Quantum-assisted Stacking Sequence Retrieval and Laminated Composite Design

Abstract

We, the QAIMS lab lab at the Aerospace Faculty of TU Delft, participated as finalists in the Airbus/BMW Quantum Computing Challenge 2024. Stacking sequence retrieval, a complex combinatorial task within a bi-level optimization framework, is crucial for designing laminated composites that meet aerospace requirements for weight, strength, and stiffness. This document presents the scientifically relevant sections of our submission, which builds on our prior research on applying quantum computation to this challenging design problem. For the competition, we expanded our previous work in several significant ways. First, we incorporated a full set of manufacturing constraints into our algorithmic framework, including those previously established theoretically but not yet demonstrated, thereby aligning our approach more closely with real-world manufacturing demands. We implemented the F-VQE algorithm, which enhances the probability shaping of optimal solutions, improving on simpler variational quantum algorithms. Our approach also demonstrates flexibility by accommodating diverse objectives as well as finer ply-angle increments alongside the previously demonstrated conventional ply angles. Scalability was tested using the DMRG algorithm, which, despite limitations in entanglement representation, enabled simulations with up to 200 plies. Results were directly compared to conventional stacking sequence retrieval algorithms with DMRG showing high competitiveness. Given DMRG's limited entanglement capabilities, it serves as a conservative baseline, suggesting potential for even greater performance on fully realized quantum systems. This document serves to make our competition results publicly available as we prepare a formal publication on these findings and their implications for aerospace materials design optimization.

Figures (10)

• Figure 1: a) Diagram of a laminated composite material, which consists of multiple layers that are oriented in different directions. b) A representation of the stress resultants $\vec{N}$, which for isotropic materials result in in-plane deformations $\vec{\varepsilon}^{\: 0}$. c) A pictographical representation of the moment resultants $\vec{M}$, which for isotropic materials result in out-of-plane bending $\vec{\kappa}$. Non-diagonal elements in the $\mathbf{ABD}$-matrix allow for coupling between all possible stress and moment resultants on the one hand, and all in- and out-of-plane deformations on the other hand.
• Figure 2: a) A depiction of the dependencies of the stiffness matrix which couples forces to deformations, and in turn is used to define failure criteria. b) A depiction of the bi-level optimization process for laminated composites. Additional manufacturing constraints that also may enter stacking sequence retrieval are not shown. c) Laminate design is often part of an outer structural design loop together with mechanical simulations.
• Figure 3: a) The parameterized quantum circuit used lamination parameter search b) The parameterized quantum circuit used for the buckling factor maximization for $N=8$. Fixed gates are shown in blue while parameterized gates are colored orange. As the sign of the partial swap gate (\ref{['eq:partialswap']}) depends on the order of the ply states, we use a circle to denote and first and a square to denote the second ply to which the gate is applied.
• Figure 4: Results of lamination parameter search with F-VQE for $N=8$ plies, with and without constraints. Each blue line represents a single run of the algorithm with varying target lamination parameters. The average is shown in black.
• Figure 5: Results of lamination parameter search with F-VQE for $N=10$ plies, with and without constraints. Each blue line represents a single run of the algorithm with varying target lamination parameters. The average is shown in black.