Many-Body Physics in the NISQ Era: Quantum Programming a Discrete Time Crystal

Time-crystalline eigenstate order on a quantum processor

“…Most recently, interesting DTC-like dynamical signatures have been observed in a range of quantum platforms from trapped ions 25 to nitrogen vacancy centres 26 to NMR spins 27 , 28 . However, each of these platforms lacks one or more necessary conditions for stabilizing an MBL-DTC 12 , 29 , either owing to an absence of the requisite type of disorder 25 , 27 or owing to the interactions being too long ranged 26 – 28 . The observed signatures, instead, have been shown to arise from slow thermalization 26 , 30 , effectively mean-field dynamics 28 , or prethermal dynamics from special initial states 12 , 29 , 31 , 32 , and are separated from the MBL-DTC by a spectral phase transition where eigenstate order disappears.…”

“…However, each of these platforms lacks one or more necessary conditions for stabilizing an MBL-DTC 12 , 29 , either owing to an absence of the requisite type of disorder 25 , 27 or owing to the interactions being too long ranged 26 – 28 . The observed signatures, instead, have been shown to arise from slow thermalization 26 , 30 , effectively mean-field dynamics 28 , or prethermal dynamics from special initial states 12 , 29 , 31 , 32 , and are separated from the MBL-DTC by a spectral phase transition where eigenstate order disappears. Thus, despite the recent progress, observing an MBL-DTC remains an outstanding challenge 12 , 29 .…”

Time Crystals at Last?

“…The theoretical requirements for the observation of an eigenstate-ordered DTC phase were elucidated in table 1 of ref. [14]. The significance of the Google AI experiment, which brings to bear many state-of-the-art tools from the field of quantum information, lies in meeting all of these.…”

“…2a) consists of a chain of qubits connected to gates which perform unitary operations. Such a device may be used to very naturally implement [14] Floquet drives. The experiment simulated, with N = 20 transmon qubits, a model closely…”

“…The discrete Fourier transform of χ(t) is shown in panel (c), and exhibits a pronounced peak at the subharmonic frequency The Delft results, for a single disorder realization and with nine spins, thus conform to the general desiderata of ref. [14], showing both subharmonic behavior in the autocorrelator χ(t) which does not vanish upon spatial averaging, and which survives up to t = 800 cycles, i.e. long-lived spatiotemporal response to the Floquet drive, as well as independence on initial conditions.…”