Quantum lattice-gas model for computational fluid dynamics

Abstract

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 specifically, 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 scale. At the mesoscopic scale, a lattice Boltzmann equation with a nonlocal collision term that depends on the entire system wave function, 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.

Twisting of filamentary vortex solitons demarcated by fast Poincaré recursion

“…the nonlinear interaction term in the Gross Pitaevskii equation, the effective equation of motion of a low-temperature BEC superfluid. With this representation, previously we have predicted solutions to a number of nonlinear classical and quantum systems [4,13,14,15,16]. An advantage of our approach over the standard computational physics GP solvers is that the simple unitary collidestream-rotate operations give rise to an algorithm that approaches pseudo-spectral accuracy [17] in much the same way as the simple collide-stream steps of a lattice Botlzmann algorithm approach pseudo-spectral accuracy for fluid dynamics simulations [18,19].…”

“…The justification for this reduction is given in Ref. [13]. The quantum gate dynamics conserves particle number and consequently the effective H GP in (3) commutes with the particle number operator.…”

Discrete Time Dirac Quantum Walk in 3+1 Dimensions

“…As such, QWs have been considered as discrete quantum simulators for particle-physics. Interestingly, it has been proven that QWs have the capability of simulating free relativistic particle dynamics [16][17][18][19][20][21][22][23][24][25][26][27][28][29], providing-in contrast with other discretisation schemes based on finite-differences and which in general do not preserve the norm-a local unitary model underlying relativistic dynamics.…”

Type II quantum algorithms

“…Algorithms have been proposed for fluid dynamics [6,7,4], for the diffusion equation [8], the Burgers equation [9], for the nonlinear Schroedinger and Korteweg-de Vries equations in one-dimensions [10], and for MHD turbulence in one dimension [11]. Some of these algorithms have also been implemented on NMR quantum computers [12,3,13].…”