  A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase
(C-phase) gate combined with single-qubit gates, has been experimentally
implemented recently for quantum-dot spin qubits in isotopically enriched
silicon, a promising solid-state system for practical quantum computation. In
the experiments, the single-qubit gates have been demonstrated with
fault-tolerant control-fidelity, but the infidelity of the two-qubit C-phase
gate is, primarily due to the electrical noise, still higher than the required
error threshold for fault-tolerant quantum computation (FTQC). Here, by taking
the realistic system parameters and the experimental constraints on the control
pulses into account, we construct experimentally realizable high-fidelity CNOT
gates robust against electrical noise with the experimentally measured
$1/f^{1.01}$ noise spectrum and also against the uncertainty in the interdot
tunnel coupling amplitude. Our optimal CNOT gate has about two orders of
magnitude improvement in gate infidelity over the ideal C-phase gate
constructed without considering any noise effect. Furthermore, within the same
control framework, high-fidelity and robust single-qubit gates can also be
constructed, paving the way for large-scale FTQC.
