• Abstract Periodically driven (Floquet) many-body systems tend to absorb energy and approach an infinite-temperature state, yet can host emergent order such as discrete time crystals (DTCs). • Here we realise a clean two-dimensional DTC and an incommensurately modulated DTC (IM-DTC) on the IBM Quantum Heron processor, a 133-qubit superconducting device with heavy-hexagonal connectivity, implementing a kicked Ising model and tracking magnetisation dynamics for up to 100 Floquet cycles. • We observe robust period-doubling oscillations that persist over the accessible time window and are stable against perturbations of the transverse field, without invoking disorder-induced many-body localisation or high-frequency Floquet prethermalisation. • Introducing a longitudinal field generates additional long-period amplitude modulations with frequencies incommensurate with the drive, realising an IM-DTC response. • Comparison with state-vector and tensor-network simulations benchmarks the hardware and reveals regimes where entanglement growth makes classical simulation challenging, underscoring the utility of gate-based quantum processors for out-of-equilibrium dynamics in two dimensions. • Similar content being viewed by others Data availability The data supporting the findings of this study are available within the paper and its Supplementary Information files.

Article Summaries:

  • IBM’s 133‑qubit Heron quantum processor has been used to create the first clean two‑dimensional discrete time crystal (DTC) and an incommensurately modulated DTC (IM‑DTC). By implementing a kicked Ising model and measuring magnetisation over 100 Floquet cycles, the team observed robust period‑doubling oscillations that persist without disorder‑induced localisation or high‑frequency pre‑thermalisation. Adding a longitudinal field produced long‑period amplitude modulations whose frequencies are incommensurate with the drive, demonstrating the IM‑DTC response. Benchmarking against state‑vector and tensor‑network simulations highlighted regimes where entanglement growth renders classical simulation difficult, underscoring the advantage of gate‑based quantum hardware for studying out‑of‑equilibrium dynamics in two dimensions.

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