  Quantum control for error correction is critical for the practical use of
quantum computers. We address quantum optimal control for single-shot
multi-qubit gates by framing as a feasibility problem for the Hamiltonian model
and then solving with standard global-optimization software. Our approach
yields faster high-fidelity ($>$99.99\%) single-shot three-qubit-gate control
than obtained previously, and our method has enabled us to solve the
quantum-control problem for a fast high-fidelity four-qubit gate.
