Quantum lattice gas algorithm for fluid flow simulations

Large numerical simulations of fluid flows are required in many engineering applications. Non-classical hardware architectures and numerical algorithms promise to speed up simulations dramatically. Recent progress in mesoscale numerical modeling, quantum computing, and algorithm design is poised to fulfill this promise. Specifically, lattice methods are well suited for quantum computing due to their inherent statistical nature, resolving the probability distributions of fictitious fluid particles on a lattice. We demonstrate this concept by devising a quantum lattice gas automata technique. It revises an existing measurement-based strategy. Instead, our algorithm approximates the qubit relative phases and subtracts them at the end of each time step, delaying the need for measurement to the end of the computation. Results are shown for archetypical PDEs: the diffusion and Burgers' equations.