Artificial Intelligence (AI) is increasingly embedded in public governance, raising questions about how institutions can anticipate its societal implications while safeguarding democratic accountability amid expanding computational infrastructures. This article examines how anticipatory AI governance can be operationalised in the age of super-computing through a mixed-methods multistakeholder approach in the Basque Country (Spain). The study focuses on the city-regional governance setting of Gipuzkoa, a de-volved historical territory with fiscal autonomy and a growing advanced-computing ecosystem centred in Donostia–San Sebastián, where regional initiatives are positioning the Basque Country as an emerging “quantum territory” within Europe’s high-performance and quantum computing landscape, including the installation of IBM Quantum System Two. Methodologically, the study combines action research with three stakeholder groups and a quantitative online survey of citizens (N = 911). The action research engaged six civil society organisations, seven provincial directorates, and eleven municipalities. Results indicate that city-regional administrations can function as labor-atories for public AI governance when policy experimentation is combined with empirical evidence and advanced computational infrastructures. The findings suggest policy recommendations for supercomputing ecosystems, including transparent AI experi-mentation, public-interest data governance, and policy sandboxes linking advanced computing, civic participation, and accountable digital public services.