Exploring Quantum Annealing for Coupled Structural Analysis Problems

In this work, we develop and explore novel methods for using quantum annealing (QA) to solve coupled structural analysis problems, specifically focusing on fluid structure interaction (FSI) problems. These problems involve the interaction between a fluid and a structural domain, making them computationally demanding. When combined with design optimization tasks, they form complex optimization problems that are difficult to solve using classical methods, creating the need to explore alternative strategies such as QA. QA is an emerging computational technique that utilizes quantum mechanical effects to solve complex optimization problems much faster and more efficiently than classical approaches. To optimize FSI problems using QA, it is first necessary to develop methods that allow using QA to solve FSI problems themselves, which is the focus of this work. Our novel method is based on the partitioned approach, where the fluid and structural subproblems are treated separately. Using energy principles, we formulate the structural subproblem as an optimization problem and express the system’s energy in a quadratic unconstrained binary optimization (QUBO) model, allowing the problem to be solved by QA. We validate our proposed method on a state-of-the-art D-Wave quantum annealer, with the results demonstrating the feasibility of QA for solving simple FSI problems. Additionally, we analyze the capabilities and limitations of current QA hardware for these applications and explore strategies to overcome existing constraints. This study should lay the groundwork for future advancements in applying QA to engineering problems involving coupled structural analysis and optimization.