User:Srjmas/sandbox/CR gate

Cross Resonant (CR) gate
Following.

Consider two qubits coupled to a resonator with a resonance at $$\omega_R$$. The the energy separation between the computational states of qubit $$i$$ is $$\hbar\omega_i$$. The detuning of qubit $$i$$ from the resonator is $$\Delta_i\equiv\omega_i-\omega_r$$. The Hamiltonian: $$ H/\hbar=\omega_1ZI/2+\omega_2IZ/2+JXX $$, where $$\{I,X,Y,Z\}$$ are Pauli operators and $$J$$ is the coupling coefficient. If