Quantum algorithm for the Navier Stokes equations by using the streamfunction vorticity formulation and the lattice Boltzmann method

Abstract

A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented. For the fluid flow equations the stream function-vorticity formulation is adopted, while the lattice Boltzmann method (LBM) is utilized for solving the corresponding system of equations numerically for one time step. Following the nature of the lattice Boltzmann method, the proposed quantum algorithm consists of five major sections: initialization, collision, propagation, boundary condition implementation, and calculation of macroscopic quantities. The collision and boundary condition step is quantumly implemented by applying the standard-form encoding approach, while the quantum walk procedure is applied for the propagation step. The algorithm is implemented by using IBM's quantum computing software development framework Qiskit, while for the verification purposes two-dimensional (2D) cavity flow is simulated and compared with classical code.

Published by the International Journal of Quantum Information in Online Ready form. https://doi.org/10.1142/S0219749921500398

References in corpus (5)

• Quantum algorithm for solving linear systems of equations
• Universal computation by quantum walk
• Synthesis of Quantum Logic Circuits
• The quest for a Quantum Neural Network
• Quantum algorithm and circuit design solving the Poisson equation

Cited by in corpus (18)

• Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation
• Variational Quantum Solutions to the Advection-Diffusion Equation for Applications in Fluid Dynamics
• Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number
• Three Carleman routes to the quantum simulation of classical fluids
• An Alternative Approach to Quantum Imaginary Time Evolution
• Incompressible Navier-Stokes solve on noisy quantum hardware via a hybrid quantum-classical scheme
• Simulating fluid flows with quantum computing
• Quantum algorithms for scientific computing
• Efficient parallelization of quantum basis state shift
• Opportunities and challenges of quantum computing for climate modelling
• Quantum Algorithm for Solving a Quadratic Nonlinear System of Equations
• Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics
• Integrating Quantum Algorithms Into Classical Frameworks: A Predictor-corrector Approach Using HHL
• Float Lattice Gas Automata: A connection between Molecular Dynamics and Lattice Boltzmann Method for quantum computers
• Adaptive Lattice Gas Algorithm: Classical and Quantum implementations
• An Efficient Decomposition of the Carleman Linearized Burgers' Equation
• The universe as a nonlinear quantum simulation: Large $n$ limit of the central spin model
• The Rise of Quantum Computing -- Take a BITE for Built Environment and Urban Microclimate Research