Magic of the Well: assessing quantum resources of fluid dynamics data

TL;DR

This paper explores the quantum resource requirements of fluid dynamics simulation data, revealing how entanglement and non-stabilizerness relate to computational complexity and flow regimes, guiding quantum-inspired CFD approaches.

Contribution

It introduces a method to quantify quantum resources in CFD data and identifies flow conditions that influence resource efficiency, advancing quantum-inspired fluid dynamics modeling.

Findings

Entanglement and non-stabilizerness track each other over time.

Flow regime transitions are identified by shear width.

Mesh resolution and sign structure impact quantum resource content.

Abstract

We investigate the quantum resource requirements of a dataset generated from simulations of two-dimensional, periodic, incompressible shear flow, aimed at training machine learning models. By measuring entanglement and non-stabilizerness on MPS-encoded functions, we estimate the computational complexity encountered by a stabilizer or a tensor network solver applied to Computational Fluid Dynamics (CFD) simulations across different flow regimes. Our analysis reveals that, under specific initial conditions, the shear width identifies a transition between resource-efficient and resource-intensive regimes for non-trivial evolution. Furthermore, we find that the two resources qualitatively track each other in time, and that the mesh resolution along with the sign structure play a crucial role in determining the resource content of the encoded state. These findings offer useful guidelines for the development of scalable, quantum-inspired approaches to fluid dynamics.