Computational Fluid Dynamics on Quantum Computers

TL;DR

This paper introduces a variational quantum algorithm for computational fluid dynamics, demonstrating its potential to solve PDEs on quantum computers and comparing its performance to classical methods.

Contribution

It presents the first variational quantum CFD algorithm and a software prototype, along with a performance model assessing quantum advantage potential.

Findings

Quantum algorithms can solve PDEs relevant to CFD.

Current prototype shows the need for significant improvements.

Identified techniques could enable quantum advantage in CFD simulations.

Abstract

QubitSolve is working on a quantum solution for computational fluid dynamics (CFD). We have created a variational quantum CFD (VQCFD) algorithm and a 2D Software Prototype based on it. By testing the Software Prototype on a quantum simulator, we demonstrate that the partial differential equations that underlie CFD can be solved using quantum computers. We aim to determine whether a quantum advantage can be achieved with VQCFD. To do this, we compare the performance of VQCFD with classical CFD using performance models. The quantum performance model uses data from VQCFD circuits run on quantum computers. We define a key performance parameter Q_{5E7}, the ratio of quantum to classical simulation time for a size relevant to industrial simulations. Given the current state of the Software Prototype and the limited computing resources available, we can only estimate an upper bound for Q_{5E7}. While the estimated Q_{5E7} shows that the algorithm's implementation must improve significantly, we have identified several innovative techniques that could reduce it sufficiently to achieve a quantum advantage. In the next phase of development, we will develop a 3D minimum-viable product and implement those techniques.