Machine learning (ML) and quantum computing have each begun to reshape computational fluid dynamics (CFD), promising speed-ups that could open up new application regimes. Yet using ML to tackle “big science” questions that are qualitatively out of reach for traditional simulation—such as uncovering underlying physical laws from limited observations—is still early-stage. Progress in quantum computing for CFD has arguably lagged further, because current hardware limitations have constrained large-scale numerical experimentation, keeping many capability assessments more theoretical and first-principled. This workshop aims to bring together contributions and discussion on how ML and quantum methods might jointly address these frontier scientific questions, while also showcasing recent advances from each field individually. Tentative themes include: 1) Turbulence closures as inverse problems: addressing non-uniqueness, hidden variables, and multi-regime physics under sparse or biased data. Bayesian/probabilistic closures with physical constraints are a baseline, potentially complemented by quantum-enhanced sampling to explore complex posteriors. 2) Scientific inference for PDEs beyond physics-informed approaches: shifting focus from accelerating known models to inferring the governing physics in unknown regimes, including unknown forcings, constitutive laws, and boundary/initial conditions. Hybrid quantum–classical variational inference for PDE-constrained problems and physics-informed methods provide starting points, with open questions on what comes next. 3) Rare events in fluids (tails, transitions, extremes): using quantum-ML to predict and characterize low-probability but high-impact phenomena (e.g., laminar–turbulent transition, blow-up events, rogue-wave analogs, intermittency) that are poorly sampled in simulations yet can dominate real-world risk and undermine numerical reliability. 4) Multi-physics CFD as a grand inverse problem: treating condensation, phase change, reactive flows, and phase-transition kinetics as inference problems where governing physics is uncertain and validation data is indirect. Key directions include constrained constitutive modeling, posterior exploration in stiff kinetics/phase change, multi-fidelity/multi-scale data assimilation, and regime classification from sparse samples.