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Bulletin of the American Physical Society

The Lattice Boltzmann Method for quantum fluids and the fourth order Hermite polynomial expansion

Mauro Melchiades Doria, Rodrigo C. V. Coelho, Anderson Ilha, R. M. Pereira, V Y Aibe

Published Mar 4, 2014• 0 citations
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Computational Fluid Dynamics simulations are crucial in industrial applications but require extensive computational resources, particularly for extreme turbulent regimes. While classical digital approaches remain the standard, quantum computing promises a breakthrough by enabling a more efficient encoding of large-scale simulations with a limited number of qubits. This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM). The inherently non-linear LBM equations are linearized via a Carleman expansion and solved using the quantum Harrow Hassidim Lloyd algorithm (HHL). We evaluate this method on three benchmark cases featuring different boundary conditions, periodic, bounceback, and moving wall, using statevector emulation on high-performance computing resources. Our results confirm the validity of the approach, achieving median error fidelities on the order of 10−310^{-3}10−3 and success probabilities sufficient for practical quantum state sampling. Notably, the spectral properties of small lattice systems closely approximate those of larger ones, suggesting a pathway to mitigate one of HHL's bottlenecks: eigenvalue pre-evaluation.
Computational Fluid Dynamics simulations are crucial in industrial applications but require extensive computational resources, particularly for extreme turbulent regimes. While classical digital approaches remain the standard, quantum computing promises a breakthrough by enabling a more efficient encoding of large-scale simulations with a limited number of qubits. This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM). The inherently non-linear LBM equations are linearized via a Carleman expansion and solved using the quantum Harrow-Hassidim-Lloyd algorithm (HHL). We evaluate this method on three benchmark cases featuring different boundary conditions—periodic, bounce-back, and moving wall—using state-vector emulation on high-performance computing resources. Our results confirm the validity of the approach, achieving median error fidelities on the order of10−310^{-3}10−3and success probabilities sufficient for practical quantum state sampling. Notably, the spectral properties of small lattice systems closely approximate those of larger ones, suggesting a pathway to mitigate one of HHL's bottlenecks: eigenvalue pre-evaluation.