  In this report, we have studied exceptional spectra of the two-qubit quantum
Rabi model in two situations. Firstly, an exceptional spectra is achieved in
resonant condition, in which the frequencies of two qubit and photon field
satisfy resonant relation. With transformed rotating-wave approximation (TRWA)
method, the Rabi model can be mapped into the solvable formation in
qubit-photon Fock states space. Based on the quantum supperconducting circuits
experiment setup, the best value range of the system parameters are discussed.
In the resonant station working window, the energy spectrums are calculated.
Secondly, a special quasi-exact solution of two qubits Rabi model in reservoir
is achieved. The algebraic structure of Hamiltonian is analyzed in the photon
number space, a closed quasi-exact eigenstates space is found, and the
quasi-exact solution can be clearly found from the algebraic structure of
Hamiltonian. The results could be used to test quantum Rabi model.
