The study investigates the relaxation dynamics of initially prepared product states in a kicked Ising model under periodic driving using the IBM Quantum Heron processor, which consists of 133 superconducting qubits arranged on a heavy-hexagonal lattice. The researchers identify a prethermal regime characterized by magnetization oscillations at twice the period of the Floquet cycle and demonstrate its robustness against perturbations to the transverse field. They provide evidence for the realization of a period-doubling discrete time crystal (DTC) in a two-dimensional system. Additionally, they discover that the longitudinal field induces additional amplitude modulations in the magnetization with frequencies incommensurate with the driving period, leading to the emergence of discrete time quasicrystals (DTQCs). These findings enhance our understanding of clean DTCs in two dimensions and highlight the utility of digital quantum computers for simulating the dynamics of quantum many-body systems. The study also compares the results with tensor-network and state-vector simulations, validating the reliability of the quantum device outcomes.The study investigates the relaxation dynamics of initially prepared product states in a kicked Ising model under periodic driving using the IBM Quantum Heron processor, which consists of 133 superconducting qubits arranged on a heavy-hexagonal lattice. The researchers identify a prethermal regime characterized by magnetization oscillations at twice the period of the Floquet cycle and demonstrate its robustness against perturbations to the transverse field. They provide evidence for the realization of a period-doubling discrete time crystal (DTC) in a two-dimensional system. Additionally, they discover that the longitudinal field induces additional amplitude modulations in the magnetization with frequencies incommensurate with the driving period, leading to the emergence of discrete time quasicrystals (DTQCs). These findings enhance our understanding of clean DTCs in two dimensions and highlight the utility of digital quantum computers for simulating the dynamics of quantum many-body systems. The study also compares the results with tensor-network and state-vector simulations, validating the reliability of the quantum device outcomes.