Abstract
Discrete time crystals (DTCs) are novel out-of-equilibrium quantum states of matter which break time translational symmetry. DTCs have been extensively realized in experiments, particularly their subclass that is characterized by period-doubling dynamics due to its natural occurrence in a system of periodically driven two-level, e.g., spin-1/2, particles. The realization of DTCs beyond period-doubling, including their generalizations termed discrete quasicrystals has also been made in recent years, though such experiments typically involve higher spin particles. Constructing and observing DTCs beyond period-doubling in systems of two-level particles are generally still considered an open challenge due to the latter's symmetry that natively only leads to period-doubling. In this work, we developed an intuitive interacting system of two-level particles (qubits) that supports the more non-trivial period-quadrupling DTCs (-DTCs). Remarkably, by utilizing a variational algorithm, we are able to observe clear signatures of such -DTCs in a quantum processor despite the presence of considerable noise and the small number of available qubits. Our findings extend the landscape of time crystalline behavior by demonstrating a distinct realization of time crystallinity beyond standard period-doubling dynamics with qubits (two-level particles) on a NISQ-era digital quantum computer, as well as the potential of existing noisy intermediate-scale quantum devices for simulating exotic non-equilibrium quantum states of matter.