Finite-temperature criticality through quantum annealing.

Critical phenomena at finite temperature underpin a broad range of physical systems, yet their study remains challenging due to computational bottlenecks near phase transitions. Quantum annealers have attracted significant interest as a potential tool for accessing finite temperature criticality beyond classical reach, but their utility in precisely resolving criticality has remained limited by noise, hardware constraints, and thermal fluctuations. Here we overcome these challenges, introducing a sampling protocol that combines real-time temperature inference with fine control of the energy scales throughout experiments. A careful embedding strategy allows us to fully capture the finite-temperature critical behavior of the paradigmatic two-dimensional Ising ferromagnet on toroidal lattices up to 2640 spins. By tuning the energy scale of the system and mitigating device defects, we sample effective Boltzmann distributions extracting both the critical temperature and the associated universal critical exponents. Our approach opens the study of equilibrium and non-equilibrium critical phenomena in a broad class of systems at finite temperature.