Abstract
Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2–8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)7,9–15. Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order7,16,17. In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states7,9,10. Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors.
Highlights
30 November 2021Xiao Mi1,11, Matteo Ippoliti[2,11], Chris Quintana[1], Ami Greene[1], Zijun Chen[1], Jonathan Gross[1], Frank Arute[1], Kunal Arya[1], Juan Atalaya[1], Ryan Babbush[1], Joseph C
This is a PDF file of a peer-reviewed paper that has been accepted for publication
ACCELERATED Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases[2,3,4,5,6,7,8] that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)[7,9,10,11,12,13,14,15]
Summary
Xiao Mi1,11, Matteo Ippoliti[2,11], Chris Quintana[1], Ami Greene[1], Zijun Chen[1], Jonathan Gross[1], Frank Arute[1], Kunal Arya[1], Juan Atalaya[1], Ryan Babbush[1], Joseph C. The scaling with L of the spectrally-averaged autocorrelator, at a time t ∼ poly(L), provides a sharp diagnostic: this saturates to a finite value in the MBL-DTC, while it scales to zero with increasing L in the thermal phase and in prethermal cases where, for instance, a vanishing fraction of the spectrum of an appropriate Heff shows order (see SI). While the averaged autocorrelator may be unduly affected by outlier states and/or long (but O(1)) thermalization times at small system sizes and times (thereby making the complementary bitstring analysis of Fig. 3 essential), the polynomial scaling of this protocol establishes a proof of principle for efficiently verifying the presence or absence of an MBL-DTC in a range of models as quantum processors scale up in size to surpass the limits of classical simulation[40].
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