A symbolic approach to discrete structural optimization using quantum annealing

TL;DR

This paper addresses discrete structural optimization of 2D truss systems using a quantum annealer by translating the problem into a QUBO/Ising formulation via a symbolic finite element method. It introduces a pipeline that encodes cross-sectional-area choices with qubits, builds a symbolic K(\mathbf{q}) and u(\mathbf{q}), and derives a fractional objective based on stress deviation from the material limit; an iterative non-fractional surrogate and quadratization render the problem QA-friendly. Across 2-, 3-, and 4-truss cases, the authors demonstrate that the quantum annealer can find the global optimum given enough reads and QPU time, but scalability is hindered by the exponential growth of symbolic expressions and the high qubit-connectivity required for larger systems. The work provides a proof-of-concept for quantum-assisted discrete structural optimization and highlights critical scalability barriers related to symbolic FEM, problem connectivity, and hardware time limits, suggesting directions for future methodological and architectural improvements. Overall, this study shows a feasible, albeit challenging, path to integrating quantum annealing into practical structural optimization workflows.

Abstract

With the advent of novel quantum computing technologies, and the knowledge that such technology might be used to fundamentally change computing applications, a prime opportunity has presented itself to investigate the practical application quantum computing. The goal of this research is to consider one of the most basic forms of mechanical structure, namely a 2D system of truss elements, and find a method by which such a structure can be optimized using quantum annealing. The optimization will entail a discrete truss sizing problem - to select the best size for each truss member so as to minimize a stress-based objective function. To make this problem compatible with quantum annealing devices, it will be written in a QUBO format. This work is focused on exploring the feasibility of making this translation, and investigating the practicality of using a quantum annealer for structural optimization problems. Using the methods described, it is found that it is possible to translate this traditional engineering problem to a QUBO form and have it solved by a quantum annealer. However, scaling the method to larger truss systems faces some challenges that would require further research to address.

Figures (16)

• Figure S1: Two-truss system
• Figure S2: Three-truss system
• Figure S3: Four-truss system
• Figure S4: Fractional objective function for the two-truss problem. Global minimum is found to be solution number 7, corresponding to $\mathopen{}\mathclose{\left[ 0,0,1,1,0,0 \right]$.
• Figure S5: Fractional objective function for the three-truss problem. Global minimum is found to be solution number 21, corresponding to $\mathopen{}\mathclose{\left[ 0,0,1,1,0,0,0,0,1 \right]$.