Quantum repetition codes as building blocks of large-period discrete time crystals

Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is response to a periodic drive at fraction its frequency. Current successful experiments are, however, only limited realizing DTCs period-doubling and period-tripling dynamics, forming very small subset DTC phases. Creating larger in the laboratory remains longstanding challenge, yet it necessary for developing technological applications DTCs, e.g., as quantum memory highly entangled qubits, or exploring interesting beyond subharmonic condensed phenomena domain. By highlighting connection between error correction, we devise general realistic scheme building exhibiting any large-period which even sufficiently system sizes. Our proposal uses an array spin-1/2 chains simulate repetition code hardware level, has essential properties realize robust It readily implemented existing superconducting trapped-ion processors, making new families experimentally accessible immediate future.