  We report the observation of a symmetry-protected topological time crystal,
which is implemented with an array of programmable superconducting qubits.
Unlike the time crystals reported in previous experiments, where spontaneous
breaking of the discrete time translational symmetry occurs for local
observables throughout the whole system, the topological time crystal observed
in our experiment breaks the time translational symmetry only at the boundaries
and has trivial dynamics in the bulk. More concretely, we observe robust
long-lived temporal correlations and sub-harmonic temporal response for the
edge spins up to 40 driving cycles. We demonstrate that the sub-harmonic
response is independent of whether the initial states are random product states
or symmetry-protected topological states, and experimentally map out the phase
boundary between the time crystalline and thermal phases. Our work paves the
way to exploring peculiar non-equilibrium phases of matter emerged from the
interplay between topology and localization as well as periodic driving, with
current noisy intermediate-scale quantum processors.
