Quantum Algorithms for Fluid Simulations

René Steijl

doi:10.5772/intechopen.86685

Abstract

This chapter describes results of a recent investigation aiming to assess the potential of quantum computing and suitably designed algorithms for future computational fluid dynamics applications. For quantum computers becoming available in the near future, it can be expected that applications of quantum computing follow the quantum coprocessor model, where selected parts of the computational task for which efficient quantum algorithms exist are executed on the quantum hardware. For example, in computational fluid dynamics algorithm, this hybrid quantum/classical approach is discussed, and in particular it is shown how the approximate quantum Fourier transform (AQFT) can be used in the Poisson solvers of the considered method for the incompressible-flow Navier-Stokes equations. The analysis shows that despite the inevitable errors introduced by applying AQFT, the method produces meaningful results for three-dimensional example problems. A second example of a quantum algorithm for flow simulations is then described. This method based on kinetic modeling of the flow was developed to reduce the information transfer between quantum and classical hardware in the quantum coprocessor model. It is shown that this quantum algorithm can be executed fully on quantum hardware during a simulation. The conclusion summarizes further challenges for algorithm developments and future work.

Highlights

In recent years, the field of quantum computing [1] has developed into an active and diverse field of research, and significant progress has been made in a number of important areas
Only recently have quantum computing applications appeared in other areas of science and engineering, e.g., work in computational electromagnetics [2, 3], mixing in turbulent flow [4], and computational fluid dynamics [5]
This chapter describes results of a recent investigation aiming to assess the potential of quantum computing and suitably designed algorithms for future computational fluid dynamics application, for noisy intermediate-scale quantum (NISQ)-type quantum hardware

Summary

Introduction

The field of quantum computing [1] has developed into an active and diverse field of research, and significant progress has been made in a number of important areas. This chapter describes results of a recent investigation aiming to assess the potential of quantum computing and suitably designed algorithms for future computational fluid dynamics application, for NISQ-type quantum hardware. As an example of this hybrid classical/quantum approach, the author introduced a quantum computing application in which the vortex-in-cell method was used to solve the incompressible-flow Navier-Stokes equations in a regular domain [5]. In this algorithm, the Poisson solvers dominating CPU time requirements are based on the quantum computing equivalent of the fast Fourier transform, i.e., the quantum Fourier transform.

Elements of quantum computing relevant in current work

Mapping a computational problem onto the quantum state vector

Approximate quantum Fourier transform (AQFT)

Quantum algorithm for discrete-velocity method

Conclusions