  We develop a rigorous theoretical framework for interaction-induced phenomena
in the waveguide quantum electrodynamics (QED) driven by mechanical
oscillations of the qubits. Specifically, we predict that the simplest set-up
of two qubits, harmonically trapped over an optical waveguide, enables the
ultrastrong coupling regime of the quantum optomechanical interaction.
Moreover, the combination of the inherent open nature of the system and the
strong optomechanical coupling leads to emerging parity-time (\PT) symmetry,
quite unexpected for a purely quantum system without artificially engineered
gain and loss. The $\mathcal{PT}$ phase transition drives long-living
subradiant states, observable in the state-of-the-art waveguide QED setups.
