A Quantum Lattice-Gas Model for Computational Fluid Dynamics

Quantum-computing ideas are applied to the practical and ubiquitous problem of fluid dynamics simulation. Hence, this paper addresses two separate areas of physics: quantum mechanics and fluid dynamics (or specially, the computational simulation of fluid dynamics). The quantum algorithm is called a quantum lattice gas. An analytical treatment of the microscopic quantum lattice-gas system is carried out to predict its behavior at the mesoscopic and macroscopic scales. At the mesoscopic scale, a lattice Boltzmann equation, with a non-local collision term that depends on the entire system wavefunction, governs the dynamical system. Numerical results obtained from an exact simulation of a one-dimensional quantum lattice-model are included to illustrate the formalism. A symbolic mathematical method is used to implement the quantum mechanical model on a conventional workstation. The numerical simulation indicates that classical viscous damping is not present in the one-dimensional quantum lattice-gas system.