Enabling Large-Scale and High-Precision Fluid Simulations on Near-Term Quantum Computers

TL;DR

This paper presents a scalable quantum computational fluid dynamics method that leverages hybrid quantum-classical algorithms to simulate complex fluid flows with high precision on near-term quantum hardware.

Contribution

It introduces a novel iterative quantum linear solver and a subspace method to enable large-scale, high-precision fluid simulations on current quantum computers.

Findings

Achieved less than 0.2% error in Poiseuille flow simulation.

Successfully simulated a 5043-dimensional matrix for acoustic waves.

Demonstrated the feasibility of near-term quantum computers for practical CFD applications.

Abstract

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method "Iterative-QLS" that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than $0.2\%$, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum-classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science.