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

Abstract

In periodically driven (Floquet) systems, evolution typically results in an infinite-temperature thermal state due to continuous energy absorption over time. However, before reaching thermal equilibrium, such systems may transiently pass through a meta-stable state known as a prethermal state. This prethermal state can exhibit phenomena not commonly observed in equilibrium, such as discrete time crystals (DTCs), making it an intriguing platform for exploring out-of-equilibrium dynamics. Here, we investigate the relaxation dynamics of initially prepared product states under periodic driving in a kicked Ising model using the IBM Quantum Heron processor, comprising 133 superconducting qubits arranged on a heavy-hexagonal lattice, over up to $100$ time steps. We identify a clean two-dimensional DTC characterised by magnetisation measurements oscillating at twice the period of the Floquet cycle and demonstrate its robustness against perturbations to the transverse field. This stability does not rely on many-body localisation or on high-frequency Floquet prethermalisation, but emerges in a clean, disorder-free setting. Moreover, we discover that the longitudinal field induces additional amplitude modulations in the magnetisation with a period incommensurate with the driving period, leading to the emergence of an incommensurately modulated discrete time-crystal (IM-DTC) response. These observations are further validated through comparison with tensor-network and state-vector simulations. Our findings not only provide insight into clean DTC and IM-DTC dynamics in two dimensions but also highlight the utility of gate-based quantum computers for simulating the dynamics of quantum many-body systems, complementing state-of-the-art classical simulations in regimes where entanglement growth challenges their convergence.