Recent progress on noisy, intermediate scale quantum (NISQ) devices opens exciting opportunities for many-body physics. NISQ platforms are indeed not just computers, but also interesting laboratory systems in their own right, offering access to large Hilbert spaces with exceptional capabilities for control and measurement. I will argue that nonequilibrium phases in periodically-driven (Floquet) systems are a particularly good fit for such capabilities in the near term. Focusing on the paradigmatic example of the "discrete time crystal" (DTC), I will review the idea of eigenstate order, wherein many-body localization allows the definition of phase structure away from thermal equilibrium. I will then discuss how an eigenstate-ordered DTC can be studied on NISQ hardware [1], and present recent experimental work in which these ideas are implemented on Google Quantum AI's superconducting qubit processor [2], giving a scalable blueprint for NISQ-era studies of nonequilibirum phases of matter.

[1] MI, K. Kechedzhi, R. Moessner, S. Sondhi, V. Khemani, PRX Quantum 2, 030346 (2021)

[2] X. Mi, MI, C. Quintana, A. Greene et al. (Google Quantum AI and collaborators), arXiv:2107.13571 (2021)