Quantum Lattice Boltzmann Solutions for Transport under 3D Spatially Varying Advection on Trapped Ion Hardware

TL;DR

This paper demonstrates quantum lattice Boltzmann simulations of transport phenomena with non-uniform velocity fields on trapped ion quantum hardware, advancing realistic CFD modeling with new boundary and readout techniques.

Contribution

It introduces the first implementation of transport under non-uniform velocity fields on quantum hardware, including novel boundary methods and scalable readout strategies.

Findings

Successful simulation of advection-diffusion with non-uniform velocity fields on IonQ hardware.

Identification of density readout as a bottleneck and proposal of MPS shadow tomography for scaling.

Development of a new wall boundary implementation for quantum lattice Boltzmann methods.

Abstract

The Quantum Lattice Boltzmann Method (QLBM) has emerged as one of the most promising quantum computing approaches for the numerical simulation of problems in computational fluid dynamics (CFD). The dynamics is formulated in terms of mesoscopic particle distribution functions governed by a discrete Boltzmann transport equation, comprising local streaming and collision operations. In this work, the resulting macroscopic behavior corresponds to the advection-diffusion equation, which we adopt as a canonical model problem for transport phenomena. Building upon recent progress in QLBM implementations, we advance towards more realistic problem settings that better reflect conventional CFD requirements. We address, for the first time, transport under the action of non uniform velocity fields on quantum hardware. We implement our demonstration using IonQ's trapped-ion systems including Forte generation systems and a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We identify the density readout and subsequent reloading of the fluid density as a potential bottleneck of the current algorithm and discuss several approaches to mitigate this bottleneck. We identify the use of MPS shadow tomography as a promising method to efficiently scale the readout to large system with complex density distributions. Lastly, we introduce and simulate a novel method to implement wall boundaries for advection-diffusion in QLBM, and discuss the prospects of scaling to higher-complexity problems.