We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of topological order with the spontaneous breaking of discrete time-translation symmetry. We show that many-body localization can stabilize this phase against generic perturbations and establish some of its key features and signatures. We link topological and ordinary time crystals through three complementary perspectives: higher-form symmetries, quantum error-correcting codes, and a holographic correspondence. We also propose an experimental realization of a surface-code-based topological time crystal for the Google Sycamore processor.
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