Quantum annealing computation methods to obtain a converged flow solution

In this study, we propose quantum annealing computation methods to obtain converged flow solutions, utilizing quantum superposition states. In conventional numerical simulations, converged solutions are obtained from a given initial state using time advancement or iterative methods. In contrast, the proposed methods extract a converged solution from all the possible solutions under quantum superposition states by quantum annealing. The proposed quantum annealing methods are developed for LGA and finite difference methods.

The proposed QUBO model for LGA consists of four sub-cost functions: sub-cost functions for the steady solution, collision, wall boundary, and flow field conditions. In a numerical experiment of a one-dimensional channel flow problem, the proposed approach obtains the converged solution out of 10⁶⁷ possible solutions by quantum annealing.

The proposed QUBO model for finite difference methods are built by following three steps:

1. Discretize governing equations

2. Convert fluid variables to binary

3. Build a QUBO model from the binary governing equations

In a numerical experiment of a one-dimensional channel flow problem, the proposed approach obtains the converged solution out of 10¹⁴ possible solutions by quantum annealing, and the obtained solution is in good agreement with that obtained by a conventional time integration method.

More details about the proposed quantum annealing methods will be discussed in the presentation.