulence simulations.

Findings

Quantum algorithms for nonlinear equations are advancing.

Quantum hardware developments are enabling more complex simulations.

New pairings between algorithms and hardware open opportunities for turbulence modeling.

Abstract

A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the growth of classical computing power has slowed down because the miniaturisation of chips has been approaching the atomic scale. This is marking an end to Moore's law, which calls for a new computing paradigm: Quantum computing is a prime candidate. In this paper, we offer a perspective on the current challenges that need to be overcome in order to use quantum computing for the simulation of nonlinear dynamics. We review and discuss progress in the development of both quantum algorithms for nonlinear equations and quantum hardware. We propose pairings between quantum algorithms for nonlinear equations and quantum hardware concepts. These avenues open new opportunities for the simulation of nonlinear systems and turbulence.