Entanglement of superconducting qubits via microwave fields: classical and quantum regimes

We study analytically and numerically the problem of two qubits with fixed coupling irradiated with quantum or classical fields. In the classical case, we derive an effective Hamiltonian, and construct composite pulse sequences leading to a CNOT gate. In the quantum case, we show that qubit-qubit-photon multiparticle entanglement and maximally entangled two-qubit state can be obtained by driving the system at very low powers (one quanta of excitation). Our results can be applied to a variety of systems of two superconducting qubits coupled to resonators.