Formation of Tesseract Time Crystals on a Quantum Computer

Abstract: The engineering of new states of matter through Floquet driving has revolutionized the field of condensed matter physics. This technique enables the creation of hybrid topological states and ordered phases that are absent in normal systems. Crystalline structures, exemplifying spatially ordered systems under periodic driving, have been extensively studied. However, the recent focus has shifted towards discrete time crystals (DTCs), periodically driven quantum many-body systems that break time translation symmetry under specific conditions. In this paper, we explore the theoretical predictions, experimental realizations, and emerging possibilities of utilizing DTCs on quantum computers. Additionally, the formation of time varying tesseracts using discrete time crystals is presented, allowing for the investigation of time translational symmetry in higher-dimensional lattice systems.