Benchmarking the Qubit Lattice Algorithm against CFD simulations for Classical Nonlinear Physics

The Madelung transformation maps a general kinetic quantum wave function ψ evolution to its moment closures representation, with ψ = √ρ exp[iθ]. ρ is the fluid density and u = ∇θ the fluid velocity. For a simple scalar evolution equation for ψ, quantum vortices arise when the Madelung transformation becomes singular with the density ρ → 0 at the vortex core. Meng & Yang have considered quantum computing of classical fluid dynamics by restricting oneself to incompressible flows. A more general kinetic equation for ψ than the Gross-Pitaevskii BEC evolution was consid- ered so that one could eliminate terms like the quantum pressure from the momentum equation. In particular, Meng & Yang considered a generalized Gross-Pitaevskii equation for a quaternion wave function which included the gradient of a vector spin function. The algorithm is fully unitary. A qubit lattice algorithm (QLA) of this quantum evolution equation naturally introduces a 2-qubit representation. We determine the appropriate unitary collide and stream operators which yield a second order accurate representation of the Meng-Yang fluid equations. In particular we solve the 2D Taylor-Green vortex problem and benchmark our QLA with state of the art CFD computations.

Meng & Yang, Phys. Rev. Res. 5, 033182 (2023)