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Topologically ordered phases of matter elude Landau's symmetry-breakingtheory, featuring a variety of intriguing properties such as long-rangeentanglement and intrinsic robustness against local perturbations. Theirextension to periodically driven systems gives rise to exotic new phenomenathat are forbidden in thermal equilibrium. Here, we report the observation ofsignatures of such a phenomenon -- a prethermal topologically ordered timecrystal -- with programmable superconducting qubits arranged on a squarelattice. By periodically driving the superconducting qubits with a surface-codeHamiltonian, we observe discrete time-translation symmetry breaking dynamicsthat is only manifested in the subharmonic temporal response of nonlocallogical operators. We further connect the observed dynamics to the underlyingtopological order by measuring a nonzero topological entanglement entropy andstudying its subsequent dynamics. Our results demonstrate the potential toexplore exotic topologically ordered nonequilibrium phases of matter with noisyintermediate-scale quantum processors.

Long-lived topological time-crystalline order on a quantum processor