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

Correcting correlated errors for quantum gates in multi-qubit systems using smooth pulse control