Observing quantum many-body scars in random quantum circuits

The Schwinger model describes quantum electrodynamics in 1+1-dimensions, it is a prototype for quantum chromodynamics, and its lattice version allows for a quantum link model description that can be simulated using modern quantum devices. In this work, we devise quantum simulations to investigate the dynamics of this model in its low dimensional form, where the gauge field degrees of freedom are described by spin 1/2 operators. We apply trotterization to write quantum circuits that effectively generate the evolution under the Schwinger model Hamiltonian. We consider both sequential circuits, with a fixed gate sequence, and randomized ones. Utilizing the correspondence between the Schwinger model and the PXP model, known for its quantum scars, we investigate the presence of quantum scar states in the Schwinger model by identifying states exhibiting extended thermalization times in our circuit evolutions. Our comparison of sequential and randomized circuit dynamics shows that the non-thermal sector of the Hilbert space, including the scars, are more sensitive to randomization, a feature which can be detected even on relatively short time scales.