Improved Quantum Lattice Boltzmann Method for Advection-Diffusion Equations with a Linear Collision Model

TL;DR

This paper introduces an ancilla-free quantum lattice Boltzmann method for advection-diffusion equations that reduces quantum circuit complexity and leverages quantum parallelism, confirmed by numerical simulations.

Contribution

It presents a novel quantum lattice Boltzmann algorithm that eliminates the need for ancilla qubits and quantum state tomography, enhancing efficiency for fluid dynamics simulations.

Findings

Feasibility demonstrated through numerical simulations of $D_1Q_3$ and $D_2Q_5$ models.

Reduction in quantum circuit complexity by removing ancilla qubits.

Potential for accelerated scientific computing using quantum methods.

Abstract

Quantum computing has made tremendous progress in recent years, providing potentialities for breaking the bottleneck of computing power in the field of scientific computing, like computational fluid dynamics. To reduce computational costs and achieve an acceleration, we propose an ancilla free quantum lattice Boltzmann method for advection-diffusion equations that fully leverages the parallelism of quantum computing. More significantly, there is no need to perform quantum state tomography in each previous loop, if the macroscopic variables for a certain loop is needed. The non-unitary collision operators are replaced by the unique local unitary operations, and the removal of ancilla qubit greatly diminishes the complexity of the quantum circuit. The numerical simulations of the $D_1Q_3$ and $D_2Q_5$ models have confirmed the feasibility of the proposed algorithm.