Many-body physics in the NISQ era: quantum programming a discrete time crystal

TL;DR

This paper explores how NISQ quantum devices can be programmed to realize and detect discrete time crystals, a novel non-equilibrium phase of matter, highlighting the potential of current quantum hardware like Google's Sycamore for studying many-body physics.

Contribution

It demonstrates that existing NISQ hardware can be used to realize and observe discrete time crystals, bridging the gap between theoretical proposals and experimental realization.

Findings

DTCs can be realized on NISQ devices like Google's Sycamore.

DTC spatiotemporal order observable over hundreds of periods with current noise levels.

Hardware improvements will enhance the detection and stability of DTCs.

Abstract

Recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices represents an exciting opportunity for many-body physics, by introducing new laboratory platforms with unprecedented control and measurement capabilities. We explore the implications of NISQ platforms for many-body physics in a practical sense: we ask which {\it physical phenomena}, in the domain of quantum statistical mechanics, they may realize more readily than traditional experimental platforms. As a particularly well-suited target, we identify discrete time crystals (DTCs), novel non-equilibrium states of matter that break time translation symmetry. These can only be realized in the intrinsically out-of-equilibrium setting of periodically driven quantum systems stabilized by disorder induced many-body localization. While precursors of the DTC have been observed across a variety of experimental platforms - ranging from trapped ions to nitrogen vacancy centers to NMR crystals - none have \emph{all} the necessary ingredients for realizing a fully-fledged incarnation of this phase, and for detecting its signature long-range \emph{spatiotemporal order}. We show that a new generation of quantum simulators can be programmed to realize the DTC phase and to experimentally detect its dynamical properties, a task requiring extensive capabilities for programmability, initialization and read-out. Specifically, the architecture of Google's Sycamore processor is a remarkably close match for the task at hand. We also discuss the effects of environmental decoherence, and how they can be distinguished from `internal' decoherence coming from closed-system thermalization dynamics. Already with existing technology and noise levels, we find that DTC spatiotemporal order would be observable over hundreds of periods, with parametric improvements to come as the hardware advances.