Observation of Time-Crystalline Eigenstate Order on a Quantum Processor

TL;DR

This paper reports the experimental observation of a discrete time crystal eigenstate order on a superconducting qubit array, demonstrating stable non-equilibrium phases and phase transitions using innovative protocols.

Contribution

It introduces a scalable method to observe and analyze eigenstate-ordered phases in non-equilibrium quantum systems on current quantum processors.

Findings

Observation of a stable discrete time crystal phase

Implementation of a time-reversal protocol to distinguish decoherence

Identification of the phase transition via finite-size analysis

Abstract

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dynamical phases can be defined in periodically driven many-body localized systems via the concept of eigenstate order. In eigenstate-ordered 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, wherein few select states can mask typical behavior. Here we implement a continuous family of tunable CPHASE gates on an array of superconducting qubits to experimentally observe an eigenstate-ordered DTC. We demonstrate the characteristic spatiotemporal response of a DTC for generic initial states. Our work employs a time-reversal protocol that discriminates external decoherence from intrinsic thermalization, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. In addition, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.