Turning a Quantum Computer into a Time Crystal Google's Sycamore quantum processor can simulate an elusive quantum system called a discrete time crystal.
Given recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices, we explore their implications for quantum many-body physics in a practical sense: we ask which physical phenomena in the realm of quantum statistical mechanics can these devices realize better than any other experimental platform. As a target, we identify discrete time crystals (DTCs), novel out-of-equilibrium phases of matter that break time translation symmetry, and are realized in the intrinsically nonequilibrium setting of periodically driven quantum systems stabilized by disorder and many-body localization. While precursors of time-crystals have been observed across a variety of experimental platforms - ranging from trapped ions to nitrogen vacancy centers - each of these lacks one or more of the necessary ingredients for realizing a true incarnation of this phase, and detecting the long-range spatiotemporal order that is its defining feature. We show that a new generation of quantum simulators, such as Google's Sycamore processor, can be programmed to realize the DTC phase and to experimentally verify its dynamical properties using a wide range of observables and initial states. We also discuss the effects of environmental decoherence, and show that already with existing technology one could observe the persistence of DTC spatiotemporal order over hundreds periods, with parametric improvements to come as the technology advances in the future.
Time crystals are a dynamical phase of periodically driven quantum many-body systems where discrete time-translation symmetry is broken spontaneously. Time-crystallinity however subtly requires also spatial order, ordinarily related to further symmetries, such as spin-flip symmetry when the spatial order is ferromagnetic. Here we define topologically ordered time crystals, a time-crystalline phase borne out of intrinsic topological order-a particularly robust form of spatial order that requires no symmetry. We show that many-body localization can stabilize this phase against generic perturbations and establish some of its key features and signatures, including a dynamical, time-crystal form of the perimeter law for topological order. We link topologically ordered and ordinary time crystals through three complementary perspectives: higher-form symmetries, quantum error-correcting codes, and a holographic correspondence. Topologically ordered time crystals may be realized in programmable quantum devices, as we illustrate for the Google Sycamore processor.