Thermalization and criticality on an analogue–digital quantum simulator

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators¹,². Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble-Zurek scaling predictions³ in the XY model, as well as signatures of the classical Kosterlitz-Thouless phase transition⁴. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis⁵⁻⁷ in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.