Toward end-to-end quantum simulation of rapidly distorted turbulence

TL;DR

This paper introduces a quantum algorithm for simulating rapidly distorted turbulence, demonstrating potential quantum speedup and accurate results, which could advance quantum approaches to complex fluid dynamics.

Contribution

It presents the first end-to-end quantum algorithm for turbulence simulation using linear combination of Hamiltonians, including state preparation, evolution, and measurement.

Findings

Quantum algorithm matches classical results for turbulence statistics.

Numerical validation shows excellent agreement with ground-truth solutions.

Potential for quantum speedup in large-scale turbulence simulations.

Abstract

We propose an end-to-end quantum algorithm to simulate rapidly distorted turbulence via linear combination of Hamiltonian (LCHS). The algorithm comprises three primary stages: the efficient preparation of an initial turbulent state with a prescribed energy spectrum, its subsequent time evolution via LCHS, and the direct measurement of key turbulence statistics. Our analysis indicates that the algorithm can offer a practical quantum speedup over the classical simulation methods for a sufficiently large computational grid. We evaluate the quantum resource requirements for simulating a minimal instance of non-trivial turbulence with classical validation. The numerical results show excellent agreement with ground-truth solutions, capturing both the qualitative evolution of turbulent fields and the quantitative behavior of statistics, including the Reynolds stresses and the fluctuating velocity spectrum. Despite its linearity, rapidly distorted turbulence captures essential turbulence mechanisms and may inform the development of quantum algorithms for the Navier-Stokes equations. Our work establishes a foundation for addressing more complex turbulent phenomena on future fault-tolerant quantum computers.