Parity-time-symmetric (PT-symmetric) Hamiltonians are generally non-Hermitian and give rise to exotic behavior in quantum systems at exceptional points, where eigenvectors coalesce. The recent realization of PT-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here, we use a programmable integrated photonic chip to simulate a model composed of twin pairs of PT-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two-and three-particle interference, and a particle-trembling behavior that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.