Collaborative Research: Noise-Aware Optimization Algorithms for Hybrid Quantum Computing

Quantum computing has the potential to transform scientific discovery and technological innovation in areas such as artificial intelligence, molecular simulation, biotechnology, and secure information processing. Variational quantum algorithms are among the most promising approaches for near-term quantum computing, but existing optimization methods used to train these algorithms often become unreliable when quantum measurements are highly noisy or when problems become very large. These limitations present major difficulties to realizing the practical benefits of quantum computing technologies. This research addresses these challenges by developing mathematically rigorous and scalable optimization frameworks that remain effective under severe noise and computational uncertainty. The project advances the mathematical and computational foundations needed for trustworthy quantum algorithm training and evaluation, while also enabling systematic assessment of when quantum computing can provide advantages over classical methods. By strengthening core capabilities in quantum computing, the research supports national priorities in scientific innovation. The project also contributes to workforce development through interdisciplinary training opportunities for undergraduate and graduate students in computational mathematics, optimization, and quantum computing. Research outcomes, including open-source software, benchmark test problems, and educational materials, will be broadly disseminated to accelerate adoption by the scientific community and support the emerging quantum technology workforce in the United States. This project studies large-scale unconstrained and constrained quantum-specific optimization problems arising in variational quantum algorithms. The research develops advanced noise-aware, derivative-free, and factorization-free optimization algorithms that rely solely on noisy objective and constraint evaluations, avoid costly matrix factorizations, and accommodate realistic quantum hardware conditions, including stochastic and potentially unbounded measurement noise. Rigorous convergence, complexity, and robustness analyses establish theoretical guarantees for algorithmic performance, scalability, and resource efficiency. The research also integrates modern linear-system solution techniques to improve scalability while maintaining convergence behavior comparable to leading factorization-based methods. The resulting frameworks will be validated across a broad range of quantum computing applications, including quantum approximate optimization algorithms, variational quantum linear solvers, and quantum neural networks, with potential downstream applications in artificial intelligence, molecular design, and computational biotechnology. The resulting methodologies are also broadly applicable to large-scale stochastic optimization problems arising in science, engineering, and advanced computational technologies. 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. NSF Award ID: 2608763 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Xiu Yang | Institution: Lehigh University, BETHLEHEM, PA | Award Amount: $100,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2608763 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2608763.html