Constructing large period discrete time crystals with quantum repetition codes

Discrete time crystals (DTCs) represent a class of time-periodic systems characterized by robust observable dynamics that displays n times longer periodicity than the driving period. At present, successful experimental studies are limited to the realization of period-doubling or period-tripling DTCs. My work establishes a connection between the physics of DTCs and the mechanism of quantum repetition codes. This in turn allows the systematic and realistic construction of virtually any large period DTCs, achieved by utilizing a series of spin-1/2 chains and devising a time-periodic Hamiltonian that simulates appropriate quantum gates in a fault-tolerant manner.  As a very important feature, explicit numerical studies demonstrate that the proposed DTCs can be directly observed in existing trapped ions and superconducting circuit platforms under the accessible number of particles used in previous successful DTC experiments. This work thus opens an exciting opportunity to bring a new family of DTCs into reality and potentially explore their technological applications in the immediate future.