Quantum lattice Boltzmann method for several time steps: A local Carleman linearization algorithm

TL;DR

This paper introduces a quantum lattice Boltzmann algorithm using Carleman linearization that maintains local collision rules and improves result accuracy, scaling efficiently with lattice size and channels.

Contribution

It presents a new encoding for quantum lattice Boltzmann methods that enables local collision rules and better accuracy, with scalable complexity using dynamical circuits.

Findings

Higher probability of correct results (~1%) compared to previous methods

Algorithm scales as O(log_2^2(N)+Q^3) per time step

Maintains local collision rules in quantum lattice Boltzmann simulations

Abstract

This article presents a novel encoding for quantum Lattice Boltzmann method algorithm using Carleman linearization. In contrast to previous articles \cite{Sanavio2024LatticeBC,sanavio2025carleman}, the encoding used allows for local collision rules while keeping a higher probability to obtain the right result, which is of the order of $10^{-2}$. The algorithm scales as $O(log_2^2(N)+Q^3)$ each time step with $N$ the number of lattice sites of the 2D lattice and $Q$ the number of channels with a constant number of qubits when using dynamical circuits.