Utilization of Quantum Monte Carlo Algorithm for Uncertainty Quantification

Efficient and robust uncertainty quantification (UQ) is essential in aerospace systems, as emphasized by both NASA’s CFD Vision 2030 and Certification by Analysis (CbA) 2040 initiatives. However, the extensive computational resources required by traditional UQ methods, especially when coupled with high-fidelity computational fluid dynamics (CFD) simulations, pose significant barriers. Quantum computing (QC) has been identified by the CFD Vision 2030 study as a promising technology to address these challenges, but has not yet been extensively explored in the context of UQ. In this study, a Quantum Computing-based Monte Carlo (QCMC) algorithm is implemented using a Qiskit simulator. This method utilizes Quantum Amplitude Estimation (QAE), specifically tailored for near-term Noisy Intermediate-Scale Quantum (NISQ) computers. The QCMC method demonstrates comparable accuracy to classical Monte Carlo (MC) methods on a two-dimensional heat diffusion problem while reducing the required number of samples (oracle calls) by ∼8X. By substantially lowering the computational overhead of UQ, this quantum computing-based algorithm could be a promising tool required to enable robust uncertainty-informed aerospace design.