CDS&E: Collaborative Research: Unlocking the Power of Quantum Computing for Topology Optimization

This Computational and Data-Enabled Science and Engineering (CDS&E) project addresses the growing need for computational methods capable of designing advanced manufacturing systems with spatially varying material properties. While advanced manufacturing enables functionally graded materials and multi-material structures with unprecedented mechanical performance, their computational design requires solving large-scale optimization and simulation problems that challenge the limits of classical computing. This project explores how emerging quantum computing technologies can transform computational engineering by accelerating multi-material topology optimization and enabling new approaches for engineering design. The project will develop a quantum-enabled computational framework that integrates quantum optimization and quantum partial differential equation solvers to improve the efficiency and scalability of topology optimization. The resulting methods will support the design and manufacturing of high-performance functionally graded materials for applications in biomedical engineering, soft robotics, aerospace, energy, and electronics. The project will also educate the next generation of scientists and engineers through interdisciplinary training for graduate and undergraduate students and outreach activities that introduce K–12 students to computational design and quantum computing. The novelty of the framework lies in establishing an end-to-end quantum computing paradigm for computational design while rigorously evaluating both its opportunities and its fundamental limitations. The project is organized around three main thrusts: (1) Quantum optimization: to accelerate multi-material topology optimization, the project develops quantum algorithms for large-scale optimization problems arising in engineering design and investigates their computational complexity and scalability. (2) Quantum simulation: to improve the efficiency of physics-based design, the project develops quantum algorithms for solving the partial differential equations that govern topology optimization, while evaluating quantum resource requirements, including ancilla qubits, gate counts, and circuit depth, and assessing compatibility with near-term and analog quantum hardware. (3) Quantum-enabled manufacturing: to translate computational advances into engineering practice, the project integrates these quantum algorithms into a computational framework for designing functionally graded materials suitable for advanced manufacturing and quantifies end-to-end computational performance through complexity analysis and resource estimation. If successful, the project will establish a rigorous foundation for quantum-enabled computational engineering, advance the integration of quantum computing with advanced manufacturing, and provide new computational capabilities for designing next-generation high-performance engineering systems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.