  Topologically ordered phases of matter elude Landau's symmetry-breaking
theory, featuring a variety of intriguing properties such as long-range
entanglement and intrinsic robustness against local perturbations. Their
extension to periodically driven systems gives rise to exotic new phenomena
that are forbidden in thermal equilibrium. Here, we report the observation of
signatures of such a phenomenon -- a prethermal topologically ordered time
crystal -- with programmable superconducting qubits arranged on a square
lattice. By periodically driving the superconducting qubits with a surface-code
Hamiltonian, we observe discrete time-translation symmetry breaking dynamics
that is only manifested in the subharmonic temporal response of nonlocal
logical operators. We further connect the observed dynamics to the underlying
topological order by measuring a nonzero topological entanglement entropy and
studying its subsequent dynamics. Our results demonstrate the potential to
explore exotic topologically ordered nonequilibrium phases of matter with noisy
intermediate-scale quantum processors.
