Abstract

Noisy intermediate-scale quantum devices provide a promising platform for exploring non-equilibrium quantum dynamics. Building on this opportunity, we theoretically explore open-system evolution implemented on digital quantum computers via repeated interactions between a quantum system and auxiliary qubits. After each interaction, the auxiliary qubits are measured, and the resulting sequence of measurement outcomes defines a quantum trajectory. By interpreting trajectories as microstates of an effective ensemble, we construct dynamical analogues of equilibrium concepts such as free energy and entropy. This framework allows us to bias quantum trajectories and tailor their properties—e.g., temporal correlations—in a controlled manner. Applying our approach to a many-body model inspired by dual-species Rydberg-atom experiments, we uncover rich heterogeneous behaviour and glassy dynamics that remain hidden in the average-state evolution. By leveraging the aforementioned thermodynamic-like functionals, we identify these features as signatures of a first-order dynamical phase transition.