  In multi-qubit system, correlated errors subject to unwanted interactions
with other qubits is one of the major obstacles for scaling up quantum
computers to be applicable. We present two approaches to correct such noise and
demonstrate with high fidelity and robustness. We use spectator and intruder to
discriminate the environment interacting with target qubit in different
parameter regime. Our proposed approaches combines analytical theory and
numerical optimization, and are general to obtain smooth control pulses for
various qubit systems. Both theory and numerical simulations demonstrate to
correct these errors efficiently. Gate fidelities are generally above $0.9999$
over a large range of parameter variation for a set of single-qubit gates and
two-qubit entangling gates. Comparison with well-known control waveform
demonstrates the great advantage of our solutions.
