  We study the equilibrium and non-equilibrium physics of two qubits
interacting through an ultrastrong coupled qubit-cavity system. By tuning the
qubits energy gap while keeping the ultrastrong coupling system to its ground
state, we demonstrate a strong two-qubit interaction as well as an enhanced
excitation transfer between the two qubits. Our proposal has twofold
implications: a means to attain multipurpose parity-protected quantum
information tasks in superconducting circuits, and a building block for
ultrastrong coupled cavity-enhanced exciton transport in disordered media.
