ZZ Freedom in Two-Qubit Gates

Superconducting qubits on a circuit exhibit an always-on state-dependent phase error. This error is due to sub-MHz parasitic interaction that repels computational levels from noncomputational ones. We study a general theory to evaluate the "static" repulsion between seemingly idle qubits as well as the "dynamical" repulsion between entangled qubits under microwave driving gate. By combining qubits of either the same or opposite anharmonicity signs we find the characteristics of static and dynamical ZZ freedoms. The latter universally eliminate the parasitic repulsion, leading us to mitigate high-fidelity gate operation. Our theory introduces the opportunities for making perfect entangled and unentangled states, which is extremely useful for quantum technology.