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

Abstract

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.