Momentum exchange method for quantum Boltzmann methods

TL;DR

This paper introduces a quantum algorithm for efficiently calculating flow quantities in quantum fluid dynamics simulations, specifically using a quantum version of the momentum exchange method and implementing bounce back boundary conditions.

Contribution

It presents the first quantum method for directly computing quantities of interest in quantum CFD, including a quantum momentum exchange method and boundary condition scheme.

Findings

Proposes a quantum algorithm for flow force calculations.

Implements bounce back boundary conditions on a quantum computer.

Enables efficient measurement of flow properties in quantum simulations.

Abstract

The past years have seen a surge in quantum algorithms for computational fluid dynamics (CFD). These algorithms have in common that whilst promising a speed-up in the performance of the algorithm, no specific method of measurement has been suggested. This means that while the algorithms presented in the literature may be promising methods for creating the quantum state that represents the final flow field, an efficient measurement strategy is not available. This paper marks the first quantum method proposed to efficiently calculate quantities of interest (QoIs) from a state vector representing the flow field. In particular, we propose a method to calculate the force acting on an object immersed in the fluid using a quantum version of the momentum exchange method (MEM) that is commonly used in lattice Boltzmann methods to determine the drag and lift coefficients. In order to achieve this we furthermore give a scheme that implements bounce back boundary conditions on a quantum computer, as those are the boundary conditions the momentum exchange method is designed for.