Regular and exceptional spectra of the two-qubit quantum Rabi model

TL;DR

This paper analytically studies the two-qubit quantum Rabi model and its generalizations, revealing novel quasi-exact solutions and level crossings, with implications for quantum gates and state transfer in circuit QED.

Contribution

It provides analytical solutions for the two-qubit Rabi model and discovers new quasi-exact solutions with level crossings, highlighting non-integrability and potential quantum computing applications.

Findings

Analytical eigenstates in extended coherent and Fock states.

Discovery of quasi-exact solutions causing level crossings.

Eigenstates with few Fock states, suitable for quantum experiments.

Abstract

Two-qubit system is the foundation of constructing the universal quantum gate. We have studied the two-qubit Rabi model for the general case and its generalizations with dipole, XXX and XYZ Heisenberg qubit-qubit interactions, which are commonly used in quantum computation. Their solutions are presented analytically with eigenstates can be obtained in terms of extended coherent states or Fock states and applied to the construction of the ultrafast two-qubit quantum gate in circuit QED and quantum state storage and transfer. Some novel kinds of quasi-exact solutions are found for specific sets of parameters, causing level crossings within the same parity subspace, which do not appear in the regular spectrum, indicating its non-integrability. These eigenstates are very interesting for quantum computing and single photon experiments because they are formed by just a few Fock states, and in some cases, with at most one photon. They are also easy to prepare, since they exist for all qubit-photon coupling values with constant eigenenergy and the qubit energy splittings can be fine tuned in the experiment in contrast to the coupling.