Quantum Algorithms for the Lattice Boltzmann Method: Encoding and Evolution
D.T. Duong (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M. Möller – Mentor (TU Delft - Numerical Analysis)
David de Laat – Graduation committee member (TU Delft - Discrete Mathematics and Optimization)
Johan Dubbeldam – Graduation committee member (TU Delft - Mathematical Physics)
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Abstract
This thesis explores quantum algorithms for simulating fluid dynamics using the Lattice Boltzmann
Method (LBM), with a focus on developing resource-efficient quantum implementations. A central challenge in quantum physical simulation is ensuring that algorithms not only offer computational speedups but also preserve the underlying physical structure of the system. Without this alignment, simulations can become unstable, inaccurate, or theoretically uninformative, especially in fluid dynamics, where conservation laws and symmetries are important. This thesis addresses that challenge by developing quantum versions of the LBM that are constructed with physical interpretability and mathematical consistency at their core.
The main contribution of this thesis is the design and analysis of two quantum encoding strategies for particle distribution functions in LBM: tensor-product encoding and amplitude encoding. Each approach offers different trade-offs between circuit size, precision, and interpretability. The thesis further develops quantum circuits to implement the collision and streaming steps for each of the encoding schemes, with an emphasis on utilizing conservations and symmetries to facilitate the uninterrupted and coherent flow of the multi-round LBM simulations.
To provide a realistic assessment of the methods, the thesis incorporates rigorous error analysis, including the accuracy of each step, post-selection success probabilities, and cumulative errors over multiple simulation steps. Through theoretical analysis and numerical simulations, this thesis demonstrates new physically-informed approaches to quantum LBM, offering scalable and interpretable models for fluid transport on quantum devices.