Formulation and evaluation of ocean dynamics problems as optimization problems for quantum annealing machines.

Area of Science:

• Computational science
• Oceanography
• Atmospheric science

Background:

• Quantum computing offers potential advancements for scientific computation.
• Quantum annealing (QA) is a paradigm suited for optimization problems.
• Oceanic and atmospheric dynamics, governed by Navier-Stokes equations, require advanced computational methods.

Purpose of the Study:

• To explore the applicability of quantum annealing (QA) for oceanic and atmospheric dynamics.
• To compare QA with its classical counterpart, simulated annealing (SA), on a simplified ocean model.
• To identify current limitations of QA hardware for scientific applications.

Main Methods:

• Applied QA and SA to the Stommel problem, a simplified ocean model.
• Formulated the model's linear partial differential equation as a least-squares optimization problem.
• Discretized the cost function using finite difference and truncated basis expansion.

Main Results:

• Simulated annealing (SA) successfully reproduced the expected solution for the Stommel problem.
• Quantum annealing (QA) using D-Wave hardware failed to achieve optimal solutions in some instances.
• Hardware limitations, particularly limited connectivity, restricted the scale of solvable problems for QA.

Conclusions:

• Current quantum annealing hardware has limitations for complex scientific problems like those in oceanography and atmospheric science.
• Improvements in quantum hardware connectivity or embedding algorithms are needed for QA to be viable.
• Further research is necessary to bridge the gap between quantum computation and fluid dynamics.