Dynamical mitigation of errors due to non-negligible interactions in multi-qubit system

In current architecture of quantum computing, interaction between qubits needs to be turned on and off efficiently in a multi-qubit system. Therefore, to perform single-qubit gates the interaction between the target qubit and the other qubits (spectators) must be turned off completely. While to perform two-qubit gates the interaction between the targeted two qubits must be turned on, and the interactions with the spectators must be remained off. A large on/off ratio of the tunable interaction is favorable. However, in fact, there is always residual interactions which introduces errors. We develop a framework including analytical protocol together with numerical method to dynamically mitigate such errors. Our method could be used to find robust control pulses to perform both single qubit gates and two qubit gates at the presence of unwanted interactions with other qubits. Further more, using our method one could perform perfect single-qubit rotations to a target qubit with strong always-on interaction to spectator qubits. This gives an alternative solution for quantum computing with fixed frequency qubits.