  A single-shot Toffoli, or controlled-controlled-NOT, gate is desirable for
classical and quantum information processing. The Toffoli gate alone is
universal for reversible computing and, accompanied by the Hadamard gate, forms
a universal gate set for quantum computing. The Toffoli gate is also a key
ingredient for (non-topological) quantum error correction. Currently Toffoli
gates are achieved by decomposing into sequentially implemented single- and
two-qubit gates, which requires much longer times and yields lower overall
fidelities compared to a single-shot implementation. We develop a
quantum-control procedure to construct a single-shot Toffoli gate for three
nearest-neighbor-coupled superconducting transmon systems such that the
fidelity is 99.9% and is as fast as an entangling two-qubit gate under the same
realistic conditions. The gate is achieved by a non-greedy quantum control
procedure using our enhanced version of the Differential Evolution algorithm.
