Unveiling clean two-dimensional discrete time crystals on a digital quantum computer

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.