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

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.