Robust quantum gates for qubit clusters with fixed coupling

We design robustness optimal control for implementing a universal set of quantum gates in a finite-size cluster of up to 10 interacting qubits. We find that fidelity higher than 99% can be achieved with smooth pulses varying at less than 5% of the maximum amplitude per time bin. The gates are robust against significant uncertainty, up to 5%, in the qubit-qubit and field-qubit coupling strength. This is useful for large scale quantum computing with solid state devices where fabrication uncertainty is unavoidable, and for systems with slowly fluctuating fields. Transmons are chosen as a concrete example, but the method discussed is platform independent.