Quantum Lattice Representation of Nonlinear Classical Physics

TL;DR

This paper develops a quantum lattice algorithm based on the Madelung transformation to simulate nonlinear classical fluid dynamics, offering a novel quantum computational approach compared to traditional methods.

Contribution

It introduces a quantum lattice algorithm derived from a generalized Gross-Pitaevski equation for simulating classical nonlinear fluids, bridging quantum computing and fluid dynamics.

Findings

Quantum lattice algorithm accurately simulates classical nonlinear fluids.

Comparisons show advantages over classical fluid dynamic techniques.

Provides a new quantum computational framework for fluid simulation.

Abstract

Using the Madelung transformation on a generalized scalar Gross-Pitaevski equation, a nonlinear continuum fluid equations are derived for a classical fluid. A unitary quantum lattice algorithm is then determined as a second order discrete representation of this Gross-Pitaevski equation and the simulations are compared to those using classical fluid dynamic techniques.