aqora

Schrödinger-Navier-Stokes Equation for the Quantum Simulation of Navier-Stokes Flows

Luca Cappelli, Sauro Succi, Monica Lacatus +2 more

The search for quantum-like wave formulations of the Navier-Stokes (Schrödinger-Navier-Stokes, SNS for short) equations describing classical dissipative fluids has met with increasing attention in the recent years, due to the large portfolio of potential applications in science and engineering. A SNS formulation of classical fluids was first presented in a largely un-noticed paper by Dietrich and Vautherin back in 1985(Journal de Physique). In this paper, we revisit this specific SNS approach and assess its viability for quantum implementations based on Carleman embedding/linearization techniques. Specifically, we i) Clarify in full mathematical detail why the SNS dissipator presents a steep challenge for quantum computers and propose a way out strategy based on the Hamilton-Jacobi (HJ) formulation of fluid dynamics; ii) Develop a corresponding quantum algorithm using a new technique based on a tensor-network representation of Carleman embedding of the HJ equations (CHJ) which permits substantial memory savings; iii) Emulate the CHJ quantum algorithm on a classical computer and analyse its convergence and accuracy for the specific case of Kolmogorov-like flows at moderate Reynolds numbers. To the best of our knowledge, this is the first quantum algorithm based on a quantum-like wave formulation of the genuine Navier-Stokes equations, including pressure, dissipation and vorticity.The search for quantum-like wave formulations of the Navier-Stokes (Schrödinger-Navier-Stokes, SNS for short) equations describing classical dissipative fluids has met with increasing attention in the recent years, due to the large portfolio of potential applications in science and engineering. A SNS formulation of classical fluids was first presented in a largely un-noticed paper by Dietrich and Vautherin back in 1985(Journal de Physique). In this paper, we revisit this specific SNS approach and assess its viability for quantum implementations based on Carleman embedding/linearization techniques. Specifically, we i) Clarify in full mathematical detail why the SNS dissipator presents a steep challenge for quantum computers and propose a way out strategy based on the Hamilton-Jacobi (HJ) formulation of fluid dynamics; ii) Develop a corresponding quantum algorithm using a new technique based on a tensor-network representation of Carleman embedding of the HJ equations (CHJ) which permits substantial memory savings; iii) Emulate the CHJ quantum algorithm on a classical computer and analyse its convergence and accuracy for the specific case of Kolmogorov-like flows at moderate Reynolds numbers. To the best of our knowledge, this is the first quantum algorithm based on a quantum-like wave formulation of the genuine Navier-Stokes equations, including pressure, dissipation and vorticity.

quant-pharXiv:2604.11113Quantum Science and TechnologyApr 14, 20261 citation

Operator for Time Delay Induced by Scattering

Bernard A. Lippmann

Physical ReviewNov 25, 196632 citations

Hydrodynamical Model of Quantum Mechanics I

西岡, 道夫

A Brownian particle-like properties of a quantum mechanical particle is examined and it is found that Schrodiner equation to a kind of Navier-Stokes equation from the formal stand of view.

Nov 1, 19700 citations

Analysis of Analog-State Resonances by Coupled Optical Equations

E. H. Auerbach, C. B. Dover, Arthur K. Kerman +2 more

Physical Review LettersDec 5, 196628 citations

The Hydrodynamic Origin of Quantum Mechanics and the Regularity of Navier-Stokes

Ford, Nicholas

Dec 5, 20250 citations

Quantum Mechanical Description of Fluid Dynamics

H. Y. Cui

In this paper, we deal with fluid motion in terms of quantum mechanics. Mechanism accounting for the appearance of quantum behavior is discussed.

arXiv:physics/0103019Mar 8, 20010 citations