Nonlocal discrete time crystals in periodically driven surface codes

Abstract

Discrete time crystals (DTCs) are nonequilibrium phases of matter characterized by robust subharmonic order parameter dynamics. We report a new type of DTC in a periodically driven surface code, the subharmonic signature of which is only observable with respect to some nonlocal order parameter. By modifying the commonly used metrics for characterizing ordinary DTCs, i.e., the spectral functions, spin-glass order parameters, and two-point correlators, we numerically investigate the different phases of the proposed system. Specifically, depending on the system parameters and boundary conditions, we find that the system may fall into either a "surface code" phase, trivial paramagnet phase, nonlocal period-doubling DTC phase, or nonlocal period-quadrupling DTC phase. Our work thus demonstrates the prospect of exploring topological codes for discovering novel phases of matter.

10 pages, 8 figures. Published in PRB

References in corpus (11)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Surface codes: Towards practical large-scale quantum computation
• Topological Quantum Distillation
• Many-body localization in periodically driven systems
• Absence of Quantum Time Crystals
• Periodically driven ergodic and many-body localized quantum systems
• A Brief History of Time Crystals
• Anderson localization and Mott insulator phase in the time domain
• Many-body localization caused by temporal disorder
• Floquet Majorana zero and $\pi$ modes in planar Josephson junctions
• Six-dimensional time-space crystalline structures

Cited by in corpus (1)

• $Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain