Quantum collision circuit, quantum invariants and quantum phase estimation procedure for fluid dynamic lattice gas automata

• URL: http://arxiv.org/abs/2310.07362v2
• Date: Fri, 7 Jun 2024 11:58:37 GMT
• Title: Quantum collision circuit, quantum invariants and quantum phase estimation procedure for fluid dynamic lattice gas automata
• Authors: Niccolo Fonio, Pierre Sagaut, Giuseppe Di Molfetta,
• Abstract summary: We develop a quantum algorithm that allows for the simulation of fluid dynamic LGCA on a quantum computer. We also develop a phase estimation procedure for detecting quantities of interest such as mass and momentum, avoiding reinitialization of the cell.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Lattice Gas Cellular Automata (LGCA) is a classical numerical method widely known and applied to simulate several physical phenomena. Among these phenomena, we find fluid flows described by the Navier-Stokes equations. We develop a quantum algorithm that allows for the simulation of fluid dynamic LGCA on a quantum computer. Furthermore, we prove the conservation of the quantities of interest, but finding more quantum invariants than expected. Finally, we develop a phase estimation procedure for detecting quantities of interest such as mass and momentum, avoiding reinitialization of the cell. In addition, we discuss a sublinear encoding of the lattice which admits a unitary streaming but constrains the collision step.

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