Quantum algorithm for the lattice Boltzmann method with applications on real quantum devices
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Classical high-performance computing often struggles with computational fluid dynamics and other complex partial differential equation (PDE) problems in fields like acoustics and electromagnetics. The immense computational resources and data required for these simulations can make them intractable, representing a significant hurdle in scientific computing and engineering. This work presents an efficient quantum algorithm based on the one-step simplified lattice Boltzmann method (OSSLBM) to address these challenges. Our quantum algorithm leverages the local and parallelizable structure of the OSSLBM, and makes efficient use of the quantum circuit resources in terms of both qubits and gates. Unlike traditional quantum PDE solvers like HHL or variational methods, our approach avoids computationally expensive subroutines and loops that require repeated state tomography and reinitialization. For linear problems, we demonstrate potential for end-to-end advantage by concatenating time steps using mid-circuit measurements and dynamic circuits, allowing for a single final measurement. Furthermore, we discuss the extension to nonlinear cases. To demonstrate the viability of the method, we carry out example computations on statevector simulators and on a noisy intermediate-scale quantum computer for several different physics simulation problems, including a Navier-Stokes simulation on a superconducting quantum computer.
