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