Complete quantum-inspired framework for computational fluid dynamics

TL;DR

This paper introduces a quantum-inspired, matrix-product state framework for simulating incompressible fluid flows efficiently, achieving poly-logarithmic scaling in mesh size and handling complex geometries with boundary conditions.

Contribution

It presents a complete, self-consistent quantum-inspired method for fluid dynamics that significantly reduces computational complexity compared to traditional approaches.

Findings

Achieves poly-logarithmic scaling in mesh size

Handles arbitrary geometries and boundary conditions

Retrieves solutions directly from compressed representations

Abstract

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large vector dimensions required by discretized meshes. We present a full-stack method to solve for incompressible fluids with memory and runtime scaling poly-logarithmically in the mesh size. Our framework is based on matrix-product states, a powerful compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without ever passing through the expensive dense-vector representation. This machinery lays the foundations for a new generation of potentially radically more efficient solvers of real-life fluid problems.