Dynamical Information Preservation with Dissipative Time Crystals

We demonstrate that the time-crystalline behaviour observed in the thermodynamic limit of dissipative systems can be utilised to preserve dynamical information. As a physical model we focus on the driven-dissipative BHD, which has been shown to exhibit both Z2 and time-translation symmetry breaking. These symmetries enable the encoding of information into the system that does not decay in the long-term, provided only certain dissipative errors are present. Our quantum dynamical analysis underscores the closing of the dissipative gap, seen within the eigenspectra of the Liouvillian of the BHD, constructed from a truncated Fock basis at the boundary of computational limits. We generalize the gap closing behaviour to dissipative systems and pave the way for the potential encoding of a qubit that can be passively error-corrected within a noiseless subsystem to retain dynamical information.